2.1.1.

Spiral phase plate theory

The spiral phase plate, a commonly used device for generating OAM-carrying light beams, is a transmissive or reflective optical device with its thickness gradually varying around the center^[528–531]. In general, the thickness ($H$) of the spiral phase plate at different positions is expressed as^[532,533]

For the transmissive-type spiral phase plate, the relationship between the thickness $H$ and the topological charge $\ell$ of an OAM-carrying light beam, light wavelength $\lambda$ in vacuum, and material refractive index $n$ is

For the reflective-type spiral phase plate, the thickness $H$ is independent of the material of the spiral phase plate, and the relationship is written by

Note that the spiral phase plate is mainly used for producing OAM-carrying light beams with a helical phase front. Following the similar mechanism, customized phase plates can be also designed to generate other structured light with specific spatial phase structure.

2.1.2.

Mode-field superposition theory

Both vector eigenmode and LP mode can form a set of completely orthogonal mode bases, and LP mode is basically obtained from the orthogonal transformation of vector eigenmode bases^{[104,534,535]}. It is expected that other forms of orthogonal mode bases could be also generated by similar orthogonal transformation processes, such as the currently widely used circular polarization or linear polarization OAM mode bases. The relation for synthesizing circular polarization OAM modes by vector eigenmodes is

In addition to the circular polarization OAM mode described above, the linear polarization OAM mode is also a set of commonly used mode bases. The relationship between the linear polarization OAM mode and the vector eigenmode, LP mode, and circular polarization OAM mode is

2.1.3.

Phase control theory

A metasurface composed of subwavelength artificial structures (also known as meta-atoms) enables unprecedented wavefront manipulation and has gradually become an alternative to traditional curved optical components^[536–543]. A metasurface manipulates the light field at the micro-nano scale, which is more commonly achieved through phase control^[544–547]. At present, the phase control of the light field by a metasurface mainly depends on several basic principles: resonant phase, geometric phase, propagation phase, and compound phase.

1) Resonant phase

The resonant phase originates from the resonance between the incident light and unit metasurface structure or periodic array. When the wavelength, phase, and direction of the incident light match the resonant mode supported by the metasurface structure, resonance occurs on the metasurface. Resonance generally brings about a significant change in amplitude, phase, and polarization. At present, common resonances can be divided into the resonance of metal antennas and Mie resonance of dielectric structures due to different materials. The resonance of metal antennas generally comes from the interaction between incident light and surface plasma at the interface between the metal antenna and the interface. Metal antennas are often able to support multiple resonance modes. Mie resonance is a widely studied and utilized scattering mechanism that typically occurs in structures with dimensions ranging from a few tenths to several wavelengths. In addition, for the multi-layer structure of metal, dielectric, and metal, an equivalent magnetic resonance mode is often supported. Moreover, there are more drastic changes in the light field via resonance, which can achieve a larger phase and amplitude modulation in smaller and thinner dimensions. It is beneficial to the integration and miniaturization of the structured light emitter.

2) Geometric phase

Light has two typical angular momenta, in which the SAM of light is related to quantum spin and light with circular polarization. When a light beam is circularly polarized, each photon carries $\mathrm{a}\pm \hslash$ SAM, where the positive (negative) sign is corresponding to left-handed (right-handed) circular polarization. In addition, light can also rotate with its spatial phase structure to generate a specific helical phase front and carry OAM. The geometric phase, also known as the Pancharatnam-Berry (PB) phase, originates from the interaction between polarized light beams and anisotropic units. For the phase control of the light field, the geometric phase can make the SAM of the photon interact with the OAM, which is the manifestation of the SAM-OAM interaction.

For easy understanding, the Jones matrix is used to simplify its internal physical processes expressed as

The following assumptions are proposed: the anisotropic structure corresponding to the $u\mathrm{–}v$ coordinate system and the entire metasurface corresponding to the $x\mathrm{–}y$ coordinate system have an in-plane rotation angle of $\theta$ with respect to the $x$ axis. Based on the above assumptions, the Jones matrix of the anisotropic metasurface can be further expressed as

Then, by incorporating Eq. (9) into Eq. (8) and simplifying it, we can obtain

When the incident light is a circularly polarized one, i.e., ${[1\pm i]}^{\mathrm{T}}$, with “+” the left-handed circular polarization (LCP) and “−” the right-handed circular polarization (RCP), the outgoing light field can be expressed as

According to Eq. (11), in addition to the same polarization component, the output light also produces a cross-polarization component. In particular, the cross-polarization component carries a geometric phase of $\pm 2\theta$, which is twice the in-plane rotation angle. It can be concluded that the geometric phase is only related to the rotation direction of the incident circular polarization light and the rotation angle of the structure, but not to the frequency of the incident light and the material of the structure. Therefore, different from other phase modulations, the geometric phase does not increase with the accumulation of light paths, but is the manifestation of spin-orbit interaction and linked to the evolution of the geometric properties of light, such as polarization and propagation direction.

3) Propagation phase

The propagation phase depends on the optical path accumulation of a certain thickness medium. Changes in the structural geometric parameters, shape, and material of the metasurface element will result in changes in its effective refractive index ($n_{\mathrm{eff}}$). When ignoring the reflection of light waves at the interface, the phase of their transmission will change as follows:

4) Compound phase

According to the above analyses, the propagation phase can be adjusted by changing the size of the subwavelength structure, and the geometric phase can be introduced by changing the rotation direction of the subwavelength structure. Therefore, when the rotation and size of the subwavelength structure are both changed, the geometric phase and propagation phase can be introduced to realize the compound phase modulation. For the sake of analysis, the phase delay introduced by a transparent subwavelength structure along its fast and slow axes is assumed to be $\beta \mp \delta /2$. The corresponding complex amplitudes are expressed as $t_u=\exp (i\beta -i\delta /2)$ and $t_v=\exp (i\beta +i\delta /2)$. If it is rotated counterclockwise by an $\theta$ angle, according to Eq. (11), the resulting output light field of a circular polarization light ${[1\pm i]}^{\mathrm{T}}$ can be expressed as

According to Eq. (14), the co-polarized component carries only the propagation phase $\beta$, while the cross-polarized component carries the compound phase $\beta \pm 2\theta$ composed of the propagation phase $\beta$ and the geometric phase $\pm 2\theta$. According to the principle of propagation phase and geometric phase, the propagation phase has the characteristics of being spin-independent, frequency-dependent, and material-dependent, while the geometric phase with the opposite characteristics is spin-dependent, frequency-independent, and material-independent. The combination of the propagation phase and geometric phase uses their composite control in spin, frequency, and material to solve the problems of circular polarization multiplexing, bandwidth, and tunability of traditional phase metasurfaces in light field control.

2.1.4.

Holographic theory

For the integrated photonic platform, taking the OAM mode generation as a typical example, the holographic pattern is obtained by the interference between the target OAM mode and in-plane waveguide mode^[548–554]. The OAM mode and in-plane waveguide mode can be expressed as^[555,556]

The hologram is transferred onto the upper surface of the waveguide. When the hologram on top of the waveguide is illuminated with the in-plane waveguide mode, the out-of-plane OAM mode can be generated.

Similarly, other types of holograms might also, in principle, be produced by the interference between the specific structured light and the in-plane waveguide mode, and then transferred onto the upper surface of the waveguide^[557–560]. Illuminating the transferred hologram with propagating in-plane waveguide mode could facilitate the flexible generation of out-of-plane specific structured light.

2.1.5.

Coupled mode theory

Optical waveguides are composed of media with different dielectric constants, and the waveguide walls serve as interfaces between different media. Although most of the power usually remains inside the waveguide when light propagates, a small portion of the light always propagates near the outside of the waveguide wall. For two waveguides close to each other, when the distance between the two waveguides is small enough, power coupling occurs between them. The coupling characteristics are determined by the distance, length, and propagation mode between the two waveguides^[561,562]. The basic formula and amplitude equations of two coupled waveguides can be described as

In general, only modes with equal or nearly equal propagation constants (${\beta }_1={\beta }_2$ or ${\beta }_1\approx {\beta }_2$) can be effectively coupled. To prove this conclusion, the following assumption is made: there is no light field in waveguide 2 at $z=0$ [i.e., $z=0$, $A_2(0)=0$], and the light field in waveguide 2 at $z=L$ is calculated according to the coupled wave equation

If the difference between two propagation constants (${\beta }_1\ne {\beta }_2$) is large, the period of the high-speed oscillation factor $e^{-j({\beta }_1-{\beta }_2)z}$ is much smaller than the propagation distance $L$, and the integral value of $A_2(L)$ within the integral distance ($0\sim L$) is very small, resulting in a negligible power coupling between the two waveguides. When the propagation constants (${\beta }_1={\beta }_2$) of two waveguides are equal or almost close to each other, the integral result of $A_2(L)$ may reach a certain value, leading to efficient power coupling between the guided modes in the two waveguides. Remarkably, the condition with two equal propagation constants (${\beta }_1={\beta }_2$) is called the phase matching condition. The corresponding coupling length $L_c$ for achieving the maximum power coupling can be derived by

2.1.6.

Whispering gallery mode theory

The whispering gallery modes carrying high-order OAM can be generated in circular optical resonators, such as microrings and microdisks^{[296,472,563–567]}. The periodic micro-etch structure embedded in the microresonator, such as the angular grating structure, can periodically modulate the refractive index in the azimuthal direction to extract the constrained whispering gallery mode in the resonator. Theoretical derivation shows that whispering gallery mode can be emitted from the microring resonator only when the following angle-phase matching conditions are satisfied^[296,472]:

By adjusting the $n_e$ such as introducing a high-order mode, the microring resonance can obtain multiple OAM modes with topological charges at one wavelength.

2.1.7.

Non-Hermitian theory

The Hermitian system is a closed system that does not exchange energy with other systems and does not have gain or loss, and its physical quantities can be described by Hermitian operators^[568–572]. The eigenvalues of Hermitian operators are real numbers and their eigenstates are completely orthogonal. On the contrary, the non-Hermitian is an open system that has gain or loss or open boundary conditions, and the eigenvalues of non-Hermitian operators are generally complex. In the non-Hermitian system, there are many novel physical phenomena, such as exceptional points. The exceptional point is a degenerate state of different eigenstates and eigenvalues, which brings many interesting phenomena and applications. For a general two-component system, the non-Hermitian can be described by the evolution equation

2.1.8.

Phased array theory

Optical phased arrays extend the operating frequency band of radio frequency phased arrays to the optical frequency range. This technology controls the direction of a light beam by adjusting the phase of each element in an antenna array. The fundamental principle involves altering the phase difference of transmitted or received signals, causing the light waves emitted by the array elements to coherently combine in space, forming a structured light beam in a specific direction^[573,574]. In an optical phased array system, the antenna array consists of multiple independent elements, each with its own transmitting and receiving modules. These modules adjust the signal phase using phase shifters. The core of the optical phased array technology lies in the precise control of the phase difference between each array element. By doing so, the transmitted or received signals interfere constructively in the desired direction, enhancing the signal strength in that direction while suppressing it in others. This precise phase control enables the formation of a well-defined light beam, which can be steered electronically without mechanical movement. Optical phased arrays may find applications in various fields^[575–577], including light detection and ranging (LiDAR) systems for autonomous vehicles, optical communications, and advanced imaging systems, where they offer significant advantages in terms of speed, accuracy, and flexibility.

2.2.1.

Integrated OAM generation on passive platforms

In this part, four types of integrated OAM emitters on passive platforms are introduced: in-plane to in-plane OAM generation, in-plane to out-of-plane OAM generation, out-of-plane to in-plane OAM generation, and out-of-plane to out-of-plane OAM generation.

1) In-plane to in-plane OAM generation

For the in-plane to in-plane OAM generation, the input light is the in-plane waveguide mode, and the output light (generated OAM) is also the in-plane waveguide mode. 3D waveguide structures are usually used to implement the in-plane to in-plane OAM generation, such as a hybrid device consisting of a silica planar lightwave circuit (PLC) coupled to a 3D waveguide structure, asymmetric directional coupling vortex beam emitter embedded in a photonic chip, and the trench waveguides on a silicon/silica chip.

