The adjoint method is an efficient technique for the topology optimization of complex nanophotonic systems, including nanostructures, metasurfaces and integrated optical circuits. While such method has been traditionally used in the frequency domain, its extension to the time domain opens new opportunities for wideband optimization of dispersive materials for applications ranging from broadband absorbers to enhanced quantum emitters in dispersive environments. We propose a topology optimization technique for the inverse design of linear optical materials with arbitrary dispersion and anisotropy. We introduce a general adjoint scheme in the time-domain based on the complex-conjugate pole-residue pair (CCPR) model. This approach has the advantage of treating dispersive media and broadband response naturally in a single simulation run. We implement this framework within the finite-difference time-domain (FDTD) method and investigate the method for optimizing metallic and dielectric nanoantennas over the optical spectral range of 350 to 1000nm. The combination of the method with parallel computing enables the large-scale inverse design of nanostructures in 3D with extreme field confinement. Nanostructures found via inverse design and featuring the intriguing anapole effect are also discussed. This effect enables nanostructures that show field enhancement, negligible scattering, and low losses. The possibility of reducing losses in plasmonic nanostructures via inverse design is an interesting possibility offered by the method and may open new avenues towards the realization of transparent plasmonic metamaterials for applications in linear and nonlinear nanophotonics.
We investigate the emergence and development of collective resonant effects in finite-size arrays of silicon nanoparticles. We focus our research on two different scenarios of collective resonances: the lattice resonant Kerker effect and the quasi-bound state in the continuum. In the coupled dipole approximation, the implementation of such resonances is explored depending on the number of particles in the arrays and the conditions of external excitation. The results of the work are important for the prediction and experimental observation of collective resonances in real finite-size structures.
Multipole mechanisms of light propagation control and trapping effect in structures composed of dielectric nanoparticle supporting the electric and magnetic optical resonances are discussed. First, a concept of multipole coupling is introduced for explanation what type multipoles and why can be coupled in periodic nanoparticle structures (metasurfaces). Then the implementation of such coupling for light trapping, which does not require any special irradiation conditions for the incident light or geometrical distortion of the symmetry of the periodic structures, is presented. Realization of accidental quasi bound states in the continuum (BICs) associated with multipole coupling is also discussed. Next, magnetoelectric multipole coupling effects in metasurfaces and separate structures composed of particles with bianisotropic electromagnetic response are demonstrated. The presented mechanisms are of a general nature and can be implemented in many structures, which opens up new application prospects.
Gradient-based topology optimization via the adjoint method has been successfully used in nanophotonics to uncover shapes with superior performances compared to what would be possible with traditional design methods. Here, we have used this technique to optimize a dielectric object to engineer its induced multipole moments. As an example, we show the method's application to realize the first Kerker effect in a silicon nanoparticle. The final result shows a rather complex shape with highly suppressed backscattering due to the excitation of in-phase electric and magnetic dipoles with the same amplitude. This promising approach can pave the way for the inverse design of photonic structures based on a set of desired multipole moments, which can exhibit a variety of complex photonic phenomena.
We study the optical properties of hybrid silicon-gold nanocylinders and show that the internal material inhomogeneity can lead to their strong bianisotropic response associated with the distortion of their symmetric properties. The spectral response of the metasurfaces composed of such particles can have narrow resonance features associated with resonant multipole coupling and excitation of quasi-BIC states. We demonstrate that the metasurface resonant features are accompanied by the field enhancement in the metasurface plane and strongly depend on the polarization of the incident waves. The latter circumstance makes it possible to implement switching control of the resonant response of metasurfaces by changing the polarization of the incident wave.
We reveal the peculiarities of the trapped mode manifestation in metasurfaces composed of an array of MoS2 disk-shaped resonators. The corresponding resonance arises as a result of the excitation of the electric octupole moment existing in each meta-atom of the metasurface and multipole coupling effects in the array. In particular, we show that the effect appears due to a lattice-induced coupling between the electric octupole and electric dipole moments in the metasurface. The coupling effect between the resonant quasi-trapped octupole mode and the suppressed electric dipole results in the appearance of the narrow-band transparency conditions in the metasurface spectra with a simultaneous storing of electromagnetic energy inside the resonators. The discussed approach is quite general and can be implemented in metasurfaces supporting Mie-type modes in meta-atoms made of different materials.
Dielectric nanophotonics became a hot topic during the last decade. Particularly, a lot of relevant studies were devoted to metasurfaces and their optical properties. Here we propose and numerically study the quadrumerbased silicon metasurface supporting magnetic octupole response. Specific meta-atoms allow to excite magnetic octupole moment in optical range without going beyond the diffraction limit. Comparing to a metasurface based on solid blocks of similar size, the quadrumer-based metasurface feature significant absorption enchantment and strong change of a reflection spectrum. Obtained results can be exploited in development of novel sensors, optical elements and energy harvesting devices.
