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Abstract
High-index dielectric metasurfaces are rarely reported around 0.1-0.3 THz, as an extremely large etching depth is needed according to the millimeter-scale wavelength. In this work, we propose an easy solution to sub-THz wideband polarization control by utilizing 3D-printed low-index (n~1.5) metagratings. The metagrating with subwavelength lattice is shown as a very efficient half-wave plate (net polarization conversion of 87%) at 0.14 THz but showing noisy spectrum. The design with superwavelength lattice offers a smooth and wide bandwidth for linear polarization rotation. Study of the mechanism shows that the lattice size slightly above wavelength is a better choice for the low-index metadevice as it maintains high efficiency in the zero diffraction order and wide bandwidth due to the small mode dispersion. Such designs offer a feasible solution especially suitable for sub-THz polarization and phase control, complementary to the existing high-index dielectric and metallic metasurfaces.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The past decade has witnessed remarkable progress in the so-called terahertz (THz) gap from 0.1 THz to 10 THz [1,2]. Such progress ensures wide usage of THz technology in many fields including next-generation communications [3], biological imaging and quality monitoring [4–6]. Functional passive devices such as lenses [7], splitters [8], wave plates [9], and waveguides [10] are indispensable in various THz systems.
To overcome the limitations of natural materials, metamaterials, their 2D counterpart, metasurfaces, have offered an outstanding platform for compact wave-front manipulation and polarization control [11]. Generally, metallic metasurfaces usually lead to poor efficiency due to the absence of magnetic response [12,13]. In contrast, high-index dielectric metasurfaces offer a simple and effective solution with one-step lithographic fabrication. Recently silicon metasurfaces working at 1THz have been reported for Bessel beam and vortex beam generation [14,15]. However, at sub-THz frequencies, i.e. the G-band around 0.1-0.3 THz, dielectric metasurfaces need an extremely large etching depth according to the millimeter-scale wavelength, which is quite challenging. On the other hand, the computer numerically controlled milling tools used in microwave cannot offer enough lateral resolution for the subwavelength inclusions. As such, there forms a gap of the metadevices working at the sub-THz range. The most promising application of the sub-THz band is the body scanning and package inspection for safety control in air and rail transport [16,17], where compact metasurface devices are highly desired for phase and polarization manipulation in the system.
3D printing has been found to be especially suitable for structure processing in this spectrum due to the following reasons: fine enough in-plane resolution, large enough printing depth and THz-transparent polymer materials, with additional merits of low-cost, versatile and fast fabrication process. Examples of 3D-printed prototypes include waveguides and splitters at 0.12 THz [18], lenses and axicons at 0.3 THz [19,20], diffraction gratings and phase plates at 0.2 THz [21,22]. Most of the printed structures share the same shapes as the conventional ones, which rely on the profile curvature for beam shaping. The printable materials are usually polymers with extremely low index around 1.5. Metasurfaces made of such low-index dielectric are rarely studied until now. The constitutive inclusions will be larger and thicker compared to that of high-index dielectric. The increased thickness will bring undesired disruption in the spectrum, as will be studied in detail. And the increased lateral size of the inclusions leads to phase profile with poor spatial resolution if wave-front shaping is needed.
In this work, we explore the problems and the solutions specific to the low-index metasurfaces through the half-wave plate (HWP) application around 140 GHz. We find the spectral response of the device is accompanied with dense resonance dips. Further study shows that the dense resonance comes from low form birefringence and thus increased grating thickness, which is finally attributed to the low refractive index. We propose a simple and effective solution to avoid the resonances and demonstrate a wideband HWP by using the grating with superwavelength lattice for the first time. The physics behind is thoroughly studied.
2. Half-wave plate with subwavelength lattice
2.1 Design
The schematic of a dielectric grating is depicted in Fig. 1(a). With the lattice period P smaller than the wavelength, there exists only the zero-order diffraction. The grating exhibits the form birefringence resulting from different effective permittivities in the TE and TM modes of the slab when the electric field is y-polarized and x-polarized, respectively. A HWP can be demonstrated by suitably designing the lattice period P, the width of the slab a and the thickness H of the grating in order to achieve near unity transmission and the phase retardation of π between the two modes.
Fig. 1 (a) Schematic of a dielectric grating. (b) Top view and (c) side view of the 3D-printed HWP sample.