As shown in Figs. 5(a) and 5(b), a hybrid photonic integrated circuit device composed of a silica PLC and a 3D waveguide structure is used to generate 15 OAM modes with TE and TM polarizations and relatively low loss at 1.55 µm^[467]. In this work, the 2D silica PLC has a free propagation region (FPR), which is utilized to create linearly tilted wavefronts that correspond to diverse OAM states. Then, the laser inscribed 3D waveguide structure performs the geometric transformation of the linear phase tilt to azimuthal phase variation at the output apertures. In addition, the direct generation of optical vortex beams inside a photonic chip is proposed using a femtosecond laser direct writing technique. As shown in Figs. 5(c) and 5(d), the OAM generator is an asymmetric direction coupler including a standard single-mode waveguide and a doughnut-shaped waveguide in a photonic chip^[578]. The Gaussian beam in the single-mode waveguide evanescently couples to the adjacent doughnut-shaped waveguide and converts it into an OAM beam. Another commonly used integrated OAM generator is based on the trench waveguide structure. Due to the asymmetric structure, the single-trench waveguide breaks the original rotation symmetry and supports two orthogonal LP-like modes whose optical axes are rotated by around 45° with respect to the horizontal and vertical directions, as depicted in the inset of Fig. 5(e)^[469]. These two nondegenerate LP-like modes have different propagation constants and can be combined into two OAM modes (topological charges of $+1$ or $-1$) after propagating through different distances, corresponding to phase differences of $\pi /2$ and $-\pi /2$, respectively. Because of its simple and easy structure, the trench waveguide can be designed and fabricated not only in photolithographic silicon chips, as shown in Fig. 5(e), but also in femtosecond laser inscribed 3D silica chips, as shown in Fig. 5(f)^[470].

Fig. 5

Typical examples of in-plane to in-plane OAM generation^{[467,469,470,578]}. (a) Conceptual view of the hybrid photonic integrated device composed of a silica PLC and 3D waveguide structure. (b) Silica PLC image^[467]. (c) An asymmetric direction coupler including a standard single-mode waveguide and a doughnut-shaped OAM waveguide is employed to generate different-order OAM beams based on phase matching. The coupling length and coupling spacing are 4 mm and 15 µm, respectively. (d) The cross-section of the doughnut-shaped OAM waveguide structure consisting of 12 slightly overlapping waveguides^[578]. (e) The OAM beam generator based on a trench silicon waveguide^[469]. (f) The OAM beam generator based on a femtosecond laser direct writing trench silica waveguide^[470].

2) Out-of-plane to in-plane OAM generation

The in-plane OAM generation can be obtained not only by directly converting the light inside the waveguide but also by coupling the light outside the waveguide into guided mode. For the out-of-plane to in-plane OAM generation, the input light is the out-of-plane light beam, while the output light (generated OAM) is the in-plane waveguide mode. In general, diffraction structures are popular to achieve the out-of-plane to in-plane OAM generation, such as the dielectric antenna waveguide and grating coupler.

The universal design strategy is presented to utilize the dielectric antenna waveguide for coupling incident radiation into an integrated waveguide. Figs. 6(a) and 6(b) illustrate the conceptual view and top view of the silicon-nanoantenna-patterned silicon-nitride photonic waveguide^[275]. Similar to the design principle in the trench waveguide, the dielectric antenna waveguide generates the optical vortex carrying ${\mathrm{OAM}}_{+1}$ by synthesizing two high-order ${\mathrm{TE}}_{01}$ and ${\mathrm{TE}}_{10}$ modes with $\pi /2$ phase difference, as displayed in Fig. 6(c). The left two panels of Fig. 6(d) are calculated output electric field $|\mathrm{Ey}|$ distributions when only the ${\mathrm{TE}}_{01}$ mode antenna and ${\mathrm{TE}}_{10}$ mode antenna exist, respectively. The right two panels of Fig. 6(d) give the electric field $|\mathrm{Ey}|$ and phase distributions when the ${\mathrm{TE}}_{01}$ mode antenna and ${\mathrm{TE}}_{10}$ mode antenna both exist, which indicates the optical vortex generation with ${\mathrm{OAM}}_{+1}$^[481]. To further verify the mode-control flexibility and configurability, higher-order (from $-3$ to $+2$) OAM modes can also be implemented by the mode mixing method. Figures 6(e) and 6(f) depict the top views of antenna waveguides and the output electric field $|\mathrm{Ey}|$ distributions for individual antenna arrays and the OAM field inside (and outside) the meta-waveguide, where OAM topological charges are $\ell =-2$ and $\ell =-3$, respectively^[471]. In addition to the dielectric antenna waveguide, the grating coupler can also be used to generate ${\mathrm{OAM}}_{\pm 1}$ modes within the photonic integrated circuit based on the mode mixing method, as shown in Fig. 6(g). Figure 6(h) gives the numerically calculated amplitude and phase distributions of the field component $|\mathrm{Ex}|$ in the target waveguide for the grating coupler formation with OAM states of $+1$ and $-1$^[579]. Compared to other proposed schemes of in-plane OAM generation, the strategy has a simple structure and is compatible with standard planar nanofabrication technology.

Fig. 6

Typical examples of out-of-plane to in-plane OAM generation^{[471,481,579]}. (a) Conceptual view and (b) top view of the silicon-nanoantenna-patterned silicon-nitride photonic waveguide. (c) Electric field $|\mathrm{Ey}|$ and phase distributions for ideal ${\mathrm{TE}}_{01}$, ${\mathrm{TE}}_{10}$, and mixed ${\mathrm{OAM}}_{+1}$ mode. (d) Calculated output electric field $|\mathrm{Ey}|$ distributions when only the ${\mathrm{TE}}_{01}$ mode antenna or ${\mathrm{TE}}_{10}$ mode antenna (left two panels) exists and both ${\mathrm{TE}}_{01}$ and ${\mathrm{TE}}_{10}$ mode antenna waveguides (right two panels) exist. Right most panel is the phase distribution at waveguide right port^[481]. (e), (f) The on-chip OAM generators with higher-order (e) ${\mathrm{OAM}}_{-2}$ and (f) ${\mathrm{OAM}}_{-3}$. Left panels are the top views of the antenna waveguides. Right panels are the output electric field $|\mathrm{Ey}|$ distributions for individual antenna arrays, the overall OAM field inside the meta-waveguide, and the output optical fields after exiting waveguide right ports after a propagation length of around 20 µm^[471], respectively. (g) Conceptual view of the grating coupler formation by superimposing the ${\mathrm{TE}}_{10}$ mode and ${\mathrm{TE}}_{01}$ mode antennas. (h) Numerically calculated amplitude and phase distributions of the field component $|\mathrm{Ex}|$ in the target waveguide for the grating coupler formation when the target OAM states are $+1$ and $-1$^[579].

3) In-plane to out-of-plane OAM generation

For the in-plane to out-of-plane OAM generation, the input light is the in-plane waveguide mode, while the output light is the out-of-plane OAM-carrying light beam. Figure 7 shows four different structures typically used for the in-plane to out-of-plane OAM generation, including a grating array, microring, fork grating, and subwavelength structure.

Fig. 7

Typical examples of in-plane to out-of-plane OAM generation^{[472–475,550–553,580–583]}. Four different structures of the in-plane to out-of-plane OAM generation include (a), (b) grating array, (c)–(f) microring, (g)–(j) fork grating, and (k), (l) subwavelength structure. (a) The schematic and optical image of the silicon photonic integrated circuit, which consists of an FPR, tunable-phase arrayed waveguides, and vertical grating couplers^[580]. (b) OAM emitter structure including one bus waveguide, one ring, and eight download units, where each download unit includes a grating and an arc waveguide^[581]. (c) Optical vortex beams extracted in whispering gallery modes microring^[472]. (d) Compact tunable integrated OAM emitters^[473]. (e) OAM mode emitters based on multimode microring^[474]. (f) Multimode vortex beam microring emitter based on vertical modes^[475]. (g) The principle and schematic illustration of the holographic fork grating on ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide^[550]. (h) Schematic illustration of the silicon waveguide surface holographic fork grating for generating the ${\mathrm{OAM}}_{+1}$ mode, ${\mathrm{OAM}}_{-1}$ mode, and their synthetization of two modes^[551]. (i) Concept of the holographic fork grating with uniform width grooves and the scanning electron microscopy (SEM) image with flat apodization^[552]. (j) Concept of multi-waveguide holographic gratings^[553]. (k) Schematic illustration of the principle of the OAM emitter with subwavelength structure and the details of the subwavelength structure design^[582]. (l) Concept of the OAM beam generation using the phase delays^[583].

As shown in Fig. 7(a), the silicon photonic integrated circuit consisting of an FPR, tunable-phase arrayed waveguides, and vertical grating arrays is proposed to generate the OAM states over a topological charge range from $-2$ to $+2$^[580]. At the output of FPR, the wavefront acquires the tilt of the linear phase based on the different input waveguide positions. Then, after the propagation through the tunable-phase arrayed waveguides, the array gratings maintain the phase relationship and generate the corresponding OAM mode. Another structure with array gratings is shown in Fig. 7(b), including one bus waveguide, one microring, and eight download units, where each download unit includes a grating and an arc waveguide. When the resonance condition of a microring is satisfied, the whispering gallery mode in the microring can be downloaded and transformed into OAM mode by the eight download units^[581].

To further reduce the footprint of the device, the silicon-based integrated optical vortex microring emitters use angular gratings to extract the OAM beams confined in whispering gallery modes. The radius of the smallest microring is 3.9 µm. As shown in Fig. 7(c), three identical microring emitters can form an OAM emitter array that is coupled to the same access waveguide^[472]. Then, based on such angular-grating-assisted microring emitter, a compact vortex emitter with the ability to actively tune different OAM modes is demonstrated using a single electrically contacted thermo-optic control, as shown in Fig. 7(d)^[473]. The thermo-optic tuning of the OAM modes achieves the on-off keying at rates of 10 µs and OAM mode switching at rates of 20 µs. Furthermore, in order to address the issue that only two OAM modes can be excited by clockwise and counterclockwise whispering gallery modes, the vortex emitter with a multimode microring is designed and fabricated, which can convert four in-plane waveguide modes into four free-space vector OAM beams with high mode purity. Figure 7(e) displays the schematic of the vortex emitter with a multimode microring and the ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ modes in the multimode microring^[474]. Except for the high-order horizontal waveguide, high-order vertical modes can also be used to increase the OAM number of microring emitters, as shown in Fig. 7(f)^[475].

The holography method can also be used to enable the in-plane to out-of-plane OAM generation, as explained in Fig. 7(g)^[550]. In the inset of Fig. 7(g), when the target OAM mode is incident vertically to the waveguide propagating an in-plane guided mode (from left to right), there is a string with dark and bright patterns caused by the interference of the two light fields (incident OAM mode, in-plane waveguide mode). The numerically calculated results show a guiding wave propagating along the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide with a holographic fork grating producing the target OAM mode with high purity in the broadband visible wavelength range. The holographic fork grating can also be introduced on the top of the silicon waveguide to generate OAM mode. The experimental results show that the silicon waveguide surface holographic grating produces not only a single OAM mode but also a synthetization of two OAM modes with opposite topological charges, as shown in Fig. 7(h)^[551]. In addition, the holographic fork grating is designed with the focused forked grating to reduce the feed length and with apodization to improve OAM mode fidelity, as shown in Fig. 7(i)^[552]. For the high-order OAM, the multi-waveguide holographic gratings are proposed to generate the high-order OAM modes with a topological charge from $+4$ to $+8$ by the manipulation and configuration of the incident light phase, as shown in Fig. 7(j)^[553].

Subwavelength structures with advanced algorithms are also used to enable the in-plane to out-of-plane OAM generation. A 1.2-μm-radius circular silicon device divided into 288 subpixels is proposed to emit the ultra-broad bandwidth ${\mathrm{OAM}}_{\pm 1}$ modes, as shown in Fig. 7(k)^[582]. To achieve an accurate phase modulation, the subwavelength structure is optimized via the global optimization method combining the genetic algorithm and the annealing algorithm. The experimental results show OAM emission efficiencies of $>35\%$ and OAM mode purity of $>97\%$. Furthermore, studying the relationship between the input phase delays, the subwavelength structure fed by four single-mode waveguides is presented to generate the tunable OAM beam. Figure 7(l) depicts the concept of the OAM beam generation using phase delays. The relative phase delay decides the generated OAM order. The subwavelength structure tailors the transformation function with a direct binary search (DBS) algorithm to support different tunable OAM order ranges^[583].

