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Abstract
We designed and fabricated beam steering subwavelength grating (BS-SWG) with high efficiency, wide angles, and broadband beam steering in the terahertz (THz) range. Beam steering technology in the THz range by a fixed structure and frequency sweep has to date lacked a device combining high efficiency and a wide beam steering angle. A subwavelength structure using float zone Si, a low-loss dielectric, could combine both of these aspects, but no experimental demonstration in the THz range has been performed to our knowledge. The BS-SWG was designed with an efficiency of 0.708 at 0.4 THz and beam steering angles of −72.1°–−34.8° by sweeping the incident frequency from 0.3 THz to 0.5 THz including the Beyond 5 G/6 G communication bands. An efficiency of 0.354 at 0.400 THz and beam steering angles of −74°–−34° were experimentally achieved, demonstrating the potential of high-efficiency, wide-angle beam steering for THz communications, imaging, and radar applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves have attracted interest for applications in nondestructive imaging [1,2], THz wave radar [3,4], and Beyond 5 G/6 G communications [5,6]. THz waves must be propagated in a highly directional beam form because of atmospheric attenuation and high transmission loss [7,8]. Beyond 5 G/6 G, highly directional beams with narrow spot sizes can cause narrow communication coverage without steering beams [9]. Beam steering technology to control THz beams at wide angles is indispensable to overcome the challenge in realizing Beyond 5 G/6 G communications and to apply to THz imaging and radar. Beam steering systems in the THz range can be classified into two categories: those that perform beam steering at a fixed frequency and those that perform beam steering by a frequency sweep using a fixed structure.
The former approach involves phased-array antennas [10,11], lenses [12,13], optical pumping [14], and mirrors [15,16], which have complicated electrical circuits or precise control of moving parts. The latter approach includes leaky-wave antennas [17,18], diffraction gratings [19], and metallic metamaterials [20,21], which have the advantage of structural simplicity and do not require a power-feeding network. However, leaky-wave antennas have poor radiation efficiency due to ohmic losses in transmission lines, although they can steer a beam at wide angles [22,23]. One of the leaky-wave antennas demonstrated beam steering angles of −48°–43° with an efficiency of 0.5 at 0.23–0.33 THz [17]. Blazed gratings, which achieve superior efficiency among diffraction gratings, exhibit decreased diffraction efficiency as the diffraction angle increases due to the shadowing effect [24]. One of the blazed gratings demonstrated beam steering angles of 10°–60° with an efficiency of 0.9 at 0.18–1.0 THz [19]. Metamaterials using metal resonators generally have ohmic losses and do not achieve both wide beam steering angles and high efficiency. One of the metallic metamaterials demonstrated beam steering angles of 19.5°–42.8° with an efficiency of 0.25 at 0.6–1.2 THz [20]. Table 1 lists characteristics and examples of beam steering devices by a frequency sweep using a fixed structure. Passive devices such as diffraction gratings and metallic metamaterials can be transmissive or reflective. Reflective types restrict the reflected angles because a THz incident element can block the path of the reflected beam [25]. Hence, transmissive types need to be developed for wide-angle beam steering but are generally susceptible to losses.
Table 1. Characteristics and examples of beam steering devices by a frequency sweep using a fixed structure.
Materials with low loss over broadband operation that can be candidates for transmissive devices include dielectrics, and a typical example is float zone Si (FZ-Si) [26,27]. To modulate the transmission phases, blazed gratings use differences in substrate thickness, while metallic metamaterials use electromagnetic resonance. Dielectrics can provide beam steering using differences in the effective refractive index. By designing a unit of a periodic structure with a subwavelength size, a nonuniform medium can be regarded as a uniform medium with an effective refractive index neff [24,28,29]. The subwavelength structure can be planar and consists only of dielectrics; thus, it is not affected by the shadowing effect or ohmic losses. Hong et al. designed a transmissive subwavelength post array with FZ-Si and demonstrated (by calculation) beam steering angles of 8°–14° with a high efficiency of 0.88 at 1.0–1.3 THz [30]. Zhang et al. designed a transmissive subwavelength rectangle array with FZ-Si and demonstrated beam steering angles of −30°–−10° with a high efficiency of 0.6 at 0.5–1.5 THz [31]. However, these examples covered no or little of the frequency range of 0.275–0.450 THz, which is considered the Beyond 5 G/6 G communication bands [32]. To our knowledge, Si subwavelength structures have not been demonstrated experimentally to provide wide-angle, high-efficiency, and broadband THz beam steering.
