Optically controlled dielectric metasurfaces for dynamic dual-mode modulation on terahertz waves

Abstract. Dynamically controlling terahertz (THz) waves with an ultracompact device is highly desired, but previously realized tunable devices are bulky in size and/or exhibit limited light-tuning functionalities. Here, we experimentally demonstrate dynamic modulation on THz waves with a dielectric metasurface in mode-selective or mode-unselective manners through pumping the system at different optical wavelengths. Quasi-normal-mode theory reveals that the physics is governed by the spatial overlap between wave functions of resonant modes and regions inside resonators perturbed by pump laser excitation at different wavelengths. We further design/fabricate a dielectric metasurface and experimentally demonstrate that it can dynamically control the polarization state of incident THz waves, dictated by the strength and wavelength of the pumping light. We finally numerically demonstrate pump wavelength-controlled optical information encryption based on a carefully designed dielectric metasurface. Our studies reveal that pump light wavelength can be a new external knob to dynamically control THz waves, which may inspire many tunable metadevices with diversified functionalities.


Introduction
Dynamic control over terahertz (THz) waves at will with an ultracompact device is important for THz technologies (e.g., biomedical imaging, telecommunications, detection). However, tunable THz devices made of conventional materials are usually of bulky sizes, and limited modulation depths and functionalities, due to weak interactions between naturally existing materials and THz waves.
In this paper, we propose that the wavelength of pumping light can be an additional knob to achieve dynamic dual-mode modulation on THz waves (see Fig. 1). Specifically, we experimentally demonstrate that a predesigned dielectric metasurface can achieve mode-selective or mode-unselective modulations on incident THz waves, as it is excited by ultrashort pulses at two different wavelengths (e.g., 515 or 1030 nm). Analyses based on quasi-normal-mode (QNM) theory reveal that the underlying physics is determined by the spatial overlap between wave functions of resonant modes and regions perturbed by the pump laser excitation at different wavelengths. Inspired by the discovered mechanism, we demonstrate two active metadevices with distinct light-modulation functionalities in experiments and simulations, respectively. The first device can dynamically change the polarization state of incident THz waves dictated by both pump wavelength and pump fluence, whereas the second one can encrypt optical information and only displays the predesigned holographic pattern when excited by a pump beam at the correct wavelength.

Dynamic Dual-mode Modulation: Experiments and Simulations
We start from experimentally demonstrating the dynamic dualmode modulations on THz waves based on an all-dielectric metasurface. As schematically shown in Fig. 2(a), our metasurface consists of 165 μm high silicon pillars with a cross section of 76.5 μm × 206 μm arranged in a square lattice with a periodicity of 275 μm, deposited on a 145 μm thick quartz substrate. Figure 2(b) depicts the scanning electron microscopy (SEM) image of our fabricated sample (see more fabrication details in Section 1 in the Supplementary Material). We employ homemade optical-pump terahertz-probe spectroscopy 49 Fig. 2(c) represent the measured THz transmission-amplitude spectra of our sample, under the pumping of external light at 515 nm with different optical fluence. As we increase the pump light fluence, we find that while the high-frequency resonant mode (labeled as "Mode 2") undergoes a clear blueshift in frequency and a resonant strength diminishment, the low-frequency mode (labeled as "Mode 1") is quite insensitive to the change of optical fluence (see Section 3 in the Supplementary Material for additional measured results under different excitations). Clearly, modeselective dynamic modulation is achieved with the metadevice pumped by external light at 515 nm. In stark contrast, when the metasurface is excited by pump light with λ pump ¼ 1030 nm, the two resonant modes are modulated strongly and simultaneously, manifested by both the resonant-frequency blueshifts and the mode-strength diminishments [see Fig. 2(d)]. In fact, increasing the pump fluence to 40 μJ∕cm 2 can completely "kill" two resonant modes, as shown in the transmission-amplitude spectra and transmission-phase spectra (see Fig. S6 in Section 3 in the Supplementary Material). Obviously, mode-unselective dynamic modulation is achieved with our metadevice as pumped by external light at 1030 nm.
We perform finite-difference time-domain (FDTD) simulations to calculate the transmission spectra of our metasurface under different photoexcitations. Optically pumping silicon at frequencies above its bandgap can induce free carriers in its conduction band, thus modulating the permittivity of silicon. Under different pump fluence, permittivity of silicon can be well described by the Drude model, 51 where ε ð0Þ ¼ 11.9025 denotes the static permittivity of silicon, N 0 ¼ 5 × 10 9 cm −3 is the static carrier density of intrinsic silicon (estimated at temperature 296 K), N e denotes the excited carrier density, which depends on the optical absorbed pumping fluence F through a formula established in a prior work, 52 m eff ¼ 0.16m e is the effective mass of the carrier (m e is the free electron mass 53 ), and γ D ¼ 1 × 10 13 Hz is the damping rate (determined by carrier-phonon collisions at low carrier densities 54 ). We note that the optically excited carriers are only distributed in the region of silicon where pump light can penetrate inside.  The thickness δ of such an "excited" layer is inversely proportional to the absorption coefficient α at different pump wavelengths, which can be retrieved from the refractive index of silicon. 55 Figure 3