Although the above OAM generators based on the holographic fork grating show distinct performance, most of them have either single-polarization operation or narrow bandwidths, or complicated structures with a relatively large footprint. The ideal OAM generator, compatible with existing physical dimensions of light, offers impressive features of polarization diversity, broadband, and ultra-compact footprint. A multiport fork grating OAM generator with a simple two-dimensional (2D) surface structure (superposed holographic fork gratings) is presented and illustrated in Fig. 8(a). As shown in Figs. 8(b) and 8(c), two different direction fork gratings [${\mathrm{G}}_1(x,y)$ and ${\mathrm{G}}_2(x,y)$] are formed on top of the silicon waveguide by the interference between the vertically incident $x$-polarization ($y$-polarization) OAM mode and the $x$-polarization ($y$-polarization) in-plane ${\mathrm{TE}}_0$ mode. Then, the superposed holographic fork gratings $\mathrm{G}(x,y)$ are acquired by the superposition of two fork gratings [G₁ (x, y) and G₂ (x, y)]. Finally, the four polarization diversity OAM modes ($x$-polarization ${\mathrm{OAM}}_{+1}$, $x$-polarization ${\mathrm{OAM}}_{-1}$, $y$-polarization ${\mathrm{OAM}}_{+1}$, and $y$-polarization ${\mathrm{OAM}}_{-1}$) are realized by different incident conditions of the silicon waveguide with superposed holographic fork gratings. As shown in Fig. 8(d), the polarization diversity OAM generator has a favorable performance in terms of purity and operating bandwidth. Figure 8(e) is the measured SEM image of the ultra-compact fork grating, which has a superposed footprint of $3.6\mathrm{\mu m}\times 3.6\mathrm{\mu m}$. Figure 8(f) displays the far-field intensity profiles and interferograms for the polarization diversity OAM modes in the C-band. To evaluate the influence on each other for the OAM mode generation, Fig. 8(g) demonstrates the measured $4\times 4$ crosstalk matrix and the real accumulated crosstalk. The worst accumulated crosstalk is approximately $-8.84\mathrm{dB}$. The obtained simulated and measured results depicted in Figs. 8(a)–8(g) show that the ultra-compact polarization diversity OAM generator with a $3.6\mathrm{\mu m}\times 3.6\mathrm{\mu m}$ footprint is implemented on the silicon platform with a broadband working wavelength^[555]. To improve the emitting efficiency, as shown in Fig. 8(h), a backside metal mirror is placed below the device layer of the superimposed holographic fork gratings, to reflect the energy leaking down to the device substrate back to air. The layer thickness of ${\mathrm{SiO}}_2$ sandwiched between the holographic fork grating layer and the mirror is optimized to ensure the higher emitting efficiency of the upward-emitting OAM beam. The measured powers of different OAM modes with/without a mirror depicted in Fig. 8(i), show that the backside metal mirror achieves an improvement of $>4.65\mathrm{dB}$ in the emitting efficiency^[556].

Fig. 8

The in-plane to out-of-plane OAM generation with the superposed fork grating^[555,556]. (a)–(c) Concept and principle of the silicon-based OAM generation with the superposed fork grating. (d) Simulated purity of four polarization diversity OAM modes versus wavelength. (e) Measured SEM image of the superposed fork grating. (f) Measured results (intensity profile and interferogram) for the generation of the polarization diversity OAM modes in the C-band (1530–1565 nm). (g) Measured $4\times 4$ crosstalk matrix and accumulated crosstalk summing up all the noise^[555]. (h) Schematic structure of the high-efficiency OAM generator with a backside metal mirror. (i) Measured power of different emitting OAM modes with/without a mirror^[556].

Another subwavelength structure using the DBS algorithm is the digitized subwavelength surface structure, which enables the generation of wavelength/polarization-/charge-diverse OAM mode. Figures 9(a) and 9(b) depict the digitized nanostructure with a $3.2\mathrm{\mu m}\times 3.2\mathrm{\mu m}$ footprint and the concept of an OAM generator for generating the $x/y$-polarization ${\mathrm{OAM}}_{\pm 1}$. Figure 9(c) shows simulation results of intensity profiles, interferograms, and phase distributions for $x/y$-polarization ${\mathrm{OAM}}_{\pm 1}$. Figures 9(g) and 9(i) show the fabricated OAM generator with a $3.2\mathrm{\mu m}\times 3.2\mathrm{\mu m}$ footprint and measured $4\times 4$ mode crosstalk matrix. One can see that the worst crosstalk is less than $-14\mathrm{dB}$. Similar design, fabrication, simulations, and measurements are carried out for generating the $x/y$-polarization ${\mathrm{OAM}}_{\pm 1/\pm 2}$, as shown in Figs. 9(d)–9(f), 9(h), and 9(j). Moreover, the digitized subwavelength structure also shows the possibility of the generation of much higher-order OAM modes (e.g. $x/y$-polarization ${\mathrm{OAM}}_{\pm 3/\pm 4}$), as shown in Figs. 9(k) and 9(l). The demonstrated optical OAM generator provides the possibility of multi-dimensional optical communications with efficient capacity scaling^[584].

Fig. 9

The in-plane to out-of-plane OAM generation with digitized subwavelength structure^[584]. (a)–(c), (g), (i) Integrated OAM emitter for generating the $x/y$-polarization ${\mathrm{OAM}}_{\pm 1}$. (d)–(f), (h), (j) Integrated OAM emitter for generating the $x/y$-polarization ${\mathrm{OAM}}_{\pm 1/\pm 2}$. (a), (d) Digitized nanostructures. (b), (e) Concept and principle of integrated OAM generators. (c), (f) Simulation results of the intensity profiles, interferograms, and phase distributions. (g), (h) Measured optical microscope and SEM images of the fabricated OAM emitters. (i), (j) Measured $4\times 4$ mode crosstalk matrix. (k), (l) Simulation results of the intensity profiles, interferograms, and phase distributions when the digitized subwavelength structure is designed to generate the third-order and fourth-order OAM modes, respectively^[584].

4) Out-of-plane to out-of-plane OAM generation

For the out-of-plane to out-of-plane OAM generation, the input light is the out-of-plane light beam, while the output light is also the out-of-plane OAM-carrying light beam. There are several primary design proposals using the compact devices to implement the out-of-plane to out-of-plane OAM generation, including a metasurface, spiral phase plate, and holographic grating.

The metasurface has drawn extensive attention for its ability to manipulate light flexibly (phase, amplitude, polarization) over subwavelength propagation distances. Therefore, the metasurface offers unparalleled opportunities for OAM generation in terms of reliability, flexibility, and miniaturization. Most of the metasurfaces are divided into two categories according to the material of a unit cell, including plasmonic metasurfaces and dielectric metasurfaces. For the plasmonic metasurface, there are two main operating principles: resonant phase and geometry phase.

The resonant phase metasurface depends on the resonance from the unit cell or periodic array structure of the metasurface. When the wavelength, phase, and direction of incident light match the resonant mode supported by the metasurface, the resonance generally causes a more obvious change in amplitude, phase, and polarization. A V-shaped phase antenna is designed, which consists of two gold nanorods of equal length with a certain angle between them. Two resonance modes (symmetric and antisymmetric) are excited when the polarized beam is vertically incident. By adjusting the length of the antenna arm and the angle between the two arms, the amplitude and phase of the beam orthogonal to the incident polarization can be controlled. When the antenna is set to eight different dimensions as shown in Fig. 10(a), the full-wave simulation indicates that the transmission amplitude keeps unchanged and the phase changes from 0 to $2\pi$ with $\pi /4$ increments. Thus, the eight antennas achieve all-phase manipulation. Figure 10(b) exhibits the SEM image of a representative antenna array. When the eight antennas are arranged into the array distribution as depicted in Fig. 10(c), the phase distribution of the eight antennas changes $2\pi$ around the center. When the linearly polarized beam illuminates the array, the OAM beams with the topological charge of $\pm 1$ are generated, where its polarization state is orthogonal to the incident polarization direction^[585].

Fig. 10

The out-of-plane to out-of-plane OAM generation with plasmonic metasurface^[585–587]. The plasmonic metasurface mainly includes (a)–(c) resonance phase metasurface and (d)–(k) geometry phase metasurface. (a) Schematic unit cell of V-shaped phase metasurface. (b) SEM image of a representative antenna array. (c) SEM image of the plasmonic interface that produces an OAM beam. The plasmonic metasurface includes eight regions, each occupied by a unit cell of the eight-element set of (a)^[585]. (d) Schematic of L-shaped metasurface for generating the OAM beam. (e) SEM image of L-shaped phase metasurface. (f) Generated ${\mathrm{OAM}}_{\pm 2}$ beams at 780 nm^[586]. (g) Superposed phase distributions of axicon, spiral phase plate, and Fourier transform lens. (h) Interferometry patterns of OAM with topological charges ($\ell =1,3$, 5, 8) at 633 nm, when the axicon periods are 8 and 4 µm, respectively. (i) Measured results of multiple OAM beams with different topological charges and arbitrary location arrangement^[587].

The geometric phase originates from the interaction between the polarized beam and the anisotropic unit cell. At the same time, through the control of the light field, the geometric phase achieves the interaction between the SAM and OAM of the photon. Different from the traditional dynamic phase, the value of the geometric phase is determined by the rotation angle of the anisotropic unit cell and the polarization state of incident light, rather than the accumulation of light paths. An L-shaped metal metasurface is proposed, as shown in Fig. 10(d). The L-shaped structural elements, as a subwavelength birefringent device, are distributed in a circular rotation on a glass substrate, which realizes the $2\pi$ phase shift. Figure 10(e) illustrates the SEM image of the fabricated L-shaped metasurface. The vortex beams with the topological charge of $\pm 2$ are generated by the vertically incident circularly polarized light with a wavelength of 780 nm, as shown in Fig. 10(f). The experimental results confirm the conservation of angular momentum of the photon, as well as the conversion from SAM to OAM realized through the metasurface^[586]. Based on the PB phase, the phase distributions of the axicon, spiral phase plate, and Fourier transform lens are superposed to generate focused 3D broadband OAM beams, as shown in Fig. 10(g). The obtained OAM beams with different topological charges have the same beam divergence and almost constant vortex ring radius. The OAM beam is easily adjusted by the parameters of metasurface design, i.e., axicon period, operation wavelength, and lens focal length. Figure 10(h) demonstrates the interferometry patterns of OAM with topological charges at 633 nm, when the axicon periods are 8 and 4 µm, respectively. Furthermore, the superimposed metasurface is designed to produce multiple OAM beams with different topological charges and arbitrary location arrangements, as shown in Fig. 10(i)^[587].

In addition, there are some different metasurfaces to produce the specific OAM-carrying light beams. The compact metal-assisted metasurface is proposed as a broadband OAM-carrying vector beam emitter, which modulates the phase and polarization of the light beam simultaneously. The designed metasurface is composed of rectangular holes etched on the gold film, as shown in Fig. 11(a). 84 rectangular holes are distributed in two rings, and the geometric phase is introduced and varied by changing the rotation direction of the rectangular holes. Each rectangular hole is used as a separate linear polarizer due to the local waveguide resonance, which converts the incident circular polarization state into a vector spatial polarization distribution, and generates an OAM-carrying vector beam with topological charges from $-3$ to $+3$, as illustrated in Fig. 11(b)^[588]. A reflection-enhanced plasmonic metasurface is designed and fabricated to efficiently generate a structured light with a phase helix and intensity helix at 2 µm, as shown in Fig. 11(c). A self-reference intensity helix against ambient noise is generated without the use of spatially separated light^[589]. Besides, a metasurface structure on the facet of large-core fiber is proposed and designed to excite the linearly polarized and circularly polarized ${\mathrm{OAM}}_{\pm 1}$ beams from either the meta-facet side or planar-facet side, as shown in Fig. 11(d). Figure 11(e) shows the measured phase purity of twisted light excited from the meta-facet fiber, which is higher than 93% within a broadband wavelength range from 1480 to 1640 nm with incident linearly polarized light beams^[590].

Fig. 11

The out-of-plane to out-of-plane diverse OAM generation with metasurface^[588–590]. (a) Concept of the metasurface consisting of 84 rectangular holes etched on the gold film. (b) Schematic illustration of OAM-carrying vector beam generation^[588]. (c) Structured light generation with phase helix and intensity helix utilizing the reflection-enhanced plasmonic metasurface at 2 µm^[589]. (d) Concept of metasurface at the end/facet of large-core fiber for twisting ultra-broadband light. The incident Gaussian light is coupled into the fiber from either the meta-facet side (scheme 1) or the planar-facet side (scheme 2). (e) Measured phase purity of the ultra-broadband OAM generation with meta-facet fiber tip structure^[590].

