Applied Physics A

, Volume 115, Issue 1, pp 83–86

Investigations on polarimetric terahertz frequency domain spectroscopy

Authors

    • Institute for Infocomm ResearchA*STAR
  • Banghong Zhang
    • Institute for Infocomm ResearchA*STAR
  • Takashi Notake
    • RIKEN Sendai
  • Hiroaki Minamide
    • RIKEN Sendai
  • Malini Olivo
    • Singapore Bioimaging ConsortiumA*STAR
  • Shigeki Sugii
    • Singapore Bioimaging ConsortiumA*STAR
Invited paper

DOI: 10.1007/s00339-013-8000-0

Cite this article as:
Gong, Y., Zhang, B., Notake, T. et al. Appl. Phys. A (2014) 115: 83. doi:10.1007/s00339-013-8000-0

Abstract

A polarimetric Terahertz frequency-domain spectroscopy system is presented which has an additional polarization measurement function at the Terahertz band. The achromatic Terahertz waveplate, which acts as the key device in the system, is also presented.

1 Introduction

Terahertz (THz) technology has achieved great progress in the recent years due to T-rays’ special features and broad potential applications. Among the THz technologies, polarization related issues are attracting more and more attention [1], e.g., polarimetric Terahertz Time-domain Spectroscopy (polarimetric THz-TDS), polarization imaging, polarization effects of bio-sample [2] at THz band and so on. All these reports and applications require full polarization information at THz band, like Stokes parameters, birefringence, Polarization dependent loss, Mueller matrix, and so on.

Actually, polarization optics and devices/equipments are very mature at optical wavelength, but they are new issues and challenging at the THz band. If people do not fully understand polarization at THz in a test of an unknown material with polarization effects, mis-explaining of the data/results may be induced, e.g., one may mistakenly explain a polarization-filter effect as an absorption peak. All these occurrences are due to the lack of polarization related equipments at the THz frequencies on the market. Currently THz-TDS and THz Frequency-domain Spectroscopy (THz-FDS) are the major equipments and sensing tools in the Terahertz applications; its THz emitter/detector usually can only generate/response to one vector of the THz fields, therefore such THz-TDS is only suitable for isotropic materials test. The Institute for Infocomm Research had reported the first polarimetric THz-TDS to have additional polarization measurement functions [3, 4]. Here we will present another first-ever polarimetric THz-FDS.

To achieve the polarimetric THz-FDS system, a new polarization function or new devices for such applications are to be developed. Indeed, some polarization method/theory at optical wavelengths can be copied to THz band, but not in all cases, because some components and devices at THz band is still not available yet on the market, e.g., lacking an achromatic waveplate at THz. In this paper, we will systematically review and present our work on the polarization measurement issues on the polarimetric THz-FDS system with the collaboration of RIKEN Japan. It is an upgrading and add-on polarization function on top of the current basic THz-FDS systems. Then we will present the key polarization device, a wideband achromatic THz quarter-waveplate, which will have very common applications in the THz systems in future.

We believe that the investigations on the polarization at THz band will become more and more important, the polarization functions and devices will help to explore and broaden many new THz sensing applications, and push THz much closer to commercialization.

2 Principle

2.1 THz-FDS system

Our experiment was using a basic THz frequency domain spectroscopy set up, in which the quasi-CW THz source is a DAST-based tunable THz source which was developed by RIKEN Japan and had been described in references [5, 6]. The pump laser was a frequency-doubled Nd:YAG laser (532 nm, 8-ns pulse duration at 100 Hz; Nano-L, Litron Lasers). A double-crystal KTiOPO4 (KTP) optical parametric oscillator (OPO) was used to excite the DAST crystal. The vertically polarized output of KTP OPO was focused onto the DAST crystal with a lens. The emitted THz wave from the DAST crystal is collimated by a gold parabolic mirror and then focused onto a detector using another parabolic mirror. A 4K-Si-bolometer, whose sensitivity is about 100 times higher than that of a DTGS detector, was used to monitor the power of received THZ wave. A low-pass filter is used to filter out the wanted THz wave. The polarimetric measurement module was inserted between the two parabolic mirrors.

