1. Introduction

Electromagnetic radiation in the terahertz (THz) spectral range is important because it is sensitive to many characteristic phenomena, such as the response of the conduction electron of metal and semiconductor, identification of molecules and so on [1] [2] [3]. The recent development of time-domain spectroscopy (TDS) based on ultra short pulsed lasers, has made it possible to perform measurements covering a wide spectral region ranging from the far to the near infrared [4] [5].

Polarimetry in the THz spectral region has strong potential for applications such as noncontact Hall measurement by magneto-optic effect [6] [7], identification of chiral molecules, sensing, study of the chiral structure of proteins and DNA, etc [8][9]. Thus, attempts to develop polarimetry in the THz region have been reported [10] [11] [12]. However, polarimetry in the THz region is hampered by a lack of good polarization devices for the THz frequency range. Wire grid polarizers (WGP’s) are often used in the THz region [13], but no efficient wave plate or polarization modulator is available. In particular, an element that rotates the polarization of the THz wave independently of the polarization of incident wave, that is, a polarization rotator, would be needed. Such a component would be similar to the optical activity of visible light obtained with a solution of chiral molecules. Recently, much attention has been focused on the creation of artificial structures called metamaterials having a designed permittivity and permeability. In particular, various attempts to control THz waves have been proposed and demonstrated [14] [15]. THz polarization effects with arrays of screw holes were observed [16].

With advances in nano-fabrication technologies, it has become possible to fabricate gratings with structured units. Polarization-sensitive effects of visible light using two-dimensional gratings composed of metal nanostructures without mirror symmetry have been proposed [17] and strong optical activity has been reported [18] [19]. Spectroscopic measurements revealed that the excitation of surface plasmons induces enhanced optical activity [20].

It is natural to apply this method to the control of the polarization of a THz wave. By adjusting the shape of the unit and the period of the grating, the plasma frequency can be shifted to the THz region [21] [22]. Since the wavelength of a THz wave is about three orders of magnitude above that of visible light, the shape and size of the structures can be controlled accurately. Thus experiments in the THz region are suitable for systematic measurements with various configurations.

Recent analyses on polarization effects in single-layered chiral metal gratings for visible light revealed that surface plasmons induce twisted electric fields at the air-metal and metal-substrate interfaces, and induce giant optical activity [23]. In the THz region, however, thickness of the evaporated metal film which is comparable to the penetration depth of the THz wave is too thin to induce strong displaced twisting fields.

In this letter, we propose a new structure of quasi two-dimensional chiral grating for enhanced optical activity in the THz waves. The proposed structure is a planar grating consisting of two displaced thin metal layers with complimentary patterns which do not have mirror symmetry. The structure can be fabricated by a single patterning process in contrast to the recently reported double-layered structures fabricated by advanced fabrication processes [19] [27]. We also developed a method of THz polarimetry to determine the diagonal and off-diagonal parts of the complex permittivity tensor of these samples. The precise control of the structures allows us to realize an isotropic polarization rotator in the THz region.

2. Experiment

Figure 1 shows the schematic diagram of the experiment. We fabricated arrays of achiral and chiral structures by depositing a thin gold film on a resist layer (ZEP520A-7, ZEON) placed upon a high-resistance Si substrate and patterned by electron-beam lithography. The obtained samples, without lift-off treatment, have two metal layers with complementary patterns and a displacement of 180 nm, which corresponds to the thickness of the resist. We chose a typical thickness suitable for patterning in the range to obtain displacement larger than the thickness of the metal layer, 100 nm. We also fabricated usual single layer samples for comparison purposes by performing a lift-off process, in which the resist layer was removed after metal-layer deposition. The gratings are arranged in a two-dimensional square periodic structure, and the period is 100 µm. The thickness of the Si substrate is 385 µm, the thickness of the gold film is 100 nm, and the thickness of the resist layer is 180 nm. A thin Cr film of 5 nm thickness is first deposited on the bare substrate to improve adhesion [Fig. 1(b)]. The achiral structure is a cross pattern, and the chiral structures are a right- and left-twisted gammadion patterns as shown in Fig. 1(a). Having a four-fold symmetry, the structure is isotropic which allows for observation at normal incidence with no birefringence.

A regenerative amplified Ti:sapphire laser with a 120 kHz repetition rate, a center wavelength of 800 nm, and a 280 fs autocorrelation pulse width is used as a light source. For the generation and detection of THz radiation, we employ optical rectification and free-space electro-optic (EO) sampling [24][25]. (110)-oriented ZnTe crystals 0.3 and 1 mm thick are used for THz generation and EO sampling detection, respectively. The generated THz radiation is focused onto the sample at normal incidence down to a diameter of about 1 mm by a gold-coated off-axis parabolic mirror with a 150 mm focal length.

Figure 1(c) schematically shows the procedure of THz-TDS based polarimetry to determine the polarization vector of the transmitted wave. We have developed a scheme with three polarizers similar to a previously reported method [26]. We use the first wire grid polarizer (WGP1) to obtain an incident wave that is linearly polarized in the y-direction. To detect the change in the polarization states, we use another wire grid polarizer (WGP3) as a crossed analyzer detecting the x-component of the signal by EO sampling with a ZnTe crystal. To obtain the vectorial information of the arbitrary polarized THz wave, we insert a third wire grid polarizer (WGP2) and vary its orientation. With this method, WGP2 extracts the polarization components of the transmitted THz wave at -45°and +45° with the horizontal (x) axis (E₁(t) and E₂(t), respectively). The phase and amplitude of the y- component of the transmitted THz wave (E_y(t)) can be obtained by the subtraction of