In this work, we present a novel approach to the implementation of optically controlled reconfigurable terahertz (THz) waveguide filters based on photo-induced electromagnetic band gap (PI-EBG) structures using semiconductor mesa arrays. In this approach, EBG structures are dynamically generated through spatially-resolved photogeneration of free carriers in semiconductor mesa structures; the use of mesa arrays improves the spatial resolution, leading to more refined PI-EBG patterns and improved circuit operation at THz frequencies. A band-stop filter prototype in the WR-5.1 band (140-220 GHz) was designed, simulated, and analyzed in detail. Simulations show that the stop-band rejection and bandwidth of the proposed device can be adjusted by changing the filling factor of the photo-patterns illuminated onto the mesa array. The center frequency of the stop-band can also be tuned from 166 to 200 GHz by changing the period of the PI-EBG patterns. The proposed reconfigurable THz waveguide filters based on PI-EBG are promising for a wide range of applications in advanced THz sensing, imaging, and communications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Tunable and reconfigurable terahertz (THz) devices that can dynamically control THz wave propagation, such as variable attenuators/modulators, variable phase shifters, reconfigurable coded-aperture imaging masks, and tunable filters, are essential components for advanced THz imaging and adaptive THz wireless communication systems [1,2]. Although those devices are critical for THz systems, they are challenging to realize. As one of the most promising solutions for effectively manipulating electromagnetic waves over a broad range of frequencies, electromagnetic band gap (EBG) structures have been proposed and studied for more than two decades [3–5]. Although EBG structures have been demonstrated and employed in a variety of applications including filters, resonators, power amplifiers, phased array antennas, etc [3–13], existing demonstrations suffer from several drawbacks. First, most previous reports require sophisticated fabrication processes such as micromachining or combinations of wet- and dry-etching to construct periodic structures [9,10]. THz circuit implementation is especially challenging due to the tight fabrication tolerances. Furthermore, reconfigurable devices typically employ PIN diodes or MEMS (micro electro mechanical systems) devices to realize tunability and reconfigurability, which tend to result in complex systems with limited tuning capability [12,13]. These drawbacks have prevented EBG structures from being applied to a broader range of practical THz systems.
Recently, a novel optical control methodology was proposed and investigated to implement photo-induced EBG (PI-EBG) structures at microwave frequencies . This methodology takes advantage of the spatially-resolved photogeneration of free carriers in a semiconductor, and permits the formation of periodic structures in the semiconductor without any complex fabrication processes. By illuminating different virtual EBG patterns onto the semiconductor, electromagnetic waves in the microstrip structure can be dynamically perturbed by PI-EBG structures for realizing device tunability and reconfigurability. On the basis of the PI-EBG structure, an optically controlled frequency tunable band-stop filter (BSF) operating in the 8-12 GHz band has been designed and analyzed. Although satisfactory performance was achieved at microwave frequencies, it was found that circuit operation at higher frequencies would be limited because of the finite spatial resolution of the EBG patterns arising from the lateral diffusion of the free carriers (e.g., ~0.13 mm diffusion length in Si, ~0.5 mm in Ge [14,15]). To scale the microwave prototype into THz regime, artificially engineered structures consisting of mesa arrays are promising to enable higher spatial resolution.
The mesa array structure consists of a two-dimensional array of electrically isolated semiconductor islands (mesas). The dimension of each mesa is much smaller than both the wavelength of the propagating wave and the carrier diffusion length of the semiconductor. When the mesa array structure is illuminated using an optical pattern, the lateral diffusion of the photogenerated free carriers is constrained by the mesa edges since carriers are confined within each isolated mesa. This leads to higher achievable photoconductivity as well as increased spatial resolution. The higher spatial resolution enables the formation of more refined optically defined EBG patterns, facilitating circuit operation at higher frequencies [14,15]. To demonstrate this concept for high-performance tunable and reconfigurable THz devices using mesa arrays, in this work, a reconfigurable WR-5.1 (140-220 GHz) waveguide filter based on PI-EBG using a mesa array structure is designed, simulated, and analyzed in detail.