In this study, we fabricated FZ-Si beam steering subwavelength grating (BS-SWG) with through-holes and experimentally demonstrated high efficiencies and wide beam steering angles at 0.3–0.5 THz, including the Beyond 5 G/6 G communication bands. This device was designed based on multilevel diffraction gratings fabricated by micromachining processes and demonstrated beam steering with an angle of 45.5° and an efficiency of 0.708 at 0.4 THz by calculation. The calculated efficiency was 1.1 times that of an optimized blazed grating (detailed later) and 1.4–2.8 times that of devices reporting wide-angle beam steering [19–21]. By sweeping the frequency from 0.3 THz to 0.5 THz, we achieved beam steering angles of −74°–−34° and an efficiency of 0.354 at 0.400 THz experimentally, which was still higher than the efficiencies of the reported metamaterials [20,21]. FZ-Si BS-SWG provides high efficiency, wide beam steering angles, and potential for THz communications, imaging, and radar applications.
2. Concept of the BS-SWG
Figure 1 shows a schematic diagram of the structure of the BS-SWG. A subcell is a square of period P and thickness d with a through-hole of width w placed in the center. The air filling factor, FFair, is defined as ${w^2}/{P^2}$. A unit cell is a rectangle of height P and width Λ with five subcells (S1–S5) arranged in the x direction, and w of S1–S5 are w1–w5, respectively. TM polarization in which the electric field oscillates parallel to the x-axis is incident along the + z-axis for the BS-SWG, whose unit cells are periodically arranged in the xy-plane. The 1st-order (or −1st-order) diffraction angle depends on Λ and the incident frequency f [33]. The transmitted phases related to the control of the diffraction efficiency can be controlled by changing the effective refractive index neff of each subcell, and neff can also be changed as a monotonically decreasing function of FFair [24]. Therefore, the −1st-order diffraction efficiency and angle can be controlled by designing Λ and w1–w5 as variables.
3. Verification of the control of the effective refractive index
We calculated and measured the optical properties of subwavelength gratings (SWGs) with a uniform air filling factor (uniform SWGs) to verify the control of neff by the subwavelength structure. The dimensions of the through-holes of uniform SWGs are w1 = w2 = w3 = w4 = w5. The electromagnetic field calculations were performed by DiffractMOD (Synopsys Inc.), a software program based on the rigorous coupled wave analysis method. The calculation model was based on a subcell of P = 200 µm with a through-hole of width w and TM polarization incident along the + z-axis. The refractive index of the substrate, FZ-Si, was set to 3.415, and the extinction coefficient was set to 0, both were frequency independent (applied in all calculations). The refractive index of 3.415 for FZ-Si with a resistivity of over 10,000 Ω·cm and a plane orientation of (100) was determined by measuring with a THz time-domain spectroscopy system (Tera Prospector, Nippo Precision Co., Ltd.) as shown in Fig. 2. The measured both-sides-polished and single-side-polished FZ-Si wafers were 500 µm and 525 µm thick, respectively. The peaks at approximately 0.38 and 0.45 THz corresponded to the frequencies of transmittance dips and are attributed to multiple reflections. These peaks were fluctuations that were not removed by processing after measurement. The FFair and substrate thickness d were used as variables. The calculation of neff was based on the principle of thin film interference. As d is increased, the reflected power becomes periodically 0 at intervals of Δd because of this interference. The effective refractive index of uniform SWGs can be calculated by Eq. (1),
where c is the speed of light. Four kinds of uniform SWGs with FFair = 20.3%, 39.1%, 60.1%, and 81.0% (w = 90, 125, 155, and 180 µm, respectively) were designed and named gratings A, B, C, and D, respectively.