Light scattering by all-dielectric nanoparticles attract significant attention of photonics community. Single nanoparticles can be used both as nanoantennas and as building blocks to construct 2D and 3D meta-structures. In this work we study scattering effect when silicon nanoparticles are embedded in different media. To analyze the evolution of multipole moments and their contributions to the scattering cross-sections of the nanoparticles in media, we use semi-analytical multipole decomposition approach. Explicitly, we investigate the behavior of electric and magnetic multipoles, up to third order, while dielectric nanoparticle made of silicon is embedded in a media. We found that electric and magnetic multipoles experience different red shift as refractive index increases. Due to this behavior separated high-order multipole resonances overlap with each other; thereby, scattering cross section peaks, which could be observed when a particles are in air, merge to the joint scattering cross section peaks. Such resonances overlap also affect both far-field radiation diagrams and field distribution inside the nanoparticle. Importantly, we noticed that when index of a surrounding media increases, the cubical nanoparticles provide spectral broadening of forward scattering effect.
Our results provide fundamental information for understanding the scattering effect in all-dielectric nanoantennas or metasurfaces embedded in different dielectric media and operating in wide spectral range. For practical utilization, explored here dielectric nanoparticles could be used in broad range of applications such as in-vitro and in-vivo biomedical devices for sensing and drug delivering, sub-wavelength nano-amplifiers, and many other emerging applications.
The effective multipole decomposition approach is applied to study the optical features of the silicon metasurface in the near-infrared. The spectral regions of perfect transmission and reflection have been analyzed using the Cartesian multipole decomposition. It is shown that transmission peaks appear due to the mutual interaction of multipole moments up to the third order, while reflection peaks are due to the dominant contribution of one of the multipole moments. The results of this work can be broadly applied to design novel metasurfaces, sensors, and optical filters.
In this work we theoretically study spectral multipole resonances of parallelepiped- and pyramid- silicon nanoparticles excited by linearly polarized light waves. We apply the numerical finite element method to calculate the scattering cross-sections as a function of the nanoparticles geometrical parameters. We use the multipole decom- position approach to explore optical resonances in silicon nanoparticles and the influence of second and third order multipoles to scattering diagrams. In contradistinction to our previous investigations, now we explore effects in near-IR spectral range. Apart from basic study we also obtained non-symmetrical combination of multipole contributions due to illumination from top and bottom sides of pyramids. Our work provides important information about the role of high-order multipoles in the light scattering by non-spherical and non-symmetrical nanoparticles. Our results can be applied, for example, for development of metasurfaces and metamaterials in near-IR spectral range.
A theoretical approach, allowing analyzing the role of multipole modes in the extinction and scattering spectra of
arbitrary shaped nanoparticles, is developed in the framework of the discrete dipole approximation. The proposed
method can be used to control separately the positions of different multipole resonances as a function of nanoparticle
sizes, shapes and irradiation conditions. The main attention is given to the first multipole modes including magnetic
dipole and electric quadrupole moments. The magnetic quadrupole and electric octupole modes can also be involved in
the consideration. The method is applied to nonspherical Si nanoparticles with multipole responses in the visible optical
range, allowing a decomposition of single extinction (scattering) peaks into their constituting multipole contributions.
The unique property of Si nanoparticles to support magnetic optical response opens new ways for the construction of
novel nanooptical elements and can be particularly important for solving the problem of metamaterials with magnetic
properties in the visible spectral range.
The optical properties of regular nanoparticle arrays consisting of spherical semiconductor and noble metal nanoparticles
are providing interesting aspects for the development of novel and powerful sensor concepts. In this contribution, we
demonstrate femtosecond laser-induced transfer of metallic and semiconductor thin films as a unique tool for realizing
controllable structures of any desired configuration of exactly spherical nanoparticles, having diameters between 40 nm
and 1500 nm. The optical properties of nanoparticles and nanoparticle arrays fabricated by this new approach are
investigated spectroscopically and by scattering of surface plasmon-polaritons (SPPs). SPP-scattering constitutes a novel
method to obtain insight into the contribution of different multipole moments to the scattering properties of the particles.
Furthermore, the particles can be combined with 3D photonic structures fabricated using two-photon polymerization,
providing new approaches to the development of nanophotonic devices and 3D metamaterials. Here, we demonstrate an
optical sensor with a sensitivity of 365 nm/RIU and a figure of merit of 21.5 in the visible spectral range.
