25 February 2013 Thin-form birefringence quarter-wave plate for lower terahertz range based on silicon grating
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We have developed a thin quarter-wave plate (QWP) operating at low terahertz frequency of 0.51 THz by etching micro-grating on a silicon substrate. The grating period is 30 μm, and the etching depth is 156 μm. Stokes parameters are used to characterize the QWP. The QWP shows a high transmission coefficient of 0.93 and a low polarization dependent loss (PDL) of 1.4 dB at 0.51 THz.



At present, terahertz technology has drawn significant attention due to its numerous applications in material inspection,1 semiconductor and medical imaging,2 security imaging, and communications.3 A variety of devices have been demonstrated and applied in real cases, including wave plates,4 filters,5 and phase shifters6 based on birefringence materials. Devices using form birefringence have a smaller size in comparison with natural birefringence materials, hence their being more suitable for integration.7 In this letter, we aim for developing a quarter-wave plate (QWP) using grating based on form birefringence structure operating in lower terahertz frequency range (0.51 THz in our work). Previous studies have demonstrated QWPs using various materials such as one-dimensional photonic crystals,7 stacked paper,8 polyethylene (HDPE),9 transparencies,10 and silicon wafers.11 However, most of the QWPs, especially those which operate at low frequency ranges, have relatively large sizes.

In this letter, a thin QWP is presented with an operation frequency of 0.51 THz. The QWP is fabricated using a deep reactive ion etching (DRIE) technique to achieve a 156-μm-deep grating on a silicon substrate. Stokes parameters are utilized to characterize the QWP, which shows a good performance at 0.51 THz. The transmission coefficient and polarization dependent loss (PDL) are 0.93 and 1.4 dB at 0.51 THz, respectively.


Design and Fabrication

The structure of QWP is shown in Fig. 1(a), where a grating on silicon substrate consists of alternating silicon and air components, with refractive indices n1 and n2, and width l1 and l2, respectively. A quasi-static effective medium theory (EMT) is utilized to describe the interaction between the micro grating structure and a THz wave, when the wavelength of the incident wave is much larger than the period of the grating.7 When the incident wave propagates along the direction k, the grating exhibits effective birefringence, which is depicted as TE and TM in Fig. 1(a). The electrical fields transmit along the TE and TM directions with refractive indices given by




where f1 and f2 are the fill factors of the silicon and air components respectively, and f1=l1/(l1+l2), f2=1-f1. Our target operation frequency of the QWP is 0.5 THz, which corresponds to a wavelength of 600 μm. The grating period is set to 30 μm, which is much smaller than the wavelength, so that the quasi-static EMT is satisfied. Fill factors are set as f1=f2=0.5. The refractive index of silicon is 3.415. The calculated effective refractive indices are nTE=2.55, nTM=1.38. The grating depth for a QWP at 0.5 THz is calculated as 130 μm.

Fig. 1

(a) Structure of silicon grating; (b) microscope view of the fabricated QWP sample.


A 1-mm-thick, orientation 100, double side polished silicon wafer with resistivity larger than 10Ω*cm was used to fabricate a QWP described above. The wafer was coated with 1.2-μm-thick S1813 photo resist and soft baked at 100°C for 100 s. Then the wafer was exposed using a mask plate in a Suss MA8 aligner for 7 s at 17-mW/cm2 power and developed in MF-320 developer for 60 s. An MUC-21 (Surface Technology Systems) etching system was used in the DRIE process. The silicon wafer was etched in SF6 (200 SCCM, 10 s, 3 Pa) and C4F8 (85 SCCM, 3 s, 2 Pa) cycling for 50 min. The coil and plate powers were 600 Watt and 15 Watt, respectively. In our preceding measurements, the calculation of the 130 μm grating was found to deviate a bit from the real result, due to the slightly inaccurate solution of the EMT.12 The etching depth was then optimized to 156 μm. Figure 1(b) shows the fabricated grating, where the widths of the silicon and air gap are 15.5 and 14.3 μm, respectively.



The fabricated QWP is measured using our self-built polarimetric terahertz time domain spectroscopy system.13 As shown in Fig. 2, the incident THz beam is firstly linear polarized by polarizer 1, and then perpendicularly enters the QWP sample. Polarizer 2 acts as a polarization analyzer by rotating with different angles. The TE direction of the QWP sample is located at 45-deg with respect to the direction of polarizer 1. In this case, the incident wave is equally split into TE and TM components. After transmitting through the QWP, once the phase difference between TE and TM components equals to 90-deg, the output signal will become a circularly polarized beam. The time domain pulses are measured and shown in Fig. 3, when polarizer 2 is located at 45-deg (TE) and -45-deg (TM), respectively. The TE component is retarded 0.53 ps than TM component in Fig. 3. Fresnel reflection in the 1-mm-thick silicon substrate can also be observed as two small peaks separating from the main pulse by 21.6 and 19.3 ps for TE and TM components respectively.

Fig. 2

Schematic figure of measurement system.


Fig. 3

Time domain pulses measured with different angle of polarizer2.


The QWP is also characterized using Stokes matrix.14 Figure 4 shows the calculated Stokes parameters, and corresponding fitting curves. The Stokes parameters (S1, S2, S3) are close to (0, 0, 1) at around 0.5 THz, which means a circularly polarized beam as depicted in Fig. 2. The curve of S2 is deviated a little from the ideal value of 0. This deviation possibly originates in the following reasons: the inherent noise of testing system, polarization dependent loss (PDL) of the QWP sample, and the angle deviation of exactly 45 deg. By our calculations, a Stokes parameter at 0.51 THz has the minimum variance 0.0015, with respect to (0, 0, 1). The small frequency deviation from 0.5 THz may be due to the variance in fabrication and scaling of the grating.

Fig. 4

Calculated Stokes parameters which is close to (0, 0, 1) around 0.51 THz.


The transmission coefficient of the QWP is measured and shown in Fig. 5, where the measured data is fitted using a finite impulse response (FIR) low pass filter. The silicon grating has a transmission coefficient larger than 0.6 in the range of 0.3 to 1 THz. The transmission coefficient at 0.51 THz is 0.8 in calculated data and 0.93 in fitting curve. The PDL is also calculated and shown in Fig. 5. A continuous curve fitting by FIR low pass filter shows less than 2 dB PDL in the overall range. The PDL is about 1.4 dB at 0.51 THz from fitting curve. Moreover, less loss can be achieved using silicon substrate with much higher resistivity, and an anti-reflection coating can also improve the transmission coefficient.11

Fig. 5

Calculated transmission coefficient and PDL of the QWP.




In this letter, we designed and fabricated a thin quarter-wave plate operating at a lower terahertz frequency of 0.51 THz, with thickness of 156 μm, high transmission coefficient of 0.93 and low PDL of 1.4 dB at 0.51 THz. Less loss can be achieved using silicon substrate with much higher resistivity and anti-reflection coating.


This work is supported by the international joint project between A-STAR of Singapore and JST of Japan with A-STAR/SERC/SICP grant No. 1021630069. The authors would like to thank Vincent Lim from IMRE A-STAR of Singapore for mask making.


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© 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)
Banghong Zhang, Banghong Zhang, Yandong Gong, Yandong Gong, Hui Dong, Hui Dong, } "Thin-form birefringence quarter-wave plate for lower terahertz range based on silicon grating," Optical Engineering 52(3), 030502 (25 February 2013). https://doi.org/10.1117/1.OE.52.3.030502 . Submission:

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