2. Proposed structure for optically controlled waveguide component
The detailed structure of the proposed optically controlled WR-5.1 waveguide filter based on PI-EBG using a mesa array is shown in Fig. 1. A back-to-back waveguide configuration is used, with offset input and output waveguide channels (with standard WR-5.1 band dimension) connected by an E-plane microstrip chip based on a Ge-on-quartz substrate. Ge is chosen as the photoconductive material for this simulation study because it can achieve high photoconductivity under moderate light intensity due to its long effective carrier lifetime. The detailed theories and mechanisms of optically controlling photogenerated free carriers in semiconductors to realize high-performance tunable and reconfigurable devices have been reported in our previous work [15–18]. The dimensions of the microstrip channel were chosen so that single mode propagation is achieved over the frequency range of interest (140-220 GHz). For the microstrip chip design shown in Fig. 1 (c), a 6-mm-long section of transmission line (with a top conductor (i.e., signal line of the microstrip configuration) assumed to be made of 1-μm-thick gold) with waveguide probes at both ends (serving as waveguide-to-microstrip transitions) on a 70-μm-thick quartz substrate has been designed. A rectangular microstrip probe design, originally designed for THz waveguide receiver systems , was selected since by adjusting the width, length, and the position of the rectangular microstrip probe, as well as the position of the backshort, the return loss of the transition can be optimized to be better than 15 dB over the full waveguide band. A 5-μm-thick Ge layer was used on the back of the quartz substrate. The thickness was designed as 5 μm because a relatively high photoconductivity can be achieved under a moderate light intensity [14,15]. Besides, as will be discussed later, this thickness can ease the fabrication process of the mesa array structures. By projecting optical EBG patterns onto the Ge, photo-induced uniplanar EBG structures  can be dynamically generated on the Ge thin film for realizing reconfigurable circuit functionalities. This can be achieved by using 808-nm fiber-coupled laser diodes  in conjunction with a Digital Micromirror Device (DMD) chip, as shown in Fig. 1 (b). The DMD chip consists of a two-dimensional array of microscopic mirrors. By controlling the on or off state of each microscopic mirror individually, optical patterns to be generated can be dynamically changed . An opening was designed at the bottom of the waveguide block for optical illumination. Since the feature size of the required PI-EBG patterns at THz frequencies is smaller than the diffusion length in Ge (~0.5 mm ), definition of well-defined optically-generated EBG patterns is not possible due to the limited spatial resolution. To increase the spatial resolution for more refined EBG patterns, a mesa array structure consisting of a matrix of isolated Ge mesas was created on the Ge thin film.
The design of the mesa array is critical to the successful operation of the proposed filter prototype. It needs to provide sufficiently high spatial resolution and improved circuit operation at THz frequencies, while still maintaining ease of fabrication. For the device proposal reported in this work, a simplified one-dimensional mesa array structure, illustrated in Fig. 2 (a), with trenches cut only along the transverse direction (y-axis) was used. The thickness of the Ge making up the mesa array (h) is 5 μm, with the width of each mesa (w) chosen to be 25 μm for an initial demonstration. This dimension sets the effective spatial resolution of the array to be 25 μm , which enables the demonstration of reconfigurable filter performance at WR-5.1 band as will be shown later. Smaller mesa size can also be employed, which renders higher spatial resolution, enabling higher operation frequency of the device [14,15], but makes the fabrication more challenging. The trench size (g) is chosen to be 2 μm; at this dimension, the trench is much smaller than a wavelength, can be easily fabricated through photolithographic processes, and results in a small (~10%) reduction in the Ge coverage. To prevent