We study both, theoretically and experimentally the light-to-surface plasmon polariton (SPP) and SPP-to-SPP scattering
using the Green's function method and leakage radiation microscopy. The scattering structures are fabricated by
nonlinear lithography and laser induced transfer (LIT). SPPs are exited on dot- and ridge-like surface structures. We
demonstrate symmetric or asymmetric excitation of SPP beams and show that the SPP excitation efficiency strongly
depends on the component of the excitation field perpendicular to the metal surface. By adjusting the angle of the
incident beam to the maximum of the total electric field component perpendicular to the metal surface, the scattering
efficiency of light on a single nanoparticle into SPPs can be increased by a factor of 200. The SPP beams allow studying
scattering properties of perfectly spherical gold particles with diameters between 200 nm and 1600 nm fabricated by LIT
of liquid gold droplets. For these diameters, the description of scattering of electromagnetic waves with optical
frequencies has to take into account higher-order terms. Leakage radiation microscopy provides the unique possibility to
observe scattering features attributed to magnetic dipole and electric quadrupole contributions in the 2D scattering
patterns of SPPs. The results are supported by numerical modelling using the Green's tensor approach.
We study the guiding properties of laser-written dielectric-loaded surface plasmon polariton waveguides
(DLSPPWs). The guiding structures such as straight waveguides, S-bends, Y-splitter, resonant filters, and Mach-
Zehnder interferometers are realized by two-photon induced polymerization of commercial photolithographic
resists. The height of the components can be adjusted by spin-coating of the material. Minimum widths of 400
nm of the DLSPPWs fabricated directly on thin metal films can be achieved. Replica molding of polymer
surface structures allows a further reduction of the DLSPPW width down to 200 nm. The DLSPPWs are
characterized by leakage radiation microscopy in the visible and near infrared spectral region. We demonstrate
the possibility to selectively excite different modes in the waveguides. Fourier-plane imaging allows a direct
observation of the excited modes of the DLSPPWs. The simultaneous excitation of fundamental and higherorder
modes results in a mode-beating, providing the possibility to control the splitting ratio of guided SPPs in
Y-splitters. The experimental results are supported by theoretical modelling using the finite-difference time
domain method.
Excitation, focusing, and directing of surface plasmon polaritons (SPPs) with curved chains of bumps located
on a metal surface is investigated both experimentally and theoretically. We demonstrate that, by using a
relatively narrow laser beam (at normal incidence) interacting only with a portion of a curved stripe or chain
of nanoparticles, one can excite an SPP beam whose divergence and propagation direction are dictated by the
incident light spot size and its position along the structure. It is also found that the SPP focusing regime is
strongly influenced by the chain inter-particle distance. Extensive numerical simulations of the configuration
investigated experimentally are carried out for a wide set of system parameters by making use of the Green's
tensor formalism and dipole approximation. Comparison of numerical results with experimental data shows
good agreement with respect to the observed features in SPP focusing and directing, providing the guidelines
for a proper choice of the system parameters. It was found that the focusing regime of SPPs is strongly
influenced by the chain inter-bump distance, so that the focusing and directing effects with optimal properties
can be obtained only when the chain inter-bump distance is smaller than the SPP wavelength. Following the
experimental conditions, we have studied the role of the size of light spot exciting SPPs. Spectral dependence
of the focusing waist is also numerically studied for gold surface taking into account the ohmic loss.
Rapid advance of nanostructuring technologies offers new possibilities for flexible and low-cost fabrication of plasmonic
components and devices. In this contribution, we study applications of laser-based nonlinear lithography for the fabrication of dielectric surface-plasmon-polariton (SPP)-structures. These structures can be used for localization, guiding, and manipulation of SPPs on a subwavelength scale. Effective excitation of SPPs on dielectric structures and focusing of the generated SPPs are studied. The characterization of the SPP structures is performed by plasmon leakage radiation microscopy. Laser-based nonlinear lithography,
e.g. two-photon polymerization technique, allows the
fabrication of dielectric waveguides, splitters, and couplers directly on metal surfaces. The fabricated dielectric structures
on metal films are demonstrated to be very efficient for the excitation of SPPs. Using these structures, excitation,
focusing, and guiding will be demonstrated.
The near-field response of optically excited nanoparticle structure buried within thin dielectric layer is theoretically
and numerically studied. Nanostructure is modeled as a finite-size periodic array of dipole-like gold nanoparticles, the
size of the structure is assumed to be much smaller than the wavelength of the external electromagnetic wave. The
layer with the particles is located on a dielectric substrate which is irradiated by an external monochromatic optical
wave under condition of total internal reflection. For the determination of the field in the system we make use of the
Green's function formalism and the dipole approximation. The dyadic Green's function of a three layer system is used
in the unretarded approximation. In order to investigate plasmon resonance response of the nanoparticle structure
we calculated the average dipole moment magnitude of the particles as a function of light wavelength for different
parameters characterizing the layer environment and the structure. It has been found that the dielectric constant
of layer containing the particle structure can strongly effect the resonance shifts in the system. This influence is
depended on the external field polarization and inter-particle distances in the structure.
Renewed and growing interest in the field of surface plasmon polaritons (SPPs) comes from a rapid advance of
nanostructuring technologies. The desired nanostructures are usually fabricated by electron- or ion-beam lithography. An
alternative approach is the application of two-photon polymerization (2PP) or nonlinear lithography. Both these
technologies are based on nonlinear absorption of near-infrared femtosecond laser pulses. With 2PP, the fabrication of
three-dimensional micro-objects and photonic crystals with a resolution down to 100 nm is possible. In this contribution,
we study applications of advanced femtosecond laser technologies for the fabrication of SPP structures. We demonstrate
that resulting structures can be used for excitation, guiding, and manipulation of SPPs on a subwavelength scale.
Characterization of these structures is performed by detection of the plasmon leakage radiation (LR). 2PP allows the
fabrication of dielectric waveguides, splitters, and couplers directly on metal surfaces. The fabricated dielectric structures
are also very efficient for the excitation of SPPs. Using these structures, excitation and focusing of the resulting plasmon
field can be achieved.
KEYWORDS: Particles, Near field scanning optical microscopy, Dielectrics, Nanoparticles, Near field, Near field optics, Nanostructures, Dielectric polarization, Electromagnetism, Optical microscopy
The near-field response of optically excited nanoparticle structure buried within thin dielectric layer is theoretically and numerically studied for the illumination and collection modes of a scanning near-field optical microscopy. As the probe we consider a single dipole-like particle that scans the surface of the sample. Nanostructure is modeled as a finite-size periodic array of dipole-like particles, the size of the structure is assumed to be much smaller than the wavelength of the external electromagnetic wave. The electromagnetic signal in a remote detector is proportional the time-average energy flux of the scattered probe field. For the determination of the field in the system the dyadic Green's function of the one layer system is used in the unretarded approximation. We have found that field
distribution and the magnitude of the field intensity in the system strongly depend on the polarization of the exciting external waves and the inter-particle distances in the nanostructure. The near field distribution in the system under condition of local plasmon resonance, when the polarizability of every particle in the nanostructure was significantly increased, is also considered.
KEYWORDS: Dielectrics, Particles, Near field scanning optical microscopy, Near field, Signal detection, Sensors, Optical microscopy, Interfaces, Image acquisition, Polaritons
A theoretical model of the interaction between finite mesoscopic objects within the layer structure situated on a substrate and the light in the near-field zone is presented. Consideration is based on a set of self-consistent integral equations for the electric field obtained from the Maxwell equations using a Green-function technique. In the work we give special attention to construct in the quasi-electrostatic approximation the dyadic Green's function of the reference system, which includes the substrate and the solid layer embedded in an infinite homogeneous medium. Our approach also allows us to construct the Green's function for two mediums with plane interface. We use unretarded approximation due to the fact that the distances between all points, which are included in the consideration, are assumed to be much smaller than the wavelength of the light in SNOM. On the base of this approach we obtain the analytical expression of the dyadic Green's function in direct space and numerically calculate the distribution of electric field
intensity in the system. We consider two SNOM configurations. We show that the layer structure and substrate may play significant role in image formation. In the work we also discuss the scattering problem of longitudinal surface polaritons in SNOM of the collection configuration.
KEYWORDS: Semiconductors, Near field scanning optical microscopy, Dielectrics, Near field, Nanostructures, Scattering, Near field optics, Reflection, Optical microscopy, Microscopy
The near field response of semiconductor nanostructure is theoretically investigated for the collection mode of scanning near-field optical microscope (SNOM). We calculated the near-field distribution on the observation plane for several physical systems, in which the semiconductor nanostructure is approximated by the right-angled object with dielectric function including the contributions from the lattice and the free charge carriers. Our calculations take into account the nanoscale objects presence on and under the surface with electromagnetic evanescent waves which are induced by plane excitation light under condition of total reflection wave in SNOM. All calculations are carried out by using self-consistent integral equation formalism. This treatment is based on the field- susceptibility Green's function technique applied in real space. As a result we show that the near-field distribution is essentially dependent on the quantity of charge carriers and on its kinetic properties and also on the configuration of the system.
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