Reconfigurable terahertz grating with enhanced transmission of TE polarized light

Terahertz (THz) radiation occupies the region between infrared and microwave radiation in the electromagnetic spectrum. Owing to its appealing properties (low photon energy, high transparency, and high spectral resolution), THz technology has been applied in various fields, such as security inspection, disease diagnosis, and communications.^1–4 In recent years, THz sources and detectors have been a constant focus of research, and great progress has been made. However, there are not enough suitable modulators in the THz waveband, and the existing devices are bulky, which may hinder the development of THz technology. With the development of micro/nano-fabrication technology, some artificial structures are designed to modulate the THz spectrum.^5–7 

Since extraordinary optical transmission (EOT) through an array of subwavelength holes was discovered by Ebbesen et al.,⁸ many researchers have studied the transmittance properties of wire gratings. The EOT of transverse magnetic (TM) polarized waves (electric field vector perpendicular to the wire direction) was discovered for metallic wire gratings with very narrow slits, as a result of the excitation of surface plasmon polaritons (SPPs).^9,10 However, EOT may also occur for the transverse electric (TE) polarization (electric field vector parallel to the slit direction), even though the surface excitations are not allowed.¹¹ This kind of resonance behaves differently from the TM polarization resonances. Researchers realized such plasmonless EOT by combining a subwavelength slit or hole arrays with a thin dielectric slab. It is commonly believed that the waveguide mode and other residual field in the dielectric slab contribute to the TE-polarized EOT.^11–14 Also, the EOT of TE-polarized waves can be realized without the extra dielectric slab when the incident wavelength was approximately equal to the grating period.^15–17 Thus, based on the EOT, the array of the subwavelength metallic patterns can be used to realize the filter or sensor of an electromagnetic wave.

Recently, various functional THz filters^5,18,19 and absorbers^20,21 have been realized by the metallic aperture arrays. However, most of the THz spectrum modulators are not tunable; that is to say, the modulation function is fixed when the devices are processed. Furthermore, some active THz devices^22–26 have also been proposed to modulate THz waves in real time. These active devices consist of metallic structures and semiconductors and are triggered by means of electricity, light, or temperature. However, they are still unable to eliminate the processing steps. On the other hand, the frequency modulation of these dynamically tunable devices is limited to a small range around the resonance frequency due to their fixed structural geometry. Recently, some photoinduced THz devices have been proposed to overcome these limitations. These all-optical devices, which offer better flexibility than standard lithography, rely on grating patterns,^27–29 chiral patterns,³⁰ and subwavelength antennas³¹ to realize the modulation of the THz spectrum. In particular, THz polarization modulation²⁸ and enhanced transmission of TM-polarized waves²⁷ have been realized by projecting a grating pattern with small period onto a Si or GaAs substrate. However, for the all-optical gratings generated by pumping the Si or GaAs substrate, the diffusion of the photocarriers in the semiconductor has not been discussed. Moreover, none of the previous works has shown the TE-polarized EOT realized by an all-optical device in the THz region.

In this paper, we demonstrate that an optically reconfigurable grating with a 10 μm thickness allows for EOT of TE-polarized waves. Considering the diffusion of the photocarriers, we also proposed a flattened Gaussian model to describe the distribution of the photoexcited free carriers in the Si wafer. In the THz waveband, the transmission properties of such a photoinduced grating generated by a control beam with spatially modulated intensity were investigated both in the experiment and simulations. Our results are supported by simulations performed using the finite-difference time-domain (FDTD) method.

A terahertz time-domain spectroscopy system (THZ-TDS) with a projection control part was used to measure the THz transmission of the photoinduced grating, as shown in Fig. 1(a). The source of the system was a Ti:sapphire regenerative amplifier with an 800 nm center wavelength, 1 kHz repetition rate, 100 fs ultrashort pulse, and 900 mW average power. The incident wave was split into three beams, which were used as the pump beam (490 mW), the probe beam (10 mW), and the control beam (400 mW). Based on optical rectification, the y-polarized THz pulses with a frequency range from 0.2 to 2.0 THz are generated when the pump beam passes through a $⟨110⟩$ ZnTe crystal. The sample used was a Si $⟨100⟩$ wafer with a thickness of 10 μm and resistivity of approximately 1–20 Ω cm. To actively modulate the THz beam, the control beam was structured into spatial intensity patterns by a digital micromirror device (DMD), and the patterns were projected onto the Si wafer by a lens with a magnification of 1.0.