higher-order modes from propagating through the trenches and degrading the circuit performance, the length of each trench (l) also needs to be limited to a small fraction of the wavelength at the frequency of operation. Our full-wave HFSS simulations indicate that if the trench length is larger than half of the wavelength, to preventcircuit degradation the trench size needs to be kept below 0.01 μm, which cannot be defined through photolithographic processes. Although e-beam lithography (EBL) can be employed, the high aspect ratio of the structure (500:1) still makes it extremely challenging to fabricate using deep reactive ion etching (DRIE) processes. To construct smaller trench length, small Ge “tabs” with a length (i) of 2 μm have been used to break up the trenches, resulting in a small interconnection between adjacent mesas. The tabs are offset by half of the trench length along the longitudinal direction (x-axis) to form a brick configuration (see Fig. 2 (a)). Although the mesas are connected to each other through the small tabs, carrier diffusion from one mesa to another can still be greatly suppressed due to the small dimension of the tabs and the brick configuration with offset tab arrangement. Full-wave HFSS simulations have been performed on the prototype with different trench lengths, and the results indicate that a trench length of 30 μm (~0.07 λ at 180 GHz) can ensure that the mesa array has comparable THz transmission performance to that of a continuous semiconductor film. This is evidenced by the simulated S-parameters of the device (with 6-mm-long microstrip section) from 140 to 220 GHz under a uniform optical illumination level of 30 W/cm2 shown in Fig. 2 (b). A spatially averaged photoconductivity of 3 × 105 S/m was employed in the simulation for the Ge mesa array using a physics-based model [14,15,18]. The material parameters employed in the calculation were reported in . As shown in Fig. 2 (b), an average of 2.7 dB (or 0.45 dB/mm) insertion loss and larger than 12 dB return loss have been obtained. Also shown are the simulated device S-parameters when a continuous Ge film (under a uniform optical illumination level of 30 W/cm2) and a continuous gold layer, respectively, were employed as the ground plane for the microstrip structure of the same length. It is seen that the average insertion loss of the device with mesa array is ~0.6 dB higher than that of the case when a continuous photoconductive Ge is employed (2.1 dB, or 0.35 dB/mm), and ~1.5 dB higher than that of a conventional transmission line (1.2 dB, or 0.20 dB/mm) due to both the finite conductivity of the photo-induced Ge mesa array ground (which leads to a higher conductor loss) and ground discontinuities. Lower insertion loss (e.g., 1.7 dB, or 0.28 dB/mm) can be expected by employing a higher light intensity (e.g., 100 W/cm2) for higher photoconductivity. By employing the proposed mesa array structure, a spatial resolution as high as 25 μm can be achieved, and satisfactory THz circuit performance can potentially be realized.
3. Simulation and analysis of proposed optically controlled waveguide components
By illuminating EBG patterns onto the mesa array, BSF responses at THz frequencies can be realized. To demonstrate this, the frequency responses of the device with different EBG patterns illuminating the mesa array were simulated. A light intensity of 30 W/cm2 was employed in the simulation. Figure 3 (a) shows the simulated S-parameters of the device under the illumination for three different rectangular EBG patterns (as shown in Fig. 3 (b)). The three EBG patterns have the same period, p, but different filling factors, a/p, where a is the length of the “dark” (un-illuminated) portion of the EBG pattern. The feature sizes of the EBG patterns are chosen to be integer multiples of the mesa size (25 μm) to facilitate optical alignment in experiment, while keeping strong tunability and reconfigurability. For example, the length of the dark area in “Pattern I” corresponds to twice of the mesa size, and the period corresponds to 18 times the mesa size. Therefore, “Pattern I” has a filling factor of 1/9. Accordingly, the filling factors of “Pattern II” and “Pattern III” are 2/9 and 1/3, respectively.