Although a plasmonic metasurface, based on its ability to abruptly change the phase, allows subwavelength optical elements to generate the target OAM beams, most previously proposed metasurface designs suffer from low coupling efficiency due to the inevitable ohmic loss of metal at optical wavelengths. In contrast, a dielectric metasurface consisting of high-refractive-index dielectric nanoparticles provides one potential solution to deal with the ohmic loss, which relies on three main principles, i.e., resonant phase, geometry phase, and the combination of the geometry phase and propagation phase.

The dielectric metasurface based on Mie resonances in the silicon cut-wires is designed and fabricated on an ultra-thin silver film. By adjusting the size and rotation angle of the silicon cut-wires, the phase shift of $0\sim 2\pi$ can be realized for the reflection component orthogonal to the incident polarization. Arranging these arrays of silicon columns, as shown in Fig. 12(a), produces OAM beams with topological charges of $\pm 1$^[591]. Efficient phase control in the microwave region can be rendered by the appropriate adjustment of the size and rotation of the unit resonators. Figure 12(b) depicts the microwave resonant dielectric metasurface for broadband high-efficiency OAM beam generation^[592].

Fig. 12

The out-of-plane to out-of-plane OAM generation with dielectric metasurface^[591–597]. (a) Optical microscope and SEM images of the fabricated spiral phase plate composed of eight sections of silicon cut-wires and the interferogram of the generated optical vortex^[591]. (b) Concept of the microwave resonant dielectric metasurface^[592]. (c) Schematic of silicon subwavelength grating and dielectric metasurface consisting of width-modulated concentric ring grating^[593]. (d) Schematic of the designed metasurface with nanopillar arrays generating PVBs for right-circularly polarized (RCP) light^[594]. (e) Schematic of generation of generalized perfect Poincaré beams (PPBs) via dielectric metasurface^[595]. (f) Schematic of the proposed multifunctional metasurface^[596]. (g) Schematic of generation of the longitudinally varying vortex beams. (h) Simulated intensities and phase profiles of transmitted orthogonally polarized fields with LCP/RCP incidence^[597].

The all-dielectric metasurface can also rely on the PB phase (geometric phase) to generate the OAM beam, which has the advantages of broadband and robust modulation. The all-dielectric metasurface consists of a ring subwavelength grating, as shown in Fig. 12(c), which can be regarded as a spatially varying PB phase optical element^[593]. The efficiency of the ${\mathrm{OAM}}_{\pm 2}$ beam generation is as high as 90%. The generation of a fractional, quasi-focusing, and quasi-non-diffractive OAM beam is also achieved by the designed all-dielectric metasurface with width-modulated concentric ring gratings. Another metasurface is composed of ${\mathrm{TiO}}_2$ nanopillars for the generation of perfect vortex beams (PVBs), as shown in Fig. 12(d)^[594]. The measured OAM beams with different topological charges exhibit the same radial intensity profiles, confirming their “perfect” characteristics. The structure parameters (i.e., diameter and ellipticity) of the PVB can be simultaneously adjusted by changing the structural parameters of the metasurface.

Although the geometric phase metasurface performs the generation of versatile OAM beams, the cross-polarization is only affected by the PB phase and not modulated simultaneously with the phase and amplitude. To break this restriction, a unified strategy using the combination of geometric and propagation phases is presented. By utilizing the above incorporative phase modulation approach, all the states of perfect Poincaré beams (PPBs) on the hybrid-order Poincaré sphere are implemented by an all-dielectric metasurface, as shown in Fig. 12(e)^[595]. By changing the SAM of the incident light, metasurface devices can generate spin-multiplexed perfect optical vortices with arbitrary OAM. Furthermore, an all-silicon metasurface is presented to generate multiple OAM modes and arbitrary superpositions of OAM modes. The metasurface includes anisotropic unit cells and isotropic unit cells, which introduce the phase of modulation by the PB phase and propagation phase, respectively. As shown in Fig. 12(f), the left-handed and right-handed circular polarization can be used to generate multiple OAM states in three independent polarization channels^[596]. In addition, the superposition states of OAM can also be generated in longitudinal polarization due to the conversions of arbitrary SAM to OAM. The longitudinally varying vector OAM beams are generated in the terahertz band using an all-dielectric metasurface. As shown in Fig. 12(g), the topological charge of the generated OAM beam evolves from $+2$ to $-2$ (from $+1$ to $-1$) as the propagation distance increases, under the incidence of left-handed (right-handed) circularly polarized waves. Figure 12(h) depicts the simulated intensity and phase profiles of longitudinally varying vector OAM beams^[597].

In addition to metasurfaces, a spiral phase plate and holographic grating are also widely used to implement out-of-plane to out-of-plane OAM generation. As shown in Fig. 13(a), the reflected or transmitted light has a spiral-shaped wavefront, when a plane wave is incident on a spiral phase plate. An axially controllable multiple OAM generator is presented, which is based on a continuous surface profile structure with independent phase control^[598]. The device depicted in Fig. 13(b) is fabricated by femtosecond laser additive manufacturing^[599]. Numerical simulation and experimental measurement demonstrate that the parameters of collinear multiple OAM (i.e., the axial position, the rotation direction, and the number of topological charges) are arbitrarily controlled by designing different phase distributions. Furthermore, the spiral phase plate can be fabricated on the end face of the single-mode fiber, to efficiently produce the OAM beam, as shown in Fig. 13(c)^[464]. The spiral phase plate can also be fabricated on the end face of the PbSe-doped ring-core fiber to implement the OAM generation, OAM transmission, and OAM amplification, as shown in Fig. 13(d)^[465]. The obtained results indicate that the combination of spiral phase plate and fiber is beneficial to all-fiber OAM mode manipulation.

Fig. 13

The out-of-plane to out-of-plane OAM generation with spiral phase plate and holographic grating^{[464–466,598–600]}. (a) Schematic of wavefront conversion with a spiral phase plate^[598]. (b) Schematic illustration and SEM images of the generator producing multiple axially controllable OAM beams^[599]. (c) Schematic illustration and optical microscope image of the spiral phase plate fabricated on the end face of the single-mode fiber^[464]. (d) Schematic of OAM beam generation using the spiral phase plate on the end face of the ring-core fiber^[465]. (e) Schematic of OAM generation based on the holographic grating fabricated on the fiber facet^[466]. (f) Schematic illustration and SEM images of holographic fork plates with blazed grating^[600].

The holographic fork grating obtained by interfering with the optical vortex with the plane wave can also realize the generation of out-of-plane to out-of-plane OAM light beams. When Gaussian light is incident on the fork grating hologram, the grating generates different OAM modes at different diffraction orders. Remarkably, the holographic grating can also be manufactured on the end face of the few-mode fiber. The difference is that the holographic fork grating converts the input Gaussian-like beam in the low-order diffraction directions to high-order OAM modes in fiber, which is suitable for the all-fiber OAM (de)multiplexing, as shown in Fig. 13(e)^[466]. A combined subwavelength grating consisting of the holographic fork grating and blazed grating is presented to implement the superposition of two optical vortex beams with controlled topological charges, as shown in Fig. 13(f)^[600].

Moiré patterns formed in twisted bilayer two-dimensional van der Waals materials have drawn great attention in the observation and exploration of emerging electronic and photonic properties. Moreover, the concept of moiré patterns has also been extended to the twist of photonic structures, e.g., twisted photonic crystal, which broadens the field of moiré photonics and paves the way for novel application of moiré physics. Very recently, twisted stacking of two-layer photonic crystals is proposed to implement robust OAM-carrying optical vortex generation through BIC, which is insensitive to the incidence angle and the illumination position of the incident light. Figure 14(a) shows the schematic of the twisted bilayer photonic crystal. It is formed by stacking two planar photonic crystal slabs with a small twist and each slab is a honeycomb array of silicon nanodisks. The BIC modes in one slab are coupled to the guided resonances in the other slab, which are coupled to the free space. The unique interlayer channel created by the moiré structure (so called “moiré channel”) allows energy transfer between BIC modes and the free space via guided resonances. To verify the existence of the moiré channel and evaluate the radiation performance, full-wave numerical simulations are conducted on a representative twisted bilayer photonic crystal with a 300-nm spacing and a 1.5° twist angle, which is excited by a pulsed Gaussian beam. As shown in Fig. 14(b), two peaks marked as “i” and “ii” are identified in the mode intensity spectrum. Figure 14(c) shows light field distributions of the optical vortex emission at peaks “i” and “ii”. The doughnut-shaped amplitude profile and helical phase distribution confirm the generation of OAM-carrying optical vortices, corresponding to topological charges of 2 for peak “i” and 1 for “ii”. In addition, the interlayer spacing and twist angle between the two layers are also varied to show the robustness of the optical vortex emission against disturbances. Figures 14(d) and 14(e) show light field distributions under different twist angles and interlayer spacings. In all cases, the topological charges of emitted optical vortices remain 1, indicating the scheme is insensitive to experimental imperfections (e.g,. fabrication errors, thermal expansion effects) and can be used as a stable platform for robust OAM generation^[601].

Fig. 14

The out-of-plane to out-of-plane OAM generation with twisted moiré photonic crystal^[601]. (a) Schematic of the twisted bilayer photonic crystal for OAM-carrying optical vortex emission. (b) Mode intensity spectrum of the twisted bilayer photonic crystal. (c) Light field distributions of the optical vortex emission at peaks “i” and “ii” in (b). (d), (e) Light field distributions of the optical vortex emission under different (d) twist angles from 1.0° to 2.5° and (e) interlayer spacings from 200 to 350 nm^[601].

2.2.2.

Integrated OAM generation on active platforms

For the integrated OAM generation devices on passive platforms, an external separate light source is always required. Recently, integrated OAM generation devices on active platforms have also attracted increasing interest in many emerging OAM-enabled photonic technologies that do not rely on external light sources. As one typical active integrated OAM generation device, the integrated OAM laser is an important and valuable research field for diverse OAM generation.

1) Spiral phase plate laser

For the integrated OAM lasers, the straightforward method is to integrate a passive OAM generator and a compact laser on a single chip. The vertical cavity surface emitting laser (VCSEL) has numerous advantages and is suitable for integrating passive OAM generators. Figure 15(a) is the schematic of the OAM laser combining the VCSEL and the $8\times 8$ spiral phase plate array, which can emit 64 OAM modes. The topological charges of 64 OAM modes can be changed arbitrarily by adjusting the corresponding individual spiral phase plate parameter. Figure 15(b) is the spiral phase plate structure, phase distribution, and intensity profile of ${\mathrm{OAM}}_{+2}$, ${\mathrm{OAM}}_{+3}$, and ${\mathrm{OAM}}_{+4}$ modes^[602]. Figures 15(c) and 15(d) show the top view SEM images of different spiral phase plates, intensity profiles of generated OAM modes, and simulated intensity and phase profiles of individual OAM modes and their superposition^[603]. One can see that the measured intensity profiles are in good agreement with the simulated intensity profiles of OAM modes. In the experiment, the design of VCSEL integrated with a spiral phase plate can achieve low-cost wafer-scale fabrication, which is attractive for various OAM array applications.

Fig. 15

The integrated spiral phase plate OAM laser^[602,603]. (a) Schematic of integrated OAM laser combining the VCSEL and the $8\times 8$ spiral phase plate array. (b) Spiral phase plate structures, phase distributions, and intensity profiles of ${\mathrm{OAM}}_{+2}$, ${\mathrm{OAM}}_{+3}$, and ${\mathrm{OAM}}_{+4}$ modes^[602]. (c) Top view SEM images of spiral phase plates, intensity profiles of the generated OAM modes, and simulated intensity and phase profiles of OAM modes. (d) Simulated and experimental results of OAM beams with superposition states^[603].