Mechanism Analyses
We now reveal the underlying physics with the help of QNM theory. 56 Quasi-normal modes are resonant modes supported by an open system, and their eigen frequencies are generally complex values with imaginary parts characterizing the damping rates of the modes due to absorption and/or radiation. We first employ the QNM theory to compute the complex eigen frequencies of two resonant modes supported by our dielectric metasurface under different photoexcitation conditions (see Section 5 in the Supplementary Material for details of our QNM calculations). Without external pumping, we get fω  Now that the QNM-computed results have captured all salient features of the simulated and measured results well, we explore the underlying physics based on the QNM theory. Under weak photoexcitation, the shift of complex eigen frequency due to photoexcitation can be calculated by the standard perturbation theory within the QNM framework, 57,58 Equation (2) provides an analytical platform to understand the intrinsic physics. As shown in the insets of Fig. 3(a), the perturbed region is a thin layer on top of the pillar at pump wavelength 515 nm, but becomes the whole pillar at 1030 nm. Meanwhile, eigen wave functions of the two modes also exhibit distinct spatial distributions. As shown in Fig. 3(b), while Mode 1 is a dipole resonant mode with E-field mainly distributing inside the central region of the resonator (with slight asymmetry induced by the substrate), Mode 2 is a quadrupole mode with the E-field mainly localized on the resonator surface. The distinct features of the perturbed regions and eigen wave functions can help us understand the physics underlying the discovered phenomena. Since pump light at 515 nm can only perturb the surface region of our silicon pillar, we immediately understand that only Mode 2 can be strongly modulated by external pumping, since this mode has a strong E-field on the pillar surface. In contrast, Mode 1 is hardly affected by external pumping, since it does not have a strong E-field on the surface. Meanwhile, in the case of 1030 nm pumping, the perturbed region covers the entire silicon pillar, which explains why both modes are simultaneously modulated by external pumping.
The analytical formula [Eq. (2)] can also help us understand an intriguing effect displayed in Figs. 2(c)-2(f), i.e., the two ReðΔω n Þ ∼ F relations exhibit different variation slopes as compared to their corresponding −ImðΔω n Þ ∼ F curves in the case of λ pump ¼ 1030 nm. The underlying physics is that, in the case of n ð r ⇀ Þd r ⇀ of two resonant modes exhibit distinct phases so that their contributions to ReðΔω n Þ and ImðΔω n Þ can be quite different, although both ReðΔω n Þ and ImðΔω n Þ are strongly modulated by external pumping. Detailed discussions can be found in Section 5 in the Supplementary Material. Before ending this section, it is worth emphasizing that our dual-mode modulation originates from the spatial permittivity modification induced by different optical pumping with different wavelengths, which is totally different from recent works of pump light wavelength-dependent tunable metasurfaces based on a wavelength-dependent absorption feature 59 or multitype materials-induced different time responses. 46 In addition, our proposed modulation scheme does not depend on the linewidth or the spectral position of resonant modes, and it is applicable to other frequency regimes with appropriate material systems. For example, in mid-infrared or near-infrared regimes, one can use the GaAs 60 or GaN 61 to construct dielectric metasurfaces to achieve similar device functionalities, respectively (see Section 6 in the Supplementary Material for appropriate materials and their working frequency regime).

Applications
Having revealed the underlying physics of the dynamic dualmode modulation, we now employ the discovered strategy to realize two metadevices with different functionalities in experiments and numerical calculations, respectively.