2.2 Principle and algorithm for SOP measurement

Figure 1 shows the setup of the polarimetric measurement module, where the polarizer P1 is used to generate the wanted SOPs (states of polarization) with the assistance of the half-waveplate (HW); the polarizer P2 is used to realize the SOP measurement with the assistance of the quarter-wave plate (QW). In testing, P1 and P2 are fixed and their polarizing axes are considered as the x-axis of the coordinate system, for example, vertical direction.
https://static-content.springer.com/image/art%3A10.1007%2Fs00339-013-8000-0/MediaObjects/339_2013_8000_Fig1_HTML.gif
Fig. 1

The schematic of a polarimetric THz-FDS system

At the operating frequency of the QWP, by rotating the QWP to four angles θi, i=1,2,3,4, and measuring the corresponding currents Ii, i=1,2,3,4 in detector, the four Stokes parameters can be calculated from the following equation:
$$\begin{aligned} \left ( \begin{array}{l} I_{1} \\ I_{2} \\ I_{3} \\ I_{4} \end{array} \right ) = \frac{1}{2} \left ( \begin{array}{l@{\quad}l@{\quad}l@{\quad}l} 1 & \cos^{2}2\theta_{1} & \cos 2\theta_{1}\sin 2\theta_{1} & {-}{\sin2\theta_{1}} \\ 1 & \cos^{2}2\theta_{2} & \cos 2\theta_{2}\sin2\theta_{2} & {-}{\sin 2\theta_{2}} \\ 1 & \cos^{2}2\theta_{3} & \cos2\theta_{3}\sin 2\theta_{3} & {-}{\sin 2\theta_{3}} \\ 1 & \cos^{2}2\theta_{4} & \cos 2\theta_{4}\sin 2\theta_{4} & {-}{\sin2\theta_{4}} \end{array} \right ) \left ( \begin{array}{l} S_{0} \\ S_{1} \\ S_{2} \\ S_{3} \end{array} \right ) \end{aligned}$$
(1)
In practice, we can use some sets of simpler angles, for example, (−45, 0, 30, 60); using this angle set, Eq. (1) becomes
$$ \left ( \begin{array}{l} I_{1} \\ I_{2} \\ I_{3} \\ I_{4} \end{array} \right ) = \frac{1}{2} \left ( \begin{array}{c@{\quad}c@{\quad}c@{\quad}c} 1 & 0 & 0 & 1 \\ 1 & 1 & 0 & 0 \\ 1 & 0.25 & 0.433 & - 0.866 \\ 1 & 0.25 & - 0.433 & - 0.866 \end{array} \right ) \left ( \begin{array}{l} S_{0} \\ S_{1} \\ S_{2} \\ S_{3} \end{array} \right ) $$
(2)

Last but not least, the parameters we really care about are not four Stokes parameters, but the degree of polarization (DOP) \(\mathit{DOP} = \frac{\sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}}}{S_{0}}\) and the normalized Stokes parameters \(s_{i} = \frac{S_{i}}{S_{0} \cdot \mathit{DOP}}\), i=1,2,3.

2.3 Design of waveplate

As mentioned in the last section, waveplates are key components for the THz-FDS polarimetric measurement system. Moreover, to let the system work in a wide THz frequency range, the waveplate should also be achromatic. Typically, there are two ways to develop THz waveplate, where one way is using a natural birefringence material, such as widely used quartz crystal, and the other way is using a form of birefringence-based waveplates such as silicon grating or transparency grating [610]. For quartz crystal-based achromatic waveplate, it is realized by stacking multiple pieces of quartz crystals with different thickness and orientations [11]. However, it has the drawbacks of significant F-P oscillations, and being lossy and bulky. Comparing with quartz crystal, silicon grating is a better choice for THz waveplate fabricating, because it has low loss at THz band and much higher birefringence than the silicon grating. In our scheme, we developed an achromatic THz waveplate based on silicon grating.

The structure of the grating is shown in Fig. 2, where grating on silicon substrate consists of alternating silicon and air components, with refractive indices n1 and n2, width l1 and l2, and period L. A quasi-static effective medium theory (EMT) is utilized to describe the interaction between a micro grating structure and a THz wave, when the wavelength of the incident wave is much larger than the dimensions of the gratings [12]. When the incident wave propagates along the direction k, as shown in Fig. 1, the grating exhibits effective birefringence which is depicted as TE and TM in Fig. 2. The electrical fields transmit along the TE and TM direction with refractive indices given by
$$ \left \{ \begin{array} {l} n_{\mathrm{TE} 0}^{2} = f_{1} n_{1}^{2} + f_{2} n_{2}^{2} \\ n_{\mathrm{TM} 0}^{2} = \biggl( \displaystyle\frac{f_{1}}{n_{1}^{2}} + \displaystyle\frac{f_{2}}{n_{2}^{2}} \biggr)^{- 1} \end{array} \right . $$
(1)
where f1 and f2 are the fill factors of the silicon and air components, respectively, and f1=l1/L, f2=1−f1. However, when the wavelength of the incident wave is close to and the dimensions of the gratings, the refractive indices are given by second order EMT by [12]
$$ \left \{ \begin{array} {l} n_{\mathrm{TE}}^{2} = n_{\mathrm{TE} 0}^{2} + \displaystyle\frac{1}{3} \biggl( \displaystyle\frac{L}{\lambda} \pi f_{1} f_{2} \bigl( n_{1}^{2} - n_{2}^{2} \bigr) \biggr) \\ n_{\mathrm{TM}}^{2} = n_{\mathrm{TM} 0}^{2} + \displaystyle\frac{1}{3} \biggl( \displaystyle\frac{L}{\lambda} \pi f_{1} f_{2} \biggl( \displaystyle\frac{1}{n_{1}^{2}} - \displaystyle\frac{1}{n_{2}^{2}} \biggr) n_{\mathrm{TE} 0} n_{\mathrm{TM} 0}^{3} \biggr) \end{array} \right . $$
(2)
https://static-content.springer.com/image/art%3A10.1007%2Fs00339-013-8000-0/MediaObjects/339_2013_8000_Fig2_HTML.gif
Fig. 2