2) Non-Hermitian-controlled laser

Microrings are considered by many OAM lasers because the microring cavity supports whispering gallery modes with high-order OAM modes. However, owing to the rotation symmetry, the active microring structure can simultaneously excite clockwise and counterclockwise whispering gallery modes, i.e., two generated OAM modes carry two contrary topological charges. The result is that the carried OAMs from simultaneously excited whispering gallery modes cancel each other. Consequently, in order to obtain an individual OAM, it is imperative to introduce a mechanism to break the rotation symmetry. Non-Hermitian symmetry with gain or loss is an emerging and promising solution, which breaks the condition of rotation symmetry and lifts the degeneracy state of two spin-orbit modes, which is beneficial to the generation of an OAM beam of desirable chirality. By exploiting the exceptional point of a non-Hermitian system, an OAM microlaser with tunable topological charge is present, which gives full play to the advantages of the semiconductor microlasers and non-Hermitian system. Figure 16(a) displays the schematic of the OAM microlaser with a tunable topological charge. The OAM laser consists of a microring resonator and a bus waveguide with two control arms. By adjusting the gain (optically pumping) and loss (material loss), the OAM microlaser can operate at an exceptional point, to break the chiral symmetry and control the chirality of the OAM mode. The left-handed (right-handed) circular polarization with ${\mathrm{OAM}}_{+1}$ (${\mathrm{OAM}}_{-1}$) is observed when only the right (left) control arm is illuminated by the control beam, as shown in Fig. 16(b)^[604]. The multiple different OAM states are produced by the non-Hermitian-controlled OAM microlaser. Furthermore, the fast switch of the fractional OAM is demonstrated based on the OAM semiconductor microlaser and a control laser pulse, as shown in Fig. 16(c)^[605]. In a 100-ps time window, a continuous fractional OAM sweep between the topological charge 0 and $+2$ is implemented. Besides, a hyperdimensional spin-orbit microlaser consisting of two similar microrings generates the spin-orbit OAM in a four-dimensional Hilbert space, as shown in Fig. 16(d)^[606]. Another scheme for adjusting the gain and loss is the modulation of the complex refractive index. The complex refractive index is achieved by the alternate Ge and Cr/Ge structures placed on top of the InGaAsP microring, as shown in Fig. 16(e)^[607]. When the device works at an exceptional point, the microring laser also produces a single-mode OAM-carrying vortex laser beam. A unidirectional resonator including a microring resonator and an S-shaped waveguide is present to directly generate a tunable OAM, as shown in Fig. 16(f)^[608]. An S-shaped waveguide located inside the microring offers the gain or loss to break two clockwise and counterclockwise eigenmodes. The topological charge of generated OAM modes can be precisely adjusted by temperature adjustment.

Fig. 16

The integrated non-Hermitian-controlled OAM laser^[604–608]. (a) Schematic of OAM microlaser with tunable topological charge. (b) Schematic of chiral non-Hermitian control and experimental characterization^[604]. (c) Schematic of the fast switch of the fractional OAM^[605]. (d) Schematic of a hyperdimensional spin-orbit microlaser^[606]. (e) Schematic of OAM microlaser with a microring resonator and alternate Ge and Cr/Ge structures^[607]. (f) Schematic of OAM microlaser with a microring and an S-shaped waveguide^[608].

3) Micro-etching laser

Some integrated micro-etching lasers are presented to generate the OAM mode. Ge micro-gears on silicon pillars are fabricated on the Ge on silicon on an insulator wafer to obtain an OAM beam, as shown in Fig. 17(a). There are some peak resonances within the Ge direct gap, as shown in Fig. 17(b)^[609]. Using finite difference time domain (FDTD) simulation, the resonant peak of the micro-gear spectrum is studied and determined to be a vertical emission optical mode with a non-zero OAM beam. Additionally, a customizable chiral (i.e., clockwise or counterclockwise vortex) VCSEL OAM laser is proposed and demonstrated. This laser based on the optical breaking of time-reversal symmetry is formed by a semiconductor planar microcavity embedded with a single ${\mathrm{In}}_{0.05}{\mathrm{Ga}}_{0.95}\mathrm{As}$ quantum well. Figure 17(c) shows the schematic and SEM image of a benzene-like OAM laser with the cavity etched to form hexagonal rings of coupled micropillars. Figures 17(d) and 17(e) depict phase distributions of the emission, showing a $4\pi$ counterclockwise and clockwise phase vortex under $\sigma +$ and $\sigma -$ circularly polarized pumps, respectively^[610]. The subwavelength etching metasurface placed on the top of the microring can also break the degeneracy of two counter-propagating whispering gallery modes in the active microring resonator, resulting in the direct generation of OAM mode, as shown in Fig. 17(f). A nanobeam of metal-dielectric-metal sandwiched structure is designed as the meta-atom, as shown in Fig. 17(g), which can evanescently couple with guided waves propagating in the waveguide and offers an $\sim 2\pi$ phase shift. As shown in Fig. 17(h), the meta-atom is designed with uniform amplitude and phase shift covering the entire $2\pi$ phase range. Figure 17(i) shows the simulated and measured results for the far-field intensity distribution and the self-interference patterns of the OAM mode, showing the impressive quality of the OAM beam generated by the metasurface laser^[611]. An electrically pumped OAM laser is proposed and fabricated on an InGaAsP/InP multiple quantum well (MQW) epitaxial wafer, which is integrated by a distributed feedback semiconductor laser and an OAM emitter based on a microring, as depicted in Fig. 17(j). The micro-etching grating on the top of the microring waveguide extracts OAM beams from the MWGs in the microring resonator. This OAM laser effectively avoids the counter-propagating mode degeneracy, allowing for unidirectional OAM mode excitation from the whispering gallery mode. Figure 17(k) shows the mode purity values of the measured right-handed and left-handed circularly polarized components, which are 0.76 and 0.85, respectively^[612].

Fig. 17

The integrated micro-etching OAM laser^[609–612]. (a) Focused-ion beam and SEM images of the Ge micro-gears on silicon pillars. (b) Measured spectra by exciting the micro-gear from the top with laser beams of different powers^[609]. (c) Schematic and SEM image of a benzene-like OAM laser with the cavity etched to form hexagonal rings of coupled micropillars. (d), (e) Phase distributions of the emission showing $4\pi$ counterclockwise and clockwise phase vortex under (d) $\sigma +$ and (e) $\sigma -$ circularly polarized pumps^[610]. (f) Schematic of a microring OAM laser based on the guided wave-driven metasurface. (g) Schematic of meta-atom with a metal/dielectric/metal structure. (h) Phase shift of the meta-atom with different parameters. (i) Simulated and measured results for the far-field intensity distributions and the self-interference patterns of OAM mode^[611]. (j) Schematic of the OAM laser with a microring and a distributed feedback laser. (k) Measured mode purities of OAM beams^[612].

4) Topological laser

The topological photonics originates from topological phases and phase transitions in condensed matter. Since Haldane and Raghu introduced band topology to the realm of photonics in 2008^[613,614], topological photonics has attracted widespread research attention in integrated optics, nonlinear optics, and quantum optics, and can also be applied in the OAM microlaser to generate high-quality OAM beam. Figure 18(a) shows the schematic of the generated spin-momentum-locked edge mode from the topological OAM laser. Figures 18(b) and 18(c) are the SEM and zoom-in SEM images of the topological OAM laser fabricated on an InGaAsP MQW membrane. The x-shaped cavity geometry with multiple bends is designed to demonstrate the robust immune backscattering of the topological edge states at topological interfaces. Owing to the finite propagating cavity length, the edge modes are discrete, as shown in Fig. 18(d). Compared to the conventional cavity mode and whispering gallery mode in microrings, the edge modes have a near zero in-plane wave vector, facilitating directional surface emitting, as shown in Fig. 18(e). Similar to the microring resonator, the designed complex cavity also supports two topological edge modes with opposite spins, and the lasing spectra are shown in Fig. 18(f). When the pump of the laser is working, the spin-momentum-locked topological edge mode that is not coupled to its backpropagation wave can saturate gain to restrain other mode lasers, thus breaking the degeneracy of eigenmodes. Consequently, Figs. 18(g) and 18(h) show the off-center self-interference of the generated ${\mathrm{OAM}}_{-2}$ mode and side-mode suppression ratio (SMSR) versus the pump intensity, indicating that the topological edge laser has the feature of single-mode operation when pumped for lasing^[615]. In addition, the topological photonics can be used to design the low-threshold vortex and anti-vortex nanolasers. As shown in Fig. 18(i), the important part is a ${\mathrm{C}}_5$ symmetric optical cavity formed by a topological disclination. Figures 18(j) and 18(k) show the SEM images of the fabricated vortex and anti-vortex nanolasers, respectively. To demonstrate the unique characteristics of the two types of lasers, Figs. 18(l)–18(n) present polarization-resolved mode images^[616]. The top left corner shows the mode field intensity distribution of all laser modes without a polarizer, revealing a doughnut-shaped pattern. The center null intensity is a distinctive feature of the vortex/anti-vortex modes. Furthermore, the polarization-resolved mode images for each mode are fully distinguishable.

Fig. 18

The integrated topological OAM laser^[615,616]. (a) Schematic of the topological OAM laser. (b) SEM and (c) zoom-in SEM images of the topological OAM laser. (d) Calculated bulk bands of the topological photonic crystal (gray curves), and calculated discrete edge modes of the topological OAM laser (red and green dots). (e) Dispersion curves of the conventional whispering gallery modes and topological edge modes. (f) Lasing spectra of the two edge states of opposite momenta with opposite spins. (g) Off-center self-interference of the generated ${\mathrm{OAM}}_{-2}$ mode. (h) SMSR versus the pump intensity^[615]. (i) Schematic of vortex and anti-vortex disclination nanolasers. (j), (k) SEM images of fabricated (j) vortex and (j) anti-vortex nanolasers. (l)–(n) Measured polarization-resolved lasing images from the cavities of the (l) vortex and (m), (n) anti-vortex nanolasers^[616].

5) Supersymmetric microlaser arrays

Coupling multiple lasers to form an array is a common approach to enhance the output light of laser systems. In large-scale phase-locked laser arrays, complex nonlinear scaling often adversely affects performance, leading to instability and potentially damaging the laser cavity. To address this issue, a higher-dimensional supersymmetric form is proposed for precise mode control and nonlinear power scaling. As shown in Figs. 19(a) and 19(b), a $5\times 5$ array of identical microring lasers, composed of multiple InGaAsP quantum wells, exhibits phase-locked coherence and synchronization of all evanescently coupled microring lasers. This uniformly coupled 2D array achieves high radiance, low divergence, and single-frequency laser emission, enhancing the emission power by approximately 25 times compared to a single microlaser, as shown in Fig. 19(c). Moreover, the slope efficiency of the laser array is 26.3 times that of a single microlaser, and it also exhibits a lower lasing threshold. Furthermore, Fig. 19(d) demonstrates the superposition state of left- and right-handed circularly polarized fields, with a continuously varying phase delay between them, resulting in a vector beam with radial polarization. Using an appropriate combination of a quarter-wave plate and a linear polarizer, the two vortex beams with opposite spin-orbit relationships can be effectively separated, as shown in Figs. 19(e) and 19(f)^[617]. A dark stripe is clearly observed in the figures, confirming the topological charge of the OAM light as $\ell =\pm 1$.

Fig. 19

Higher-dimensional supersymmetric microlaser arrays^[617]. (a) Conceptual view and (b) measured SEM images of higher-dimensional supersymmetric microlaser arrays. (c) Light-light curve showing the lowering of the threshold and the enhancement of lasing output in the supersymmetric microlaser array compared with a single microring laser. (d) Far-field diffraction pattern of vortex emission, corresponding to the superposition of two vortex beams. (e), (f) 1D diffraction patterns of the two distinct vortex beams of (e) ℓ = $+1$ and (f) ℓ = $-1$^[617].

2.3.1.

Integrated chiral light generation

Chiral light, a special light field, has drawn much attention due to its geometric properties that cannot be coincident with its mirror image by translation or rotation operation^[618–621]. One important aspect of studying photonic chiral behavior is the efficient generation of the chiral light field. The chiral optical microcavity and nanocavity are promising integrated schemes. As shown in Fig. 20(a), the resonant chiral metasurface composed of a square lattice of tilted ${\mathrm{TiO}}_2$ uses the chiral quasi-bound states in the continuum (BIC) to achieve the effective and controllable emission of circularly polarized light. The metasurface has two deformation (asymmetric) parameters $\theta$ (in-plane) and $\alpha$ (out-of-plane), as shown in Fig. 20(b). The symmetry disruption of the combination of two parameters causes the match between the chiral filtering effect of BIC and the frequency of partially BIC radiation. Figure 20(c) depicts the emission spectra of LCP and RCP at the pumping densities of 16.5 and $58.9\mathrm{mJ}/{\mathrm{cm}}^2$, respectively. When the pumping density is $58.9\mathrm{mJ}/{\mathrm{cm}}^2$, the LCP mode intensity at 612.08 nm significantly increases and dominates the emission spectrum. Figure 20(d) is the integrated output intensity of the LCP and RCP components versus the pumping density. When the pump density is greater than $22.14\mathrm{mJ}/{\mathrm{cm}}^2$, a significant increase in intensity can be observed. Figure 20(e) is the fitted degree of polarization (DOP), absolute DOP, and full width at half maximum (FWHM) of LCP light versus the pumping density. The absolute value of DOP rapidly increases near the transparency threshold and saturates at 0.948 to 0.989, while the linewidth of the emission peak decreases from 1.0 to 0.18 nm at the transparency threshold. The divergence angle further decreases to $\sim 1.06°$, as shown in Fig. 20(f). The above experimental results demonstrate a resonant metasurface, which generates a chiral light with a purity of $>99\%$^[622].