The HWP is designed to operate at 140 GHz with the printing material chosen as polylactic acid (PLA). In order to accurately measure the refractive index of PLA at the working frequency, we print a group of slabs with different thicknesses and measure the transmission intensities. The refractive index is numerically fitted to be 1.57 + 0.0003i. THz time-domain spectrum (THz-TDS) is not accurate at such low frequency due to the small signal-to-noise ratio. Finite-difference time-domain method is utilized for characterization by sweeping the geometric parameters. The lattice period P is kept as 2 mm, which is right below the wavelength to repress higher diffraction orders. A 2 mm thick substrate made of PLA is considered to support the grating structure. The thickness H and the duty a/P of the grating are swept in the simulation. The performance of the HWP can be characterized by two parameters, the transmission efficiency (T) and the polarization conversion rate (PCR). The former implies the total transmitted power ratio, and the later characterizes the purity of the polarization conversion through the following definitions, respectively:
where and stand for the transmittance of the cross-polarized and co-polarized beam with the polarization direction towards 45° relative to the x and y axis. and can be derived based on the transmission coefficients of x (TM) and y (TE) polarizations throughT and PCR with different H and duty are shown in Figs. 2(a) and 2(b). Due to the low refractive index of PLA, reflection is weak and T is relatively large over the searched area. However, large PCR is possible only when H is large enough with proper selection of duty. The product of T and PCR is the net polarization conversion efficiency, which is plotted in Fig. 2(c). H = 8 mm and duty = 0.3 are finally chosen for the HWP to reconcile the small thickness and the large feature size. The theoretical PCR and T are 0.96 and 0.98 at this point. But wide range of duty and H around this point will offer sufficient performance, which makes the design very robust to possible fabricating errors.
Fig. 2 Simulated (a) T and (b) PCR and (c) T•PCR as functions of duty and H, with P and h both kept as 2 mm.
2.2 Fabrication and measurement
A commercial Raise3d N2 3D printer is used to produce the HWP with a nozzle diameter of 0.2 mm. The device is printed on a glass plate at the temperature of 215°C. The layer thickness and the printing speed are set as 0.15 mm and 60 mm/s, respectively. A supporting PLA slab is printed first with lateral size of 5.2 cm × 5.2 cm and thickness of 2 mm, on top of which is the grating structure. The printed sample is shown in Figs. 1(b) and 1(c). All the dimensions closely agree with the design, and the sidewall is vertical and smooth despite of the relatively large thickness.
The experimental setup is shown in Fig. 3 for characterization of the HWP. A continuous wave source IMPATT diode working at 0.14 THz radiates a vertically polarized beam with the output power of 30 mW. A HDPE lens L is used to collimate the THz radiation with the focal length of 10 cm. A polarizer P1 is inserted between the source and the lens to further purify the polarization. The sample is put in a way that the grating slab is 45° relatively to the incident polarization. Another polarizer P2 is inserted after the sample for the analysis of the polarization state when necessary. A Schottky diode detector is mounted on a 2D translational stage in order to measure the spatial intensity profile with the step resolution of 2 mm and the scanning area of 80 mm × 80 mm. A lock-in amplifier (Stanford Research System SR-830) with 500 Hz modulation rate is connected to the source and the detector to extract a reliable signal.
Fig. 3 (a) Schematic plot and (b) photograph of the experimental setup. P1 and P2 are polarizers, and L is a collimating lens.
Intensity distribution without and with the HWP is shown in Figs. 4(a) and 4(b), respectively, with intensity both normalized to the peak intensity of source. The peak transmission intensity is 0.91. To validate the polarization conversion quality, the polarizer P2 is rotated by 360°. The transmission intensities with and without the HWP are measured as the blue and red dots. The blue and read lines are the intensity distribution of perfect y and x polarized beam under different analyzer angles, respectively. Two sets of results are closely overlapped with theory, indicating a successful polarization conversion from vertical to horizontal directions. Here T of 0.91 and PCR of 0.96 are achieved in the experiment with and. The HWP works well with the net polarization conversion efficiency of 0.87.
Fig. 4 (a) Intensity distribution without and (b) with the HWP. (c) Transmission with different polarizer angles. The blue and the red lines are from perfect y and x polarized beam. The blue and red dots are the measured result without and with the HWP.