The schematic of silicon grating

Hence, to design silicon grating-based waveplate, we choose an appropriate period L and fill factors according to the operating THz frequency. Then, the birefringence can be determined by the equations above, and the depth d of the grating can be calculated based on the phase retardation of the waveplate.

3 Experimental results

For our THz TDS polarimetric measurement system, we designed normal QWPs and achromatic QWPs based on silicon grating, and the QWPs are measurement under our THz TDS system. A silicon wafer with resistivity larger than 2000 Ω∗cm was used to fabricate the QWPs described above. The deep reactive ion etching (DRIE) process is used to fabricate gratings.

Figure 3 shows the measurement scheme of the QWPs. Polarizer 1 was used to generate a linear polarized THz beam. The gratings are aligned at 45 degree with respect to polarizer 1. Hence, the output THz beam will be circularly polarized beam at a specified frequency where a grating perform as a QWP. Polarizer 2 was used as a polarizer analyzer when rotated with various angles. For circularly polarized beam, the obtained power at different angle will be same; for elliptical polarized beam at other frequencies, the obtained power varies with the angles.
https://static-content.springer.com/image/art%3A10.1007%2Fs00339-013-8000-0/MediaObjects/339_2013_8000_Fig3_HTML.gif
Fig. 3

The schematic of the QWP characterization setup

The intensities in Fig. 4 are obtained when THz radiation travels through the QWP and polarizer 2, where polarizer 2 is placed at various orientations to obtain intensity at 0, 45, −45, 90 degree. Then the intensity ratios of 0/−45, 0/45 and 0/90 are calculated and shown in Fig. 4. As mentioned above, the ratios should be of a constant value of 1 for a circularly polarized beam at right QWP operating frequency. At other frequencies, the output SOP after QWP (before polarizer 2) is most possibly an elliptical SOP orientated at any angles, which may lead to the ratios >1 or <1. Figure 4 shows the performance of two gratings. The ratios in Fig. 4(a) converge at 1 at the frequency of 5 THz, which means the grating performs as QWP at 5 THz. Similarly, ratios in Fig. 4(b) converge at 1 in the range 4∼5 THz, which means an achromatic QWP at 4∼5 THz.
https://static-content.springer.com/image/art%3A10.1007%2Fs00339-013-8000-0/MediaObjects/339_2013_8000_Fig4_HTML.gif
Fig. 4

Intensity ratios for (a) normal quarter waveplate at 5 THz; (b) achromatic quarter waveplate at 4∼5 THz

It is already mentioned in Sect. 2.2 that QWPs can be used to measure the state of polarization (SOP) of THz radiation in a THz-FDS system. To further investigate the performance of the QWPs, we use the two QWPs in Fig. 5 as an ideal device to measure the given SOP (1,0,0) of the system. Figure 5(a), which is measured by the normal QWP, shows the SOP of the system is nearly (1,0,0) and the DOP nearly 1, which agree well with the given SOP. Similarly Fig. 5(b) measured with achromatic QWP shows good agreement with the given SOP of the system in 4∼5 THz. Note that the DOP value in Fig. 5 is only valid at the working frequency point/range of the QWPs, due to the pre-assumption of the algorithm.
https://static-content.springer.com/image/art%3A10.1007%2Fs00339-013-8000-0/MediaObjects/339_2013_8000_Fig5_HTML.gif
Fig. 5

SOP and DOP measurement of (a) normal QWP at 5 THz; (b) achromatic QWP at 4∼5 THz

4 Conclusion

The polarimetric THz frequency domain spectroscopy system was described, and polarization measurement methods in polarimetric THz-FDS have been investigated. A key device of wideband achromatic THz waveplates for upper THz band has been developed. All the test results show their good performance.

Acknowledgements

This work is supported by the joint project between A-STAR of Singapore and JST of Japan with A-STAR/SERC grant No.: 102 163 0069.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013