Fig. 20

Integrated chiral light generation and LP mode generation^[622,623]. (a) Schematic of resonant chiral metasurface. (b) Top view, side view, and vector field of unit-different cell. (c) Emission spectra of LCP (solid lines) and RCP (dashed lines) in the normal direction. The pumping densities are $16.5\mathrm{mJ}/{\mathrm{cm}}^2$ (bottom) and $58.9\mathrm{mJ}/{\mathrm{cm}}^2$ (top), respectively. (d) Output intensity of LCP (dot-shaped) and RCP (square-shaped) versus the pumping density. (e) Fitted DOP (cross-shaped), absolute DOP (dot-shaped), and FWHM (square-shaped) of LCP light versus the pumping density. (f) Far-field angular intensity distribution of the generated chiral light^[622]. (g) Schematic of three-layer volume. (h) SEM image of the volume element. (i), (j) Experimental results of output intensity for (i) $+3°$ incidence angle to yield ${\mathrm{LP}}_{21}$ mode and (j) $-3°$ incidence angle to yield ${\mathrm{LP}}_{02}$ mode^[623].

2.3.2.

Integrated LP mode generation

LP mode is one kind of special light beam in radially symmetric refractive index distribution fibers or waveguides with weakly guiding approximation, which is also the solution of complex electric field wave equations in cylindrical coordinates. In optical communication systems, different LP modes can also be used as different data channels to further improve the transmission capacity of optical communications. An optical volume element is proposed to generate different LP modes under different input angles. For a micro-scale multilayer design, an optimization method named learning tomography is adopted, which is a reconstructed method of 3D phase objects. Figures 20(g) and 20(h) are the schematic and SEM images of the three-layer volume element. When the incidence angle is $+3°$ ($-3°$), the output light of the volume element is ${\mathrm{LP}}_{21}$ (${\mathrm{LP}}_{02}$) mode, as shown in Figs. 20(i) and 20(j)^[623]. In addition to these two LP modes, other higher LP modes can also be generated.

2.3.3.

Integrated Laguerre-Gaussian/Hermite-Gaussian beam generation

The Laguerre-Gaussian (LG) beam and Hermite-Gaussian (HG) beam both play an important role in laser optics. Although the symmetries of the two types of beams are different, HG functions can be expressed as a linear superposition of LG functions, and vice versa. In particular, the LG mode characterized by the radial index $p$ and the azimuthal index $l$ has attracted more and more attention due to its ability to carry OAM. For the generation of LG/HG mode, higher-order LG/HG modes can be generated by a metal metasurface composed of a series of rectangular nanoholes with different orientation angles, as shown in Fig. 21(a). Relying on the PB phase, the metasurface has a broadband operation wavelength. Figure 21(b) is the simulated phase and intensity distribution of the high-order LG mode. Figure 21(c) shows the measured intensity distributions of different LG and HG beams ($p=3$ and $p=10$)^[624]. Based on the PB phase, the metasurface consisting of Au unit cells is also designed to produce multiple LG modes and separate them, as shown in Fig. 21(d). The overall SEM image and zoom-in SEM image of the fabricated metasurface are shown in Fig. 21(e). The metasurface has a favorable performance over a 400-nm-wide wavelength range, as shown in Fig. 21(f). In principle, the metasurface can be designed to distribute the light energy into a greater number of modes. Figure 21(g) shows the simulated and measured diffraction patterns of the combined mode of ${\mathrm{LG}}_1^1:{\mathrm{LG}}_2^2:{\mathrm{LG}}_2^3=3:4:5$ at 1030 nm with favorable performance^[625].

Fig. 21

Integrated Laguerre-Gaussian (LG) beam generation and Hermite-Gaussian (HG) beam generation^[624,625]. (a) Schematic of the unit cell and SEM image of the metal metasurface. (b) Simulated phase and intensity distribution of the ${\mathrm{LG}}_{2,2}$ mode. (c) Measured intensity distributions of different LG and HG beams ($p=3$ and $p=10$) at an operation wavelength of 1000 nm^[624]. (d) Schematic of the unit cell and metasurface for generating multiple LG modes. (e) Overall SEM and zoom-in SEM images of metasurface for generating multiple LG modes. (f) Simulated and measured diffraction patterns of the combined mode of ${\mathrm{LG}}_4^2{}_{}:{\mathrm{LG}}_1^1=1:1$ with different wavelengths. (g) Simulated and measured diffraction patterns of the combined mode of ${\mathrm{LG}}_1^1{}_{}:{\mathrm{LG}}_2^2:{\mathrm{LG}}_2^3=3:4:5$ at 1030 nm^[625].

2.3.4.

Integrated non-diffracting beam generation

A non-diffracting beam refers to a light beam with a small center spot diameter that does not vary with propagation distance^[626]. Mathematically, the non-diffracting beam is the solution of a new set of Maxwell wave equations, and its light intensity and propagation distance are two irrelevant variables. This type of beam can self-recover its light field distribution after encountering obstacles, which means it has the characteristic of self-reconstruction. With the development of laser technology, researchers have found a variety of diffraction-free solutions that theoretically meet the wave equation, such as the Bessel beam, Mathieu beam, Airy beam, needle beam, pin beam, etc.

1) Integrated Bessel beam generation

The Bessel function is the accurate solution of the free-space wave equation of a non-diffracting beam in cylindrical coordinates. The zeroth-order Bessel beam exhibits a circular bright spot with the highest central light intensity on the cross-section perpendicular to the propagation direction, surrounded by many rings, and the intensity of the concentric rings gradually weakens as the radius increases. For the higher-order Bessel beam, the central intensity is zero, which is a circular central dark core structure. Due to its non-diffraction and self-healing properties, Bessel beams have wide applications in particle manipulation, optical alignment and imaging, laser microfabrication, nonlinear optics, and information extraction. In order to further realize these applications, the generation of Bessel beams is particularly important. The typical generation schemes based on integrated devices include metasurfaces, phased arrays, phase plates, 3D structures, and concentric distributed grating arrays. Using metasurfaces, the operation wavelength covers the whole visible spectrum, as shown in Fig. 22(a)^[627]. The metasurface also utilizes the functionalities of Dammann gratings and axicons to generate $5\times 5$ polarization-independent Bessel beams, as shown in Fig. 22(b)^[628]. The measured experimental results indicate that the efficiency is 66.36% and the FWHM is about 1600 nm. As shown in Fig. 22(c), optical phased arrays integrated on a CMOS-compatible platform are presented to generate the Bessel beam with an $\sim 30\mathrm{\mu m}$ FWHM and an $\sim 14\mathrm{mm}$ Bessel length^[496]. The polymer phase plate fabricated by the femtosecond laser direct writing technique is also an attractive solution to produce a high-quality Bessel beam, as shown in Fig. 22(d)^[385]. The polymer-based phase plate has a miniature size of $300\mathrm{\mu m}\times 300\mathrm{\mu m}\times 3.1\mathrm{\mu m}$. The experimental results demonstrate the 800-mm propagation invariance of the zeroth- and higher-order Bessel beam. The femtosecond laser direct writing technique can also be used to process a 3D structure device on the end face of the fiber to generate a Bessel beam. As shown in Fig. 22(e), the 3D structure includes a helical axicon, a parabolic lens, and a mechanical holder frame^[629]. After a 2-mm propagation, the pattern of the generated Bessel beam retains a nearly unchanged size. Based on an SOI standard process, an 870-μm-diameter ring structure with concentrically distributed grating arrays is present to implement a 10.24-m propagation invariance of a broadband Bessel beam, as shown in Fig. 22(f)^[630]. The 10.24 m is a long-range distance, facilitating the measure of rotation speed and distance.

Fig. 22

Integrated Bessel beam generation and Mathieu beam generation^{[385,386,496,627–630]}. (a) Metasurface for generating individual Bessel beam over the whole visible spectrum^[627]. (b) Metasurface for generating $5\times 5$ polarization-independent Bessel beam arrays^[628]. (c) Optical phased arrays for generating Bessel beam^[496]. (d) Polymer-based phase plate for generating high-quality Bessel beam^[385]. (e) 3D structure consisting of a parabolic lens, a mechanical holder frame, and a helical axicon for generating a Bessel beam^[629]. (f) 870-μm-diameter ring structure with concentrically distributed grating arrays for generating a 10.24-m propagation invariance of broadband Bessel beam^[630]. (g) Helical phase plate for generating a Mathieu beam. (h) Intensity distribution of the even Mathieu beam with $m=2$ and $q=12$ at different distances^[386].

2) Integrated Mathieu beam generation

The Mathieu beam is the solution of the Helmholtz equation for a non-diffracting beam in elliptical cylindrical coordinates. The Mathieu beam also has the typical features of the non-diffraction beam, i.e., non-diffraction and self-reconstruction. The difference is that the transverse intensity is lattice-like for the Mathieu beam. In general, the distribution pattern of the Mathieu beam is controlled by two parameters, i.e., order $m$ and ellipticity $q$. Compared with the Bessel beam, the Mathieu beam with a complex structure is more difficult to generate. Thanks to the flexible 3D manufacturing capability of the femtosecond laser direct writing technique, a helical phase plate, as shown in Fig. 22(g), can be designed and fabricated to obtain the Mathieu beam with different orders $m$ and ellipticities $q$. Figure 22(h) shows the intensity distribution of the even Mathieu beam with $m=2$ and $q=12$ at different distances, which indicates that the generated Mathieu beam has approximately no diffraction within the 800-mm propagation range^[386].

3) Integrated Airy beam generation

The Airy beam is a type of self-accelerating optical beam and a non-diffracting solution of the paraxial Helmholtz equation. Interestingly, the Airy beam shows a parabolic trajectory during its propagation. Thus, except for the peculiarities of the non-diffraction beam, the Airy beam also shows the feature of self-bending. The nanocavity array carefully designed on a silver surface implements the particular diffraction processes of light to a plasmonic Airy beam at a visible wavelength, as shown in Fig. 23(a)^[631]. The generated plasmonic Airy beam directly exhibits its properties of non-diffraction, self-reconstruction, and self-bending. Furthermore, the metasurface can also emit the Airy beam, and the all-dielectric metasurface can avoid the loss caused by metals. An ultra-thin subwavelength metasurface is proposed to produce Airy beams with high efficiency and ultra-wide bandwidth by reflecting or transmitting input light, as shown in Fig. 23(b)^[632]. The versatile and multi-feature Airy beams are designed by a synthetic-phase metasurface that superposes multiple special phase profiles in a metasurface, as shown in Fig. 23(c)^[633]. For example, the specially designed metasurface superposes the fine-tuning Fresnel lens phase to obtain the modifiable Airy beams with an impressive performance in terms of focal length, beam width, and non-diffractive propagation distance. The synthetic-phase metasurface produces the $1\times 4$ Airy array beams by combining the optimized Dammann grating phase. In addition, a dielectric metasurface composed of silicon posts is proposed to generate an achromatic terahertz Airy beam with autofocusing properties, as shown in Fig. 23(d)^[634]. To avoid accurate alignment and reduce the difficulty of the experiment, the synthetic-phase meta-optics is introduced to the silicon waveguide to demonstrate the 1D on-chip Airy-like beams near the telecommunication wavelength. It is worth noting that the silicon waveguide with the synthetic-phase meta-structure has an ultra-compact footprint of $3\mathrm{\mu m}\times 16\mathrm{\mu m}$, as shown in Fig. 23(e)^[635]. In addition, a shallow-etched silicon holography grating can also be used to generate the 2D Airy beam, as shown in Fig. 23(f)^[636].

Fig. 23

Integrated Airy beam generation^[631–636]. (a) Silver surface for generating Airy beams^[631]. (b) Reflective and transmissive metasurfaces for generating ultra-wideband Airy beams^[632]. (c) All-dielectric metasurface for generating individual and multiple Airy beams^[633]. (d) Dielectric metasurface for generating achromatic terahertz Airy beams^[634]. (e) Synthetic-phase meta-optics with an ultra-compact footprint of $3\mathrm{\mu m}\times 16\mathrm{\mu m}$ for generating 1D Airy beams^[635]. (f) Shallow-etched silicon holography grating for generating Airy beams^[636].