Fig. 2. (a) Measurement results of the refractive index of FZ-Si. (b) Schematic image of a THz time-domain spectroscopy system.
Uniform SWGs were fabricated on a 2 cm square, 300 µm thick, both-sides-polished FZ-Si substrate using micromachining processes, as shown in Fig. 3. First, a 2.2 µm thick SiO2 film was deposited on the front side of a cleaned 2 cm square Si substrate by plasma-enhanced chemical vapor deposition (PD-100ST, Samco Inc.) using tetra ethoxy silane (TEOS) as a raw material (Fig. 3(a) and 3(b)). The SiO2 deposition conditions were RF power of 70 W, TEOS flow rate of 7 sccm, O2 flow rate of 233 sccm, pressure of 53 Pa, top electrode temperature of 200°C, bottom electrode temperature of 350°C, stress of −320 MPa, and deposition time of 24 minutes. Next, both sides of the substrate were spin-coated with positive photoresist (OFPR-800 LB 200cp, Tokyo Ohka Kogyo Co., Ltd.) at 2,000 rpm, and photolithography was performed on the front side exposing at 200 mJ/cm2 and immersing in tetramethyl ammonium hydroxide 2.38% developing solution at room temperature for 150 s. (Figure 3(c) and 3(d)). The SiO2 film in the desired through-hole areas was etched by buffered HF acid at room temperature for 10 minutes to expose the Si substrate (Fig. 3(e)). Through-etching of the Si was performed by inductive coupled plasma reactive ion etching (ICP-RIE) (MPX-ASE, Sumitomo Precision Products Co., Ltd.) (Fig. 3(f)). ICP-RIE Si etching was performed for 230 cycles alternating passivation and etching phases. The passivation phase conditions were C4F8 flow rate of 400 sccm, coil power of 2,500 W, pressure of 6.0 Pa, and process time of 2.3 s. The etching phase conditions were: SF6 flow rate of 800 sccm, coil power of 2,500 W, platten power of 80 W, pressure of 4.0 Pa, and process time of 2.0 s, followed by SF6 flow rate of 400 sccm, coil power of 2,500 W, platten power of 20 W, pressure of 20.0 Pa, and process time of 6.0 s. Uniform SWGs made entirely of Si were fabricated by removing the photoresist and SiO2 with a stripping solution (Microstrip 2001, Fujifilm Electronic Materials Co., Ltd.) and buffered HF acid, respectively (Fig. 3(g) and 3(h)).
The top view of the fabricated uniform SWGs is shown in Fig. 4(a). Figure 4(b)–(e) show magnified views of the front side of gratings A–D, and Fig. 4(f)–(i) show those of the back side. Figure 4(j) shows a scanning electron microscope (SEM) image of a cross-section of grating A. The width wf of the hole on the front side and wb of the hole on the back side of the fabricated uniform SWGs were measured. Table 2 lists the design dimensions and fabrication dimensions obtained by averaging the widths of four holes selected randomly. The parameter wb = 200.0 µm was defined for the back side of grating D since it was too severely etched to be measured. The FFair was determined using the average of wf and wb. If the width of a through-hole varies linearly in the z direction and the relationship between the effective refractive index and hole width is linear, then the effective refractive index of the tapered through-hole structure is equal to the effective refractive index at the average of hole width wf and wb. As shown in Fig. 4(j), through-holes widened monotonically and the relationship between the effective refractive index and hole width is linear for small changes [24], the FFair of the through hole was the average of the FFair of the front and back sides.
Fig. 4. (a) Top view of the fabricated uniform SWGs. Magnified images of the front side of (b) grating A, (c) grating B, (d) grating C, and (e) grating D. Magnified images of the back side of (f) grating A, (g) grating B, (h) grating C, and (i) grating D. (j) SEM image of a cross-section of grating A. Each scale bar in (b)–(i) is 300 µm.
Table 2. Designed and fabricated dimensions of uniform SWGs.