3. Bandwidth performance
As the source frequency is not tunable, we cannot obtain the bandwidth of the HWP in experiment. Instead, the spectral response is obtained by simulation in Fig. 5(a). It is observed that there are many resonance dips in the spectrum of the net polarization conversion efficiency T•PCR, where 140 GHz is located between two resonances. If the dips are neglected, the HWP shows good performance from 125 GHz to 145 GHz. However, the narrow dips significantly deteriorate the wideband performance. Comparison of such noisy spectrum with the TE and TM transmittance of the grating in Figs. 5(b) and 5(c) shows that a portion of the dips is from TE polarization and the rest of them from TM polarization.
Fig. 5 (a) T•PCR over frequency in the designed HWP. Transmittance spectrum for (b) TE and (c) TM mode.
In fact, the increased resonance dips have been observed in the low-index silicon nitride metasurfaces [23], where the physics behind is not thoroughly explored. Here the metasurface is made of dielectric with even lower refractive index and the dense resonances become a big issue. For clarity, we next focus on the TE polarization and analyze the physics behind the dips. The conclusion is applicable to TM polarization.
We consider the propagation modes supported in the periodic subwavelength grating through the Rigorous Coupled Wave Analysis. The designed grating supports two eigenmodes TE1 and TE2 at 140 GHz, with the mode index shown in Fig. 6(a). The cutoff frequency of the second eigenmode is 123.0 GHz, below which the slab only supports a fundamental mode. The first two dips in TE polarization come from the self-cancellation due to the existence of the substrate, which will disappear if the substrate is neglected. The rest of the dips are densely distributed at the beginning of the two-mode region. Figure 6(b) shows the amplitude and phase retardation of TE1 and TE2 at the grating-air interface when the light is illuminated from the substrate side. A resonance dip exists whenever two eigenmodes have the same amplitude and π phase difference at the grating-air interface. As a result, the piecewise bandwidth arises from the destructive interference of the two eigenmodes. Similarly, the resonance dips in TM polarization are due to the cancellation of TM1 and TM2, as shown in Figs. 6(c) and 6(d).
Fig. 6 (a) Effective mode index of TE1 and TE2 over frequency. (b) Amplitude and phase retardation of TE1 and TE2 at the grating-air interface. (c) and (d) Same information as (a) and (b) for TM polarization.
It is observed that the dips are not distributed over the whole spectrum. They appear from the cutoff of the second mode (if the substrate effect is neglected) and disappear around 150 GHz. After that, there is no such resonance although the grating still supports two modes for either polarization. The spectrum can be divided into three zones separated by the cutoff of the second mode and 150 GHz, as indicated in Figs. 6(a) and 6(c). Concentration of the dips in zone 2 can be explained by revisiting the mode dispersion. When the second mode starts to appear, the two modes have very different dispersion. Thereafter, destructive interaction happens frequently in zone 2. In contrast, the two modes share similar dispersion in zone 3, leading to smoother spectrum. In addition, one notice that 150 GHz is exactly a critical point where the lattice size is equal to the wavelength. More than one diffraction order exists in zone 3. Therefore, there is less chance to totally inhibit the zero order.
We next explore possible approaches to reduce or avoid the resonance dips and demonstrate a wideband HWP. Figure 7 shows the transmittance of the TM polarization with different grating thickness. Reducing thickness is helpful to reduce dips. The phase delay between the two eigenmodes is proportional to in a single propagation path. With increased H, even small variation of lead to large variation of the phase delay, and thus resulting in more destructive interaction. The reported silicon metasurfaces usually have subwavelength thickness, where the bandwidth is not affected much by the two-mode interaction. However, limited by the low-index polymer, we have to use large H in order to gain enough phase delay between TE and TM polarizations, inevitably leading to denser resonance dips.
4. Half-wave plate with superwavelength lattice
Zone 3 with superwavelength lattice is found to be away from the dips since the dispersion behaviors of the two modes are close to each other. However, the superwavelength inclusions with more than one diffraction order are rarely used in metasurfaces as they are less efficient by distributing light into several directions. When it comes to the low-index designs, inclusions with the lattice size slightly beyond the wavelength still direct most of the light into the zero diffraction order. So we next design the grating in order to set 140 GHz in zone 3. A set of new parameters are optimized as P = 2.3 mm, duty = 0.4, H = 12 mm, h = 1.3 mm. Here P/λ = 1.07.