4) Integrated needle beam generation

The needle beam is an optical beam with a small focal spot size and long focal line, which is very attractive for applications that utilize the spatial and temporal localization of photons. A high-intensity extended focal depth makes fundamental progress in optical system performance, especially in optical microscopes. A custom diffractive optical element (DOE) is proposed to produce the needle beam. It is demonstrated that a needle beam generated via DOE has a degree of freedom up to 28 times the Rayleigh length, and still maintains a relatively constant beam diameter, uniform axial intensity distribution, and negligible sidelobe. To form a needle beam, the designed DOEs generate several closely adjacent focal points along the axis, as shown in Figs. 24(a) and 24(b). The beam length of the needle beam depends on the number of focal points. Figure 24(c) shows the experimentally measured optical profile of the needle beam, indicating that the needle beam can maintain the beam spot size along the $z$-axis^[637].

Fig. 24

Integrated needle beam and pin beam generation^[74,637]. (a) DOE phase pattern composed of multiple different phases of focal points. (b) Schematic of DOE for generating a needle beam. (c) Experimentally measured results of the needle beam, including $y\mathrm{–}z$ and $x\mathrm{–}y$ profiles at different $z=-100$, 0, and 100 µm^[637]. (d) Pin beam generation mechanism by eliminating the transverse wave vector components and the directed truncation of components similar to Airy beams. (e) Side view of the pin beam propagating over 8 km. (f) Intensity profiles captured at $z=0$, 4, and 8 km^[74].

5) Integrated pin beam generation

The needle beam mentioned above is essentially formed by superimposing multiple beams with different focal lengths, creating a needle-like beam that maintains a small beam waist over a long distance. Another similar structured light is known as the pin beam. This type of structured light beam uses the self-focusing of the annular Airy beam towards the center, resulting in a central main lobe that maintains a small beam waist over a long distance, similar to a needle beam. A single fused silica mask created through photolithography can be used to generate the pin beam. The novel mechanism is employed to produce the pin beam by eliminating the transverse wave vector components and the directed truncation of components similar to the Airy beam, as shown in Fig. 24(d). To better understand the underlying mechanism, the self-focusing pin beam formation is studied by assembling multiple phase elements with opposite transverse wave vectors. Figure 24(e) shows a side view of the pin beam propagating over 8 km, with optimal “focusing” occurring around $z=5.0\mathrm{km}$. Figure 24(f) shows the intensity profiles captured at $z=0$, 4, and 8 km^[74].

2.3.5.

Integrated vector beam generation

The vector beam is a peculiar light beam with a non-uniform distribution of polarization on the beam cross-section. The vector beam is proposed relative to conventional scalar beams with the same polarization state distribution at different positions on the beam cross-section, such as linearly polarized, circularly polarized, and elliptically polarized beams. Compared to scalar beams, vector beams provide more degrees of freedom in beam manipulation. With the increasing maturity of micro/nanofabrication technology, integrated devices can be used to achieve different types of beams in the polarization state. The vector beam has attracted more attention due to the non-uniform distribution of the polarization state, among which the most typical vector beam is the cylindrical vector beam (CVB). The CVB presents an axisymmetric distribution of polarization state on the cross-section, including two typical types: a radially polarized beam (RPB) along the radius direction and an azimuthally polarized beam (APB) along the azimuthal direction. With their unique focusing and axisymmetric properties, the RPB and APB enable a variety of new functions, such as sharp focusing and optical trapping. There are several reported integrated methods for producing RPB and APB. A ring structure with concentrically distributed 64 grating arrays, as shown in Fig. 25(a), is designed on the silicon platform to generate RPB and APB using TM-polarized and TE-polarized light in the waveguides, respectively^[638]. Similarly, based on the large differences between azimuthal and radial electrical distributions from different polarization waveguide modes, a silicon nitride microring resonator with shallow-etched gratings, as shown in Fig. 25(b), controls the generation of RPB and APB by configuring the TE and TM excitation waveguide modes^[639]. Then, using the microring with a width-varying waveguide, the CVB with arbitrary angle emission can be achieved by superimposing a phase profile on the microring, as shown in Fig. 25(c)^[640]. The all-dielectric metasurfaces composed of subwavelength silicon pillars and sapphire substrate convert horizontal (vertical) linear polarization to RPB (APB) in a mid-infrared band, as shown in Fig. 25(d)^[641].

Fig. 25

Integrated vector beam generation^[638–641]. (a) Ring structure with concentrically distributed 64 grating arrays^[638]. (b) Schematic of silicon nitride microring resonator with shallow-etched gratings on the top of microring waveguide^[639]. (c) Schematic, far-field intensity, and polarization map of conventional and width variation microring^[640]. (d) Schematic of metasurface for generating mid-infrared radially polarized (azimuthally polarized) beam by horizontal (vertical) linear polarization^[641].

In addition to passive integrated devices, active integrated devices can also generate vector beams. The CVB laser composed of an active microring cavity and two specially designed gratings (side grating and top grating) is designed and fabricated on a fully integrated III–V semiconductor platform. Figures 26(a)–26(c) show the schematic 3D structure, top view, and SEM image of the CVB laser. The optimized triangular side grating introduced at the circumference of the microring splits the degenerate whispering gallery modes, selects the symmetrical mode with less scattering loss as the lasing mode, and obtains a single-mode laser with a high SMSR. Another second-order top grating improves the efficiency of surface emission. Figure 26(d) demonstrates the far-field intensity distribution of measured CVBs without and with a rotating linear polarizer. One can see that the radiant intensity distribution of the RPB with zeroth azimuthal order is multiple concentric rings with a dark center, rather than a single ring^[642]. Furthermore, a structure consisting of two concentric microcavities is proposed, which realizes two CVB lasers in an electric pump based on the InP platform, as shown in Fig. 26(e). When only the top grating is added to the microcavity, the laser mode is an APB, as shown in Fig. 26(f). When the microcavity has a top and side grating, the laser mode is an RPB, as shown in Fig. 26(g)^[643].

Fig. 26

Integrated CVB laser^[642,643]. (a) Schematic 3D structure, (b) top view, and (c) SEM image of the CVB laser. (d) Far-field intensity distribution of measured RPBs without and with a rotating linear polarizer^[642]. (e) Schematic of the cross section of the CVB laser. (f), (g) Schematic of the CVB laser for generating (f) RPB and (g) APB^[643].

2.3.6.

Integrated array beam generation

An array beam is composed of multiple sub-beams arranged in a specific spatial distribution pattern. Compared with a single beam, the array beam can obtain higher laser output power. Due to the different transmission paths of each sub-beam, the sub-beams reaching the receiving system have a certain mutual compensation effect and can potentially improve the beam quality in the transmission process. There are several integration schemes for generating the array beam using a metasurface and array gratings. An ultra-thin nano-slit metasurface enables the generation of the array beam with equal power distribution, as shown in Figs. 27(a) and 27(b). The sub-beam is the OAM beam. Figure 27(c) shows the measured and simulated intensity distribution of the $6\times 6$ array beam with topological charges of $\ell =0$ and $\ell =1$^[644]. An array OAM beam with various topological charges or special arrays is obtained by designing a particular metasurface. The metasurface is applied in the laser cavity to generate a $10\times 10$ array OAM beam laser, as shown in Fig. 27(d). The charge of the vortex array is scaled up by increasing the azimuthal gradient in the metasurface design. Figure 27(e) shows the experimental near-field and far-field distributions of the array beam with a topological charge of $\ell =5$, which has high purity^[645]. In addition, as shown in Fig. 27(f), a large-scale phased array composed of $64\times 64$ gratings on a $576\mathrm{\mu m}\times 576\mathrm{\mu m}$ silicon chip is used to generate the array beam. Figure 27(g) shows the experimental near-field distributions of all $64\times 64$ gratings, which shows uniform emission of a large-scale phased array^[646].

Fig. 27

Integrated array beam generation^[644–646]. (a) Schematic and (b) SEM image of nano-slit metasurface for generating array OAM beams. (c) Measured and simulated intensity distributions of the $6\times 6$ array beam with topological charges of $\ell =0$ and $\ell =1$^[644]. (d) Schematic of metasurface laser for generating array OAM beams. (e) Experimental near-field and far-field distributions of array beam with a topological charge of $\ell =5$^[645]. (f) Schematic of phased array system with $64\times 64$ gratings. (g) Experimental near-field distributions with uniform emission of all $64\times 64$ gratings^[646].

Optical vortex lattices are named a network of optical vortex or optical vortex arrays. In general, the optical vortex lattice is produced by bulky optical elements that superpose two specific vortex beams, which is not conducive to miniaturizing the optical vortex lattice generator. Based on the principle of three-plane-wave interference, a silicon optical vortex lattice emitter using three tilt gratings is presented, as shown in Figs. 28(a) and 28(b). The thickness of the silicon strip waveguide and the etching depth of the ridge waveguide are 340 and 220 nm, respectively. Figures 28(c)–28(e) plot the simulated results of the optical vortex lattice based on the three-plane-wave interference, including intensity, phase, and interferogram distributions. It can be clearly seen that each dark point in the intensity distribution is a phase singularity. The phase singularity with a $2\pi$-phase change is regarded as an optical vortex with a topological charge of $\ell =1$ or $\ell =-1$. Figures 28(f)–28(k) present the simulated and experimentally measured results of the designed and fabricated optical vortex lattice emitter, showing favorable operation performance^[647].

Fig. 28

Integrated optical vortex lattice generation^[647]. (a), (b) Schematic of on-chip optical vortex lattice emitter and the tilt grating. (c)–(e) Simulated results of optical vortex lattice based on the three-plane-wave interference, including intensity, phase, and interferogram distributions. (f)–(h) Simulated and (i)–(k) experimentally measured results of the designed and fabricated optical vortex lattice emitter, including near-field intensity distribution of $y$-polarization electrical field, intensity, and interference of far-field distribution^[647].

2.3.7.

Integrated spatiotemporal beam generation

The goal of integrated spatiotemporal beam generation is to flexibly control all degrees of freedom of the light field both spatially (amplitude, phase, polarization) and temporally (pulse width and shape). The electro-optic effect of the free carrier in silicon can be used to modulate the resonance of the photonic crystal microcavity to achieve nearly complete spatiotemporal control of the narrow band light field filtered in space and time, as shown in Fig. 29(a). Reverse-designed high-precision microcavities provide a vertical coupling efficiency that is greater than 90%, as shown in Fig. 29(b). Figure 29(c) depicts the maximum phase shift and half-maximum switching interval versus CMOS trigger duration. $0.3\pi$ is the maximum phase shift. Figure 29(d) shows the complex reflectivity modulation with fJ-order pulse energies. One can see that it is feasible to achieve the high-contrast phase and amplitude modulation over a 1-ns interval when the pump pulse is 5 fJ. Figure 29(e) shows the modulation bandwidth of 135 MHz in the frequency-domain response^[648]. In addition, using a single-layer metasurface strongly coupled to the epsilon-near-zero (ENZ) material, the control of a synchronous spatiotemporal laser can be achieved in the fiber laser cavity. Based on the PB phase, the plasmonic metasurface for the intracavity spatial modulation converts from a Gaussian beam to an OAM beam, as shown in Figs. 29(f)–29(i). Meanwhile, the ENZ material for intracavity temporal modulation generates a pulsed laser due to the powerful nonlinear saturable absorption, as shown in Figs. 29(j)–29(m)^[649].

Fig. 29

Integrated spatiotemporal beam generation^[648,649]. (a) Schematic of a spatial light modulator based on the photonic crystal. (b) Near-field reflection spectra of inverse-designed cavities. Inset: resonant imaging. (c) Maximum phase shift and half-maximum switching interval versus CMOS trigger duration. (d) Complex reflectivity modulation with fJ-order pulse energies. (e) Frequency-domain power transfer response function^[648]. (f), (h) Transverse mode profiles and (g), (i) interference patterns of the vortex beam with topological charges of $\ell =1$ and $\ell =2$. (j) Real and imaginary parts of the indium tin oxide (ITO) film permittivity. (k) Measured and fitted transmittance of the epsilon-near-zero (ENZ)-metasurface versus pump fluence. (l) Intensity of output pulses with a 39-mW pump power. (m) Averaged spectrum of the output pulses^[649].