The neff calculations were performed on models having vertical sidewalls with FFair = 26.1, 47.2, 70.8, and 93.0%, which are the fabrication dimensions of gratings A–D. For a reflected power of 0.4 THz for the model with each FFair, Δd was calculated to be 126.8, 149.2, 200.0, and 312.0 µm. The corresponding neff values were calculated to be 2.96, 2.51, 1.87, and 1.20, from Eq. (1). Similarly, neff was calculated from 0.3 THz to 0.5 THz in increments of 0.25 THz. Figure 5 shows the calculated and measured effective refractive index neff. Transmission spectra of the sample and air reference were measured by the THz time-domain spectroscopy system. The sample was attached to an aperture with a diameter of 5.0 mm and measured by incident collimated TM polarization from the front to the back of the sample. The parameter neff increased with increasing frequency due to the modal dispersion of the waveguide. The range of errors between the measured and calculated results was −0.09–0.06 for grating A–C and 0.06–0.22 for grating D. Thus, at least for FFair ≤ 70.8%, we can expect to control neff within ±0.10 of the calculated value.
Fig. 5. Calculation results (dotted line) and measurement results (solid line) of the effective refractive index.
4. Design of the BS-SWG
The BS-SWG was designed with a frequency centered at 0.4 THz. The beam steering angle target was set to −45° at 0.4 THz. The relationship between the effective refractive index neff and the air filling factor FFair was calculated for 0.4 THz TM polarization incident on the uniform SWGs with P = 210 µm. P was set to 210 µm to obtain the unit cell width Λ = 1050 µm. The controllability of neff verified at P = 200 µm, 0.3–0.5 THz can be extended to P = 210 µm, 0.285–0.486 THz because neff is determined by the ratio of the reciprocal frequency $1/f$ to P and FFair [24]. Figure 6(a) shows the relationship between neff and FFair for 0.4 THz. The dotted line represents the second-order approximation curve, described by Eq. (2).
Fig. 6. (a) Relationship between the effective refractive index and the air filling factor at 0.4 THz, calculated value (dots) and second-order approximation curve (dotted line). (b) Theoretical value of the −1st-order diffraction angle. (c) Calculated results of the 0th-order, 1st-order, and −1st-order diffraction efficiencies.
The coefficient of determination value R2 was 0.999. FFair was designed using the neff to be achieved in each subcell and Eq. (2). The design was based on the design method of surface relief multilevel diffraction gratings in scalar diffraction theory [33]. Equation (3) shows the theoretical expression for the −1st-order diffraction angle θ−1st, and Fig. 6(b) shows the −1st-order diffraction angle for Λ = 1050 µm.
The parameter θ−1st was calculated to be −72.1°, −54.7°, −45.5°, −39.4°, and −34.8° at 0.3, 0.35, 0.4, 0.45, and 0.5 THz, respectively (Table 3). The condition for maximizing the −1st-order diffraction efficiency of the surface relief diffraction gratings is given by Eq. (4) [33],
where nSi and nair are the refractive indices of FZ-Si and air, respectively, N is the number of subcells in a unit cell, and d is the thickness of the grating parts. Equation (4) applied to the case of the BS-SWG is expressed as Eq. (5), and the difference in the effective refractive index ${n_{\textrm{step}}}$ between adjacent subcells can be expressed as Eq. (6).Here, nS5 and nS1 are the effective refractive indices of the Nth and 1st subcells, respectively. The parameter d in Eq. (5) must be larger than 310 µm because nSN and nS1 are limited to the range of the refractive index of air and FZ-Si. In addition, ${n_{\textrm{S}5}} - \,{n_{\textrm{S}1}}$ was calculated as 1.144, and nstep was calculated as 0.286 by substituting f = 0.4 THz, d = 525 µm, and N = 5. Table 4 lists the dimensions of the BS-SWG designed to have a higher −1st-order diffraction efficiency at 0.4 THz while satisfying the above conditions and the condition of FFair ≤ 70.8% for all subcells. Figure 6(c) shows the calculated 0th-, 1st-, and −1st-order transmitted diffraction efficiencies of the BS-SWG. Diffraction efficiencies were normalized by the sum of diffraction efficiencies of 0th-, 1st-, and −1st-order reflected diffraction light and transmitted diffraction light. Dips in the −1st-order diffraction efficiency were observed at 0.369 and 0.436 THz. The −1st-order diffraction efficiency was calculated to be 0.525, 0.491, 0.708, 0.600, and 0.001 at 0.3, 0.35, 0.4, 0.45, and 0.5 THz, respectively (Table 3). The BS-SWG is scalable in bands where the refractive index of Si is constant, at least in the range from 0.3 THz to 0.5 THz. There is a proportional relationship between wavelength, subcell period