As shown in the inset of Fig. 1(a), a grating with illuminated and dark regions was projected onto the Si wafer. In the illuminated region, carriers are created by photoexcitation. Owing to the fact that the skin depth of Si is 12.2 μm at a wavelength of 800 nm,³² the photoinduced carriers form a freestanding grating, which can be regarded as a metallic wire grating embedded in the Si wafer. A schematic side view of the photoinduced grating with a TE-polarized incident wave is shown in Fig. 1(b). The grating is characterized by its period P, grating thickness h, and duty cycle D. Here, the duty cycle is defined as the ratio of the width of the photoexcitation region w to the grating period, i.e., D = w/P. The width of the region between two adjacent photocarrier strips is L (L = P − w). The THz beam was focused on the Si sample with the grating pattern, and the transmitted THz wave was detected by electro-optic sampling, using a second ZnTe crystal.³³ The time delay τ between the THz beam and the control beam was controlled by a delay stage [Delay 2 in Fig. 1(a)]. The value τ < 0 indicates that the THz pulse reaches the photoinduced grating before the control beam. On the other hand, τ > 0 means that the THz pulse arrives to the photoinduced grating after the free carriers are excited. In our experiment, the THz pulse passed through the sample approximately 20 ps after the photoexcitation, i.e., τ = 20 ps. The lifetime of the photocarriers in the Si substrate is a few microseconds, and the response time of the photocarriers is about 3 ps.^24,34 Hence, our delay time was longer than the response time of the photocarriers and much shorter than the photocarrier lifetime. The duration of a THz pulse in the Si wafer was approximately 1 ps. Therefore, the photoinduced grating can be considered to be essentially static, and the carrier density depends just on the excitation fluence. The switching speed of the photoinduced grating depends on the rise time and the lifetime of the photocarriers in Si wafer. The rise time of the photocarriers is the switching-on time, and the carrier lifetime limits the switching-off time of the Si wafer.

Figure 2 shows the evolution of the transmittance spectra for various excitation fluences in the photoinduced grating with P = 200 μm and D = 0.5. The transmittance spectrum is defined as the ratio of the intensity of the transmitted THz wave through a photoinduced grating to the intensity of the transmitted THz wave through the Si wafer without optical illumination. The cases corresponding to TE and TM polarizations are displayed in Figs. 2(a) and 2(b), respectively. For TE polarization, the transmittance spectrum of the THz waves that pass through the photoinduced grating exhibits a resonant peak, as shown in Fig. 2(a). The blue, magenta, and cyan dotted curves correspond to different excitation fluences of 40, 60, and 80 μJ/cm², respectively. As the excitation fluence increases, the peak shifts to higher frequencies, accompanied by a decrease in transmittance over the entire frequency range. The photocarrier density increases with increasing excitation fluence. The blueshift of the peak is caused by a reduction in the effective permittivity of Si due to the increased carrier density. A high carrier density leads to a higher conductivity, and this is the factor that determines the absorption coefficient of the sample. Hence, the transmittance decreases as the excitation fluence increases. For the TM polarization, the transmittance is lower, and there is no obvious resonance peak in the transmittance spectrum. The transmittance also decreases as the excitation fluence increases. In Fig. 2(b), a shoulder is observed at a frequency higher than 1.3 THz, and it does not shift with the excitation fluence. These shoulders are caused by the Rayleigh anomaly, which is determined by the grating period.

In order to verify the measured results, we performed realistic simulations of the photoinduced grating using a commercial software package (FDTD Solutions) based on the FDTD method. A photograph of a photoinduced grating (P = 200 μm, D = 0.5) captured by a CMOS camera at the position of the sample is shown in Fig. 3(a). For the simulation, we need the refractive index profile of the photoinduced grating. According to the published reports,³⁵ the dielectric function $𝜀̃(ω)$ of the photoexcited Si wafer can be calculated using the Drude model,³⁶ 

where $𝜀̃∞=10.96$ is the high-frequency dielectric constant of the Si wafer, τ_D ∼ 10⁻¹⁴ s is the Drude relaxation time, and ω_p = (N_ee²/ε₀m_optm_e)^1/2 is the plasma frequency. The optical effective mass is $mopt∗=0.17$⁠.^35,36 The parameter N_e is the free carrier density, which depends on the excitation fluence Φ. In our experiment, the carrier density is estimated by the optical pump THz probe spectroscopy technique,^37,38 and the photocarrier density as a function of excitation fluence is shown in Fig. 3(b). A virtually linear relationship between the carrier density and the excitation fluence is observed, which is in agreement with Ref. 36.