In addition, the spatiotemporal optical vortex (STOV) can be generated by the synergistic usage of optical vortex emitters and frequency combs, which control the OAM and frequency, respectively. As shown in Fig. 30(a), the OAM comb device comprises a high-Q microring with inner sidewall gratings, fabricated on the emerging AlGaAs on insulator (AlGaAsOI) platform. This OAM comb exhibits tight mode confinement and strong optical nonlinearities, enabling low-threshold microcomb generation. Figure 30(b) displays SEM images of the fabricated AlGaAsOI device. To reduce the scattering loss of the fundamental mode in the OAM microring, a multimode waveguide with a cross-section of $380\mathrm{nm}\times 750\mathrm{nm}$ is employed. The grating protrusion is designed to be 30 nm to achieve notable efficiencies for vortex ejection and high Q values for comb generation. Figure 30(c) presents the measured spectra of the microcombs in soliton states with wavelength spacing of 500 GHz. Three comb lines ($\ell =4$, 5, and 6) with an intensity variation below 1 dB are filtered to generate self-torque pulses, as depicted in the red area of Fig. 30(c). The calculated and measured spatiotemporal profiles of the targeted self-torque pulse are shown as iso-surface plots in Figs. 30(d) and 30(e), focusing on the distribution of the main lobe and demonstrating varied OAM at different times in both intensity and phase^[650]. Meanwhile, an OAM comb using 800-nm-thick stoichiometric ${\mathrm{Si}}_3{\mathrm{N}}_4$ films on a silica substrate is presented and illustrated in Fig. 30(f). Figure 30(g) shows the SEM image of the ${\mathrm{Si}}_3{\mathrm{N}}_4$ OAM comb. The mean radius and width of the microresonator are set as 22 and 2 µm, leading to a free spectral range (FSR) around 1 THz, as shown in Fig. 30(h). Figures 30(i) and 30(j) show the simulated and measured 3D reconstruction of the vortex in the spatial and temporal domains, excluding points with a normalized intensity below 0.2 in each frame for better contrast^[651]. Unlike conventional OAM beams with spiraling phases, the generated beam demonstrated here features a double-helical intensity profile that dynamically revolves around the optical axis. This light field belongs to the category of “light springs,” a characteristic result of the STOV correlation. The consistency between the experimental and simulation results highlights the mutual coherence of the soliton microcomb generated in this ${\mathrm{Si}}_3{\mathrm{N}}_4$ OAM comb device.

Fig. 30

Integrated spatiotemporal optical vortex (STOV) generation^[650,651]. (a) Schematic of OAM comb for generating spatiotemporal optical pulses with varying OAMs. Each frequency (left) corresponds to the different OAM mode (right). (b) SEM images of the fabricated AlGaAsOI device. (c) Measured spectra of the microcombs in soliton states with a wavelength spacing of 500 GHz. (d) Simulated and (e) measured results of AlGaAsOI OAM comb including the space-time intensity profile of the targeted self-torque pulses and the intensity and phase distribution of transverse cross sections^[650]. (f) Schematic of ${\mathrm{Si}}_3{\mathrm{N}}_4$ OAM comb. (g) SEM images of a waveguide-coupled microresonator with angular gratings. (h) Measured optical spectra of the single-soliton ${\mathrm{Si}}_3{\mathrm{N}}_4$ OAM microcomb. (i) Simulated and (j) measured reconstructed evolution of the beam profile^[651].

2.3.8.

Integrated knotted and linked beam generation

The theory of knots is a branch of topology that is a closed line of space in math. The simplest knot is an unknotted loop. Recently, a special light field with a knot was observed and drew the attention of researchers. A metasurface is a typical strategy for the generation of knotted optical vortex lines due to its unique and powerful ability to tailor light. Based on the PB phase, a reflective-type hologram metasurface is presented to efficiently produce the broadband optical vortex knots, as illustrated in Fig. 31(a). Figure 31(b) shows the experimentally obtained Trefoil knots and Hopf links at the wavelengths of 700, 800, and 900 nm^[255]. One can see that although the size and shape of optical knots vary at different wavelengths, Trefoil knots and Hopf links are always produced. The obtained optical knots are six orders of magnitude smaller than that generated by an SLM. Relying on the combination of the PB phase and propagation phase, an all-dielectric metasurface generates two ultra-small-sized switchable optical knots with different topological configurations by changing the polarization of incident light, as shown in Fig. 31(c). Figures 31(d) and 31(e) show the simulated and experimentally measured results for the Trefoil knots and Hopf links^[256]. When the incident light is right-handed circular polarization, the output optical knot of the metasurface is a Trefoil knot. When the incident light is left-handed circular polarization, the output optical knot of the metasurface is a Hopf link.

Fig. 31

Integrated knotted and linked beam generation^[255,256]. (a) Schematic of metasurface hologram for generating the optical knots. (b) Experimentally obtained Trefoil knots and Hopf links at the wavelengths of 700, 800, and 900 nm^[255]. (c) Schematic of all-dielectric metasurface hologram for generating switchable optical knots. (d) Simulated results for generating the Hopf links and Trefoil knots, including amplitude and phase distributions at the beam waist plane, phase-only holograms, propagation phase pattern, and orientation angle pattern. (e) Experimentally obtained Trefoil knots and Hopf links. The insets are the top view of the topological structures^[256].

2.3.9.

Integrated in-plane waveguide mode generation

The in-plane waveguide mode is a light beam that is generated and propagates in the integrated photonic waveguides. With the rapid development of integrated photonics, there are many photonic platforms of various materials, including silicon photonics, lithium niobate films, silicon nitride film, silicon carbide photonics, etc. Silicon photonics is an attractive photonic integration platform to enable on-chip spatial mode manipulation due to its high-contrast index, high-density integration, low power consumption, and CMOS compatibility. The generation techniques of in-plane waveguide mode mainly include phase matching, metamaterial, beam shape, and coherent scattering.

As shown in Fig. 32(a), asymmetric directional couplers (ADCs), consisting of a bus waveguide and a narrow waveguide, are the typical structure based on the principle of phase matching^[497]. The ADC structure can convert the fundamental mode of the narrow waveguide to the high-order mode of the bus waveguide when their refractive indices are matched. Although the ADC is a very simple structure to obtain the high-order mode, it is difficult to satisfy the phase matching condition in a broadband wavelength range, due to the difference in dispersion slope between the fundamental mode and high-order mode. Metamaterial has been introduced into the silicon platform as the high-order mode generator, which is particularly attractive in two aspects. One of the advantages is shrinking the footprint of the device. The other one is that the metamaterial-based structure facilitates the generation of a very high-order mode, as shown in Fig. 32(b)^[652]. The beam shaping method consists of three stages, i.e., power splitting, controllable phase shifting, and mode combining, as shown in Figs. 32(c)^[653] and 32(d)^[654]. The mode splitting and mode combining are usually achieved through symmetric Y branches. The relative $\pi$ phase difference can be introduced by thermo-optic controlling, electro-optic controlling, and optical path difference between adjacent branches. It is a relatively complex situation. For the coherent scattering method, the inverse design method enables efficient mode conversion in an ultra-compact size, as shown in Figs. 32(e)^[655] and 32(f)^[656]. Nonetheless, due to the small feature size, the resulting irregular nanostructures inevitably require high manufacturing precision.

Fig. 32

Integrated in-plane waveguide mode generation^{[497,652–656]}. (a) Asymmetric directional couplers based on the phase matching for generating in-plane waveguide mode^[497]. (b) Metamaterial-based structure for generating high-order in-plane waveguide mode^[652]. (c) Beam shaping structure composed of a two-port Y branch and $\pi$ phase difference^[653]. (d) Beam shaping structure composed of a multiport Y branch and parallel $\pi$ phase difference^[654]. (e) Compact tapered waveguide^[655] and (f) photonic crystal waveguide^[656] based on the coherent scattering method.

2.3.10.

Integrated reconfigurable structured light generation

Although various integrated devices have realized the generation of diverse structured light beams with favorable performance, once integrated optical devices are designed and fabricated, their optical functions are usually fixed, which makes difficult to deal with application scenarios requiring flexibility such as beam scanning and zoom lenses. Reconfigurable structured light with active adjustment ability is proposed to improve the practical value of structured light and meet more complex application scenarios. The use of phase change materials such as ${\mathrm{Ge}}_2{\mathrm{Se}}_2{\mathrm{Te}}_5$ (GST) is considered to be a promising option due to its non-volatility property and strong refractive index modulation. As shown in Fig. 33(a), a resonator metasurface based on the GST materials is present to produce the reconfigurable OAM mode. As shown in Fig. 33(b), when the state of GST material is amorphous GST (aGST) [crystalline GST (cGST)], the phase profile of the generated OAM demonstrates the topological charge of $-1(+1)$^[657]. A compact SiN waveguide based on a phase-gradient metasurface replaces noble metals with phase change materials to produce the in-plane waveguide mode, as shown in Figs. 33(c) and 33(d). Figure 33(e) plots the simulation FDTD results of the SiN waveguide with a phase-gradient metasurface^[658]. When the state of GST material is cGST, the output mode of the SiN waveguide is ${\mathrm{TM}}_1$ mode. When the state of GST material is aGST, the output mode of the SiN waveguide is ${\mathrm{TM}}_0$ mode. This device provides an efficient approach for producing reconfigurable in-plane waveguide beams and may be applied to large-scale photonic neural networks.

Fig. 33

Integrated reconfigurable structured light generation by phase change materials^[657,658]. (a) Schematic of resonator metasurface for generating reconfigurable OAM mode. (b) Measured results of resonator metasurface, including the normalized intensity distribution and phase profiles, when the GST material works on the states of amorphous, crystalline, and reamorphization^[657]. (c) Schematic and (d) SEM image of SiN waveguide with phase-gradient metasurface for generating reconfigurable in-plane waveguide mode. (e) Simulation results of SiN waveguide with phase-gradient metasurface when the GST material works on the states of crystalline and amorphous^[658].

In optical systems, BIC occurs through interference between local resonance and radiation modes and is observed in the form of quasi-BIC in many systems. In addition to ultra-high-Q-factor and low-threshold lasers, it is also predicted that BIC modes can exhibit vortex behavior with different topological charges. The laser emission at the symmetry-protected BIC can be fully optically controlled in a perovskite metasurface system, as shown in Fig. 34(a). Figure 34(b) shows the SEM image of a perovskite metasurface. The perovskite metasurface is pumped with a circular laser beam to protect symmetry, resulting in a doughnut-shaped beam, as shown in Fig. 34(c). Once the pump area shifts from a circle to an ellipse, the symmetry protection will break and two linear diffraction beams will be generated, as shown in Fig. 34(d). A similar symmetry break can also be achieved through a double-beam configuration, as shown in Fig. 34(e). When the nanostructure is only pumped by the first beam, the output is a uniform doughnut. Once the second and first beams overlap in time, the optical symmetry will be broken. The switching time from an eddy current laser to a conventional linearly polarized laser is only $\sim 1.5\mathrm{ps}$, as shown in Fig. 34(f). By changing the asymmetric pump beam to a circular beam, two linearly polarized beams can also be switched back to the vortex laser, with a similar transition time of $\sim 1.5\mathrm{ps}$, as shown in Fig. 34(g). To demonstrate the high-speed repeatability of the modified device, Fig. 34(h) shows that the doughnut-lobes-doughnut state can be combined in a single process, indicating that the transition time is not limited^[659].

Fig. 34

Integrated reconfigurable structured light generation with ultrafast control^[659]. (a) Schematic of microlaser for reconfigurable generation between the LP mode and OAM mode. (b) SEM image of perovskite metasurface. (c)–(e) Schematics of the experiments and measured far-field intensity profiles when changing the pumping laser beam of the perovskite metasurface. (c) Pumped with a circular laser beam. (d) The pumping region is transferred from a circle to an ellipse. (e) Pumped with two overlapped circular laser beams. (f) Transition process from OAM mode to LP mode. (g) Transition process from LP mode to OAM mode. (g) Transition process from OAM mode to LP mode, then from OAM mode to LP mode^[659].

As a short summary, Table 1 intuitively lists the major parameters and performance of the state-of-the-art integrated structured light generation and gives a detailed comparison^{[74,255,256,385,386,464,466,467,469–475,481,496,497,550–553,555,556,579–598,610–612,615–617,622–625,627–660]}. The compared parameters and performance include the type of structured light, number of modes, generation method, material, size, working wavelength, etc.

Table 1

Parameters and Performance of State-of-the-Art Integrated Structured Light Generation