Dynamic dual-mode metapolarizer
We first experimentally realize a tunable metadevice that can dynamically manipulate the polarization of THz wave depending on external photoexcitation. The designed metadevice is of the same configuration as that shown in Fig. 2(a), but with different geometric parameters: W ¼ 74.5, L ¼ 168, H d ¼ 175, H q ¼ 170, P ¼ 285, all in the units of micrometers. Due to the rectangular shape of the meta-atom, the designed metasurface exhibits distinct transmission spectrum for xand y-polarized incident THz waves, and such anisotropic responses can be dynamically modulated by external pumping. As a result, the designed metadevice can dynamically control the polarization state of the impinging THz wave, dictated by the wavelength and fluence of the pump light [ Fig. 4(a)].
We fabricate out a sample according to the design [see inset of Fig. 4 Fig. 4(d) depict the measured spectra of transmission amplitude jt xx j and jt yy j, respectively, and blue diamonds represent the measured spectrum of phase difference ΔΦ ¼ Φ xx − Φ yy , for our metadevice without any photoexcitation (see Section 7 in the Supplementary Material for more experimental and simulated results). We find two clear resonant dips at 0.704 and 0.738 THz in the jt xx j spectrum, which exhibit similar field patterns to the two modes studied in last section (see Section 8 in the Supplementary Material for discussions at a frequency near Mode 2). Meanwhile, a broadband dip is found in the jt yy j spectrum around 0.66 THz, which contains two high-order modes coupled together (see Section 9 in the Supplementary Material for more discussions). Choosing the working frequency as 0.695 THz [denoted by a gray dashed line in Fig. 4(d)], we find jt xx j ¼ jt yy j ¼ 0.25 and ΔΦ ¼ π, indicating that the metasurface behaves as a half wave plate at this frequency. We retrieve the polarization pattern of the THz wave transmitted through our device under the illumination of normally left circularly polarized (LCP) beam at 0.695 THz and depict the obtained pattern using the black star in Fig. 4(c) labeled as "W/O pump." The polarization pattern is nearly a right circularly polarized (RCP) state with ellipticity angle of 43 deg and azimuthal angle of −44 deg, as expected.

(a) for its top-view SEM picture], and then experimentally characterize its transmission properties under different photoexcitation. Orange open stars and red open circles in
We now study how the transmission characteristics (and thus the polarization manipulation capability) of our metadevice vary under different photoexcitations. Clearly, transmission coefficient t xx (with both amplitude and phase) at the working frequency is mainly affected by the x-polarized mode at 0.704 THz. As discussed in the last section, such a mode is a dipole resonant mode, which is drastically modulated by external pumping at 1030 nm but is hardly affected by external pumping at 515 nm. It is thus not surprising to see that our measured jt xx j at 0.695 THz increases substantially as the pump fluence F varies at 1030 nm [orange star in Fig. 4(f)], but remains relatively stable as the pump wavelength changes to 515 nm [see orange open circles in Fig. 4(e)]. Meanwhile, we find t yy at 0.695 THz is influenced by two high-order y-polarized modes at frequencies below 0.695 THz (see Section 9 in the Supplementary Material for more discussions), and thus the modulation of jt yy j is quite moderate and does not exhibit obvious difference for two pump light wavelengths [see red open circles in Figs. 4(e) and 4(f)]. Finally, the measured cross-polarization phase difference ΔΦ decreases as F increases in both cases, since pumping the system essentially diminishes all resonances, and such a trend is more dramatic in the case of 1030-nm light pumping [see blue diamonds in Fig. 4(f)].
We can easily retrieve the polarization-control functionality of our device at 0.695 THz through the measured pump fluencedependent transmission characteristics. Under the pumping at 515 nm, as F increases, we find that ΔΦ gradually decreases from π to π∕2 with jt xx j ≈ jt yy j kept approximately, indicating that our device changes its functionality from a half-wave plate to a quarter-wave plate. Such a trend has been well confirmed by  pump wavelengths [see Fig. 4(b)]. From Figs. 4(b) and 4(c), we find that both increasing the pump fluence and changing the pump wavelength can modulate the polarization state of the transmitted THz wave dramatically, offering our metadevice expanded polarization-control capabilities. Here, we note that the experimentally achieved dynamic range of polarization modulation is mainly determined by the limited tunable range on transmission amplitude and phase for the x-polarized THz beam. Actually, to expand the dual-mode polarization controllability, one can use the reflection-type metasurfaces, which can provide larger tuning range in terms of reflection amplitude and phase, as shown in Section 10 in the Supplementary Material.