In fact, when the control beam profile is projected onto the Si wafer, the photocarriers will diffuse along the x and y directions. The photocarriers diffusion to the x direction will broaden the transmission peaks, and cannot be ignored. To approximate the simulated geometry as much as possible to the experiment, a flattened Gaussian model was applied to describe the distribution of photocarriers in the Si wafer. This model is written as³⁹ 

where x is the relevant coordinate, N_e−max is the maximum carrier density, w represents the width of the photocarrier strip in the photoinduced grating, L_n is the n-th Laguerre polynomial,⁴⁰ and

The parameter M is an integer that determines the boundary of the carrier strip. For M = 0, the photocarriers exhibit a pure Gauss distribution, while for larger M, it becomes more and more similar to a rectangular distribution. In our experiment, the pixel of the DMD was diamond-shaped and the diagonal length of the pixel was 10.8 μm. The diamond-shaped pixel will lead to a deviation in the size of the projected grating from the predetermined value of about 10 μm. Therefore, the parameters of the photocarrier distribution model are selected according to the intensity profile of the photoinduced grating image. Figure 3(c) shows the spatial photocarrier distribution in a period of the photoinduced grating, along the horizontal dotted line in Fig. 3(a). The solid curve represents the carrier distribution in the experiment, which resembles the intensity profile within a period obtained by the CMOS camera. The blue circles represent the flattened Gaussian model with parameters M = 20, w = 106 μm, and N_e−max = 1 × 10¹⁸ cm⁻³. It is evident that the flattened Gaussian model can be used to accurately describe the carrier distribution in the photoinduced grating. The spatial photocarrier distributions in one period of a photoinduced grating (P = 200 μm, D = 0.5) along the x direction with various excitation fluences are also plotted in Fig. 3(d). The photocarrier distributions are also described by the flattened Gaussian model with the parameters M = 20 and w = 106 μm. In Fig. 3(d), the blue, magenta, and cyan curves describe the carrier distributions of the photoinduced grating excited by the control beam with the excitation fluences of 40, 60, and 80 μJ/cm², and the corresponding parameters are N_e−max = 0.3 × 10¹⁸, 0.6 × 10¹⁸, and 1 × 10¹⁸ cm⁻³, respectively.

In the simulation, the carrier distribution described by the flattened Gaussian model is used to calculate the refractive index profile of the photoinduced grating. For a photoinduced grating, the refractive index of the illuminated region is described by the calculated profile, whereas that of the dark region is set as 3.4 (the refractive index of Si in the THz waveband). The thickness of the whole sample model was 10 μm. The mesh sizes used are 2 μm in the x-direction, 5 μm in the y-direction, and 2 μm in the z-direction. Periodic boundary conditions were applied in both the x and y directions, and perfectly matched layers were applied in the beam propagation direction. The TE/TM polarized plane waves with a frequency ranging from 0.2 to 2.0 THz were used to impinge on the sample.

According to the photocarrier distributions in Fig. 3(d), we also calculated the refractive index profiles of the photoinduced grating excited by the excitation fluences of 40, 60, and 80 μJ/cm², respectively. These refractive index profiles were loaded into the FDTD Solutions, and then the numerical simulations were performed. The simulated transmittance spectra in the case of TE and TM polarizations are shown in Figs. 4(a) and 4(b), respectively. It can be seen from Fig. 4(a) that for TE polarization, the transmittance decreases and a slight blueshift of the resonant peak appears as the excitation fluence increases. For the TM polarization, the shoulder does not shift and the transmittance decreases as the excitation fluence increases. The simulated results are in good agreement with the experimental results.