P, through-hole width w, and substrate thickness d. By tuning these factors, diffraction efficiency and beam steering angle can be shifted. The efficiency of 0.708 was larger than that of the reported THz wide-angle steerers [19–21]. Furthermore, it was larger than the efficiency of 0.628 for the Λ = 1050 µm blazed grating optimized by the scalar diffraction theory. The BS-SWG also achieved higher diffraction efficiencies than the blazed grating over most of the ranges 0.300–0.332 THz, 0.376–0.408 THz, and 0.454–0.485 THz in the calculation (Fig. 7). Figure 8(a) shows the phase distributions of the x component of the electric field Ex in the y = 0 plane for the incident TM polarization at 0.4 THz. The transmitted wavefronts of the incident waves, which were along the z-axis, were tilted to θ = −45.5°. The magnified image in Fig. 8(b) shows that phase tilting occurs inside the BS-SWG, with the phase propagating faster on the + x side.
Fig. 8. Calculated phase distributions of Ex in the y = 0 plane for incident light of 0.4 THz TM polarization. (a) Phase distributions of the overview and (b) magnified view of a unit cell.
Table 3. Beam steering angles and −1st-order diffraction efficiencies of the BS-SWG
Table 4. Designed and fabricated dimensions of the BS-SWG
5. Fabrication of the BS-SWG
The BS-SWG was fabricated on a 2 cm square, 525 µm thick, single-side-polished FZ-Si substrate using the same micromachining process as uniform SWGs, as shown in Fig. 3. The refractive index of the single-side-polished Si measured experimentally is shown in Fig. 2(a). The BS-SWG was designed to match average values of wf and wb with the design values, taking into account the taper of through-holes. Figure 9(a) shows the top view of the fabricated BS-SWG. Figure 9(b) and 9(c) show magnified views of the front and back side, respectively. Figure 9(d) shows a SEM image of a cross-section of one unitcell. FFair of each fabricated subcell is shown in Table 4, where FFair was obtained by averaging wf and wb of four randomly selected through-holes.
Fig. 9. (a) Top view of the fabricated BS-SWG. Magnified images of the (b) front and (c) back side. (d) SEM image of a cross-section of one unitcell.
6. Measurement of the BS-SWG
The BS-SWG was measured using a THz frequency-domain spectroscopy system (Terascan 1550, Toptica Photonics AG). A THz source and detector were bow-tie type InGaAs antennas with THz power of 500 µW and full width at half maximum of 15° at 0.5 THz. THz waves are generated through optical heterodyning and photocurrents are detected using a lock-in amplifier. Figure 10 shows a schematic image of the optical measurement system for the BS-SWG measurement. Continuous waves (CW) of a Gaussian beam emitted from a THz source were collimated by lenses and detected by a THz detector through the BS-SWG attached to a 12 mm diameter aperture. THz waves were incident from the front to the back of the sample with TM polarization. The detector was rotated at 2° intervals from −80° to 80°. At each frequency, the transmittance was normalized by the total transmitted power measured without the sample in the range from −80° to 80°. Figure 11(a) and 11(b) show the transmittance measured without and with samples, respectively. In the results without the sample, the angles at which the maximum transmittance was observed were 0° or 2°. In the results with the sample, the transmission peak shifted to the angle θ−1st, which was a negative value. The angle θ−1st was measured to be −74°, −54°, −46°, −36°, and −34° at 0.300, 0.350, 0.400, 0.450, and 0.500 THz, respectively (Table 3). Figure 11(c) shows the measurement results of the 0th-, 1st-, and −1st-order diffraction efficiencies. The 0th-order diffraction efficiency was evaluated by obtaining the maximum transmittance in the range from −20° to 20° and adding the values of transmittance that are more than $1/{e^2}$ times the maximum transmittance. The ideal Gaussian beam spot size is defined as the range between $1/{e^2}$ of the maximum intensity [34], and since the CW THz source emits a Gaussian beam, the THz beam reaching the detector is also considered a Gaussian beam. The 1st-order and −1st-order diffraction efficiencies were evaluated in the same way for the ranges from 22° to 80° and from −80° to −22°, respectively. The −1st-order diffraction efficiency was measured to be 0.215, 0.334, 0.354, 0.158, and 0.190 at 0.300, 0.350, 0.400, 0.450, and 0.500 THz, respectively (Table 3). The efficiency of 0.354 at 0.400 THz was 1.4 times that of Refs. [20] and [21], which reported wide-angle beam steering. The dips in the −1st-order diffraction efficiency at 0.369 and 0.436 THz in the calculation results shifted to 0.375 THz and 0.444 THz, respectively.
Fig. 11. Transmittance normalized by the sum of power measured without sample. Transmittance measured (a) without the sample and (b) with the sample. (c) Measured results of the 0th-order, 1st-order, and −1st-order diffraction efficiencies.
7. Discussion
The measured diffraction efficiency curves showed interference with a period of approximately 0.015 THz. This interference was also observed when the wave source and detector faced each other without the sample and was clearly observed when the detector was tilted. The interference is considered to be caused inside the detector.
The lack of perfect collimation of the incident light is a possible reason that the measured −1st-order diffraction efficiency was lower than the calculated efficiency. The radiation angle of the THz source was 15° at 0.500 THz, and the spot size radius of the THz waves incident on the collimating lens was 6.8 mm. The spread angle θb of the beam passing through the lens is given by Eq. (7) [34],
where r is the spot size radius. Equation (7) indicates that the THz waves entered the sample at a spread angle of 5.5°. It is considered that diffusion and interference inside the sample caused the difference between the measured and calculated results. Fabrication errors are also considered to be a reason that the measured −1st-order diffraction efficiency was lower than the calculated efficiency. In studies of metalenses and waveguides, the same Si devices as in this study, it was reported that fabrication errors such as structural fillet errors, structural tapering, and roughness of sidewalls cause transmission phase errors and scattering in each unit cell, which in turn affect focusing efficiency and scattering loss at THz frequencies [35–37]. These fabrication errors were also observed in the BS-SWG, which could have affected the efficiency decline.This study used scalar diffraction theory as a guideline for the BS-SWG design. However, the scalar diffraction theory is valid under the condition that Λ is much larger than wavelength λ. The diffraction gratings follow the vector diffraction theory under the condition that Λ is approximately equal to λ, where the diffraction properties are obtained by numerical calculations. When optimizing the BS-SWG with Λ ≈ λ, it is necessary to use numerical design methods such as the rigorous coupled wave analysis method [33]. Nevertheless, even the BS-SWG, not optimized by vector diffraction theory, showed greater efficiency than the reported blazed gratings and metamaterials. Optimization could lead to even higher efficiencies and wider beam steering angles.
8. Conclusion
In conclusion, we experimentally demonstrated that Si subwavelength structures with through-holes exhibit wide-angle, high-efficiency THz beam steering in the Beyond 5 G/6 G communication bands. First, we fabricated uniform SWGs with different FFair values and experimentally evaluated the control of the effective refractive index, which we expected to be controllable with an error of ±0.10 for FFair ≤ 70.8%. The BS-SWG was designed with a beam steering angle of 45.5° and an efficiency of 0.708 at 0.4 THz by calculation. The calculated efficiency was higher than that of an optimized blazed grating or reported wide-angle beam steerers. Measurement of the BS-SWG revealed beam steering angles of −74°–−34° at 0.300–0.500 THz and an efficiency of 0.354 at 0.400 THz. The FZ-Si BS-SWG can provide high efficiency and wide beam steering angles for THz applications.
Funding
Core Research for Evolutional Science and Technology (JPMJCR2102).
Acknowledgments
This work was partially performed in the Micro/Nano-Machining Research and Education Center, Tohoku University, Japan.
Disclosures
The authors have no conflicts to disclose.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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