Figure 8(a) shows the amplitude and phase delay of the two polarizations when the incident beam is polarized 45° relative to the grating, the cross and co-polarized beam intensities and PCR are calculated in Figs. 8(b) and 8(c). 107 GHz and 130 GHz are the boundaries of the three zones. When targeting at zone 3 and considering transmittance of cross-polarized beam above 0.8, the designed HWP works from 130GHz to 165 GHz around 140 GHz (shadow area in Figs. 8(b) and 8(c)), corresponding to the smooth bandwidth of 25%.
Fig. 8 (a) Amplitude of TE and TM mode and their phase delay when the grating geometry parameters are P = 2.3 mm, duty = 0.4, H = 12 mm, h = 1.3 mm. (b) Transmittance spectrum of cross and co-polarized beam intensities. (c) PCR over frequency.
Please note that zone 1 is the single-mode region where the inclusion can be considered as an effective medium with the refractive index equal to the mode index. The difference of the mode index in TE and TM polarization is the artificial birefringence . The design working in zone 1 has of around 0.11 with negligible dispersion, as indicated from Figs. 6(a) and 6(c) (of crystal quartz is around 0.046 [24] at THz frequencies for comparison). is generally proportional to the frequency in Fig. 8(a) where π phase difference is satisfied only at a single frequency. Therefore, the design targeting zone 1 leads to a narrow-band wave plate, similar to case of the conventional crystal quartz. Current approach to implement a wideband THz wave plate is by stacking several pieces of quartz crystal with well-designed thickness and special crystal orientation [25]. In contrast, by working in zone 3, the monolayer HWP with superwavelength lattice is a much simpler solution to achieve wideband operation.
In experiment, the bandwidth performance of the proposed HWP cannot be accurately characterized in the terahertz time-domain spectroscopy (THz-TDS) due to the low signal-to-noise ratio below 0.2 THz. Here we test the HWP indirectly by scaling the dimensions instead of sweeping the frequency. Taking the lattice period P as an example, a scaling coefficient is defined as , where GHz, mm, and are the scaled values. When all the geometric parameters (P, H, h) are multiplied by the same amount according to the current design in Fig. 8, the response of the scaled grating experiences a frequency shift proportional to . As an example, Fig. 9(a) shows the transmittance spectrum when the grating geometry is scaled to 1.07 and 0.95. The spectrum shifts to the left and the right respectively relative to the original one. By continuously scaling the grating geometry and testing at a fixed frequency 140 GHz, the response over the scaling coefficient in Fig. 9(b) has the same shape as that over frequency in Fig. 8(b). Here duty is kept as 0.4 as P is scaled.
Fig. 9 (a) Transmittance spectrum when the scaled coefficient is 1.07, 1, and 0.95. (b) Photograph of the 5 gratings with different scaling coefficients. (c) Cross and co-polarized beam transmittance (d) PCR by zooming the geometry with different scaling coefficients. The curves are simulation results and the dots with error bar are experimental data.
Considering such correspondence between frequency and dimension, a group of gratings are 3D-printed with scaling coefficients of 0.95, 1, 1.07, 1.12, 1.2, as shown in Fig. 9(b) from bottom to top. For each, three samples are printed and tested. The measured efficiency and PCR are marked on top of the simulation results in Figs. 9(c) and 9(d) as the average value and the error bar (standard error), where a good agreement is achieved. The small fluctuation, which is attributed to the limited resolution of the 3D printer, also demonstrates good repeatability. Samples 1, 2, 3, and 4 are efficient at 140 GHz with high PCR; sample 5 gives poor transmission efficiency as the lattice size is too large to avoid high-order diffraction. The trend of the 5 samples indirectly proves the wideband feature of the superwavelength grating.
5. Summary
To summarize, half-wave plates with conventional subwavelength grating and superwavelength grating are constructed by 3D printing using low-index polymer PLA. The former shows net polarization conversion efficiency of 87%. The characteristic noisy bandwidth is specific to the low-index thick grating due to the destructive interference of the highly dispersive double-modes. The superwavelength grating has been demonstrated with a wide and smooth bandwidth over 25% thanks to the weak high-order diffraction and small mode dispersion. The study here provides a new type of low-index metasurfaces complementary to the existing high-index dielectric and metallic metadevices. Besides of polarization control, flat lenses, beam deflectors, holograms can be implemented in a similar manner, with great potential to enrich low-THz devices.
Funding
National Natural Science Foundation of China (61805123, 61831012), State’s Key Project of Research and Development Plan (2017YFA0701000, 2016YFC0101002), Fundamental Research Funds for the Central Universities, Natural Science Foundation of Tianjin (18JCQNJC02200).
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