In order to further investigate the mechanism behind the observed spectral features, we set the period of the photoinduced grating P to 200 μm and varied the duty cycle D from 0.4 to 0.6 with a step of 0.1. The control beam fluence Φ was chosen as 80 μJ/cm². The measured transmittance spectra for the TE and TM polarized incident THz electric field are shown in Figs. 5(a) and 5(b), respectively. The blue, magenta, and cyan dotted curves correspond to different duty cycles of 0.4, 0.5, and 0.6, respectively. It is seen from Fig. 5(a) that, in the TE polarization case, a large blueshift of the resonance frequency and a decrease of the transmittance are observed as the duty cycle increases. The resonance frequencies for a duty cycle of 0.4, 0.5, and 0.6 are 0.96, 1.03, and 1.14 THz, respectively. For the TM polarization, the transmittance decreases and the shoulder does not shift as the duty cycle increases, as shown in Fig. 5(b).

Then, we performed some simulations of the photoinduced grating. Figures 5(c) and 5(d) show the transmittance spectra from the simulations in the case of TE and TM polarizations, respectively. In the simulation, the maximum carrier density was set as N_e−max = 1 × 10¹⁸ cm⁻³, which is excited by the control beam with excitation fluence of 80 μJ/cm². The parameters of the flattened Gaussian model were w = 80 μm and M = 5; w = 106 μm and M = 20; and w = 128 μm and M = 70 for the grating with D = 0.4, 0.5, and 0.6, respectively. It is clearly seen that the simulated transmittance spectra for different duty cycles are in good agreement with the experimental results.

Figure 5(e) shows the electric field intensity calculated along an in-plane cross-section of the photoinduced grating with P = 200 μm and D = 0.5, at the resonance frequency of 1.03 THz and for TE polarization. The white lines represent the position of the photocarriers. The THz wave was incident from the bottom. This figure shows that the phenomenon of enhanced transmission for TE polarization can be explained by a cavity resonance, which is a rather different process from the excitation of surface plasmons (SPs) that occurs for TM polarization. The field is able to couple in the dielectric and is strongly enhanced in the region between photocarrier strips. The resonator length is determined by the width of the spacing. Thus, the position of the resonance peak shifts towards longer wavelengths when the spacing between the photoinduced stripes increases. That means the resonance peak will move to lower frequencies as the duty cycle decreases.

Next, we investigated the effect of the period of the photoinduced grating on the transmittance spectra. Figure 6 shows the transmittance spectra of the photoinduced grating structure for different periods between 160 and 280 μm, and with the other parameters fixed as D = 0.5 and Φ = 80 μJ/cm². The experimental transmittance spectra for TE and TM polarizations are displayed in Figs. 6(a) and 6(b), respectively. It can be seen that, for the TE polarization, the position of the peak in the transmittance spectra shifts to lower frequencies with increasing period. For the TM polarization, the shoulders in the transmittance spectra also shift to lower frequencies as the period increases. The corresponding simulated results, which are consistent with the experimental results, are shown in Figs. 6(c) and 6(d).

In summary, we have demonstrated a photoinduced grating with EOT for the TE polarization in the THz region. Using a DMD, the spatial profile of the control beam is modulated to form a grating shape that is then projected onto a flat Si wafer with a thickness of 10 μm. This technique can be used to avoid the processing of traditional samples and provides flexibility to adjust the structural parameters of the sample. The transmission characteristics of the 1D grating in the THz region were investigated in detail for both TE and TM polarizations. The experimental results are supported by simulations performed using a FDTD method. This kind of photoinduced grating could be used as a tunable polarization-independent THz filter. The transmission peak can be tuned to a wide range of frequencies by varying the period and duty cycle of the grating, and the excitation fluence of the controlled beam. Using this technique, THz modulators with arbitrary microstructures could be realized without the need for sample fabrication.

See supplementary material for additional discussions.

This work was supported by the 973 Program of China (No. 2013CBA01702); National Natural Science Foundation of China (Nos. 11474206, 91233202, 11374216, 11174211, and 11404224); National High Technology Research and Development Program of China (No. 2012AA101608-6); Program for New Century Excellent Talents in University (No. NCET-12-0607); Scientific Research Project of Beijing Education Commission (No. KM201310028005); Beijing Youth Top-Notch Talent Training Plan (No. CIT&TCD201504080); Specialized Research Fund for the Doctoral Program of Higher Education (No. 20121108120009); Scientific Research Base Development Program of the Beijing Municipal Commission of Education.