In experiment, the modification of the filling factor will be realized by programming the DMD chipset, and carefully aligning the optical patterns to the trench edges of the mesa array under a microscope. On the basis of EBG theories [3,14], the period chosen here corresponds to half of the guided wavelength at 182 GHz (i.e., λg = 971 μm), and therefore a center frequency f0 (defined as (fL + fH)/2, where fL and fH are the frequencies where the insertion loss is 3 dB higher than that in the lower and higher pass-band, respectively) at 182 GHz should be expected. As shown in Fig. 3 (a), three distinctive BSF responses with a center frequency f0 at 182 GHz are observed in simulation, consistent with expectation. It can be seen that the stop-band rejection and bandwidth (fH - fL) have both been effectively adjusted by the change of the optical patterns. This is because with a fixed EBG period, increasing (decreasing) filling factor will lead to increasing (decreasing) stop-band rejection and bandwidth for the BSF as discussed in [14,20,23]. It should be noted that the filter responses demonstrated above can only be realized with the improved spatial resolution enabled by the proposed mesa array structure. Without the mesa array, photogenerated free carriers will diffuse across the entire Ge thin film (even at the spots where the light is not illuminating because the length of the “dark” portion is smaller than the diffusion length in Ge), and therefore no filter responses will be observed.
In addition to modification of the stop-band rejection and bandwidth, the center frequency of the BSF can also be dynamically adjusted. Since the center frequency of the BSF is inversely related to the period of the EBG structures, it can be tuned by changing the period of the EBG patterns. To demonstrate this, three EBG patterns were simulated. The periods of the PI-EBG patterns were 540 μm (λg/2 at 164 GHz), 486 μm (λg/2 at 182 GHz), and 432 μm (λg/2 at 204 GHz), respectively, which correspond to 20, 18, and 16 times the mesa size. The corresponding lengths of the dark regions within the patterns are 135 μm, 108 μm, and 81 μm, respectively, corresponding to 5, 4, and 3 times the mesa size. The simulated S-parameters of the device with these EBG patterns are shown in Fig. 4. It can be seen that the center frequency f0 increases from (a) 166 GHz to (b) 182 GHz, and then to (c) 200 GHz as the period of the EBG pattern decreases, close to expectation. In each case, the stop-band rejection exceeds 15 dB, and the return loss in the stop-band is less than 3 dB. These results demonstrate that by exposing EBG patterns with different periods onto the mesa array, BSFs with tunable center frequency can be realized. In addition, by employing mesa array structures with smaller mesa sizes (e.g., 5 μm), reconfigurable devices with higher operation frequency and larger tuning range can potentially be realized.
With the above simulation and analysis, we have successfully demonstrated an optically controlled reconfigurable WR-5.1 waveguide filter based on PI-EBG using a mesa array structure. Although other filter prototypes operating at THz frequencies have been designed and reported using either magnetically controlled birefringence in liquid crystals  or tapered hyperbolic metamaterial waveguides , the device proposed here offers significant advantages over those reports including higher tuning capability (i.e., both frequency tuning and bandwidth tuning), simpler system implementation, and higher circuit performance (e.g., lower insertion loss in the pass-band, higher tuning speed , etc.).
In conclusion, an optically controlled reconfigurable WR-5.1 waveguide filter based on PI-EBG using a mesa array structure has been designed, simulated, and analyzed. Circuit operation into the THz regime is enabled by the employment of a mesa array structure, which allows higher resolution PI-EBG patterns to be achieved. Simulations of the prototype show that both the stop-band rejection and bandwidth of the filter can be adjusted by changing the patterns illuminated onto the mesa array. The BSF center frequency can be tuned from 166 to 200 GHz by changing the period of the PI-EBG patterns. The proposed reconfigurable THz waveguide filter based on PI-EBG is promising for a wide range of applications including constructing advanced THz sensing, imaging, and communication systems.
National Science Foundation (NSF) (ECCS 1711631, ECCS 1711052); Harvard-Smithsonian Center for Astrophysics (PTX-Smithsonian 17-SUBC-400SV787007).
The authors would like to thank the support from Notre Dame’s Center for Nano Science and Technology (NDnano) and Advanced Diagnostics & Therapeutics (AD&T) at the University of Notre Dame.
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