Optical information encryption
The newly discovered strategy can also enable the application for optical information encryption. Figure 5(a) schematically depicts the proposed metadevice. Different from the metasurfaces discussed in previous sections, here we add a gold (Au) substrate to the bottom of our structure serving as a reflection mirror. In the spirit of phase hologram, our metasurface consists of two basic meta-atoms arranged in predesigned sequence [see Fig. 5(a)]. These two meta-atoms (labeled as "A" and "B," respectively) exhibit distinct geometrical parameters and thus different optical responses. As shown in Fig. 5(b), as illuminated by normally incident x-polarized THz wave, two different meta-atoms exhibit similar reflection amplitudes (jr A j ¼ 0.90, jr B j ¼ 0.87) and phases (Φ A ¼ 0, Φ B ¼ 0) at the working frequency 0.63 THz (see dashed line) without photoexcitation. As pumped by external light, resonant modes related to different meta-atoms exhibit distinct pump fluence dependence dictated by the mode wave functions and the pump light wavelength. In particular, in the case of 515-nm light pumping, Φ A remains nearly unchanged, whereas Φ B changes dramatically as F increases, while both Φ A and Φ B vary simultaneously against F as the pump wavelength is switched to 1030 nm. Thus, at the working frequency, the reflection phase difference between the two meta-atoms Φ A − Φ B reaches about −2∕3π as the meta-atoms are pumped by external light at 515 nm with F ¼ 50 μJ∕cm 2 , whereas Φ A − Φ B is nearly 0 as the pump light wavelength is switched to 1030 nm, being the same as the unpumped case. We can thus employ two meta-atoms as building blocks to construct a metahologram based on their phase responses at λ pump ¼ 515 nm and F ¼ 50 μJ∕cm 2 . Intriguingly, under x-polarized THz illumination at 0.63 THz, while the designed metadevice can exhibit the predesigned hologram image as pumped by 515-nm light with F ¼ 50 μJ∕cm 2 , we expect that the image must be destroyed as the pump wavelength changes to 1030 nm or the pump light is turned off. We verify the above predictions based on numerical calculations. Based on the phase responses of two meta-atoms at λ pump ¼ 515 nm and F ¼ 50 μJ∕cm 2 , we design a metasurface that can exhibit the image of "FD" as shone by the x-polarized THz wave at 0.63 THz. Retrieving the desired phase distribution of the metasurface based on the modified Gerchberg-Saxton algorithm, we then construct the device using 80 × 80 metaatoms according to the retrieved phase distribution. We perform analytical calculations based on the dyadic Green's function method to compute the output holographic images detected on a plane at z ¼ 25λ above the metasurface, as it is shone by the

Conclusions and Discussions
In conclusion, we propose a new strategy to achieve dynamic dual-mode light modulation, and experimentally verify the concept in the THz regime. Specifically, we demonstrate that a specifically designed dielectric metasurface can realize modeselective or mode-unselective dynamic modulation on THz waves, as pumped by external light at different wavelengths. QNM calculations reveal that the physics is governed by distinct overlapping between resonant wave functions and perturbed regions in resonators under different pumping conditions. Recently, Cong et al. 62 introduced the temporal loss boundary to temporally engineer the photonic cavity. We expect that the combination of spatial overlap decided by wave function and temporal overlap determined by the Q factor of the resonant mode may lead to a fancier dynamic spatiotemporal modulation. Two metadevices are demonstrated experimentally and numerically, respectively, with the first one being a metapolarizer exhibiting expanded polarization-control capabilities dictated by the strength and wavelength of pump light, and the second one displaying the encrypted holography image as pumped by light with correct wavelength and fluence. Our studies reveal that pump light wavelength can be another degree of freedom to tune the functionality of a dielectric metadevice, which significantly expand our capabilities to dynamically control light waves. The discovered mechanism can inspire many new tunable devices with distinct light-modulation functionalities, being highly desired for applications such as sensing, security, and next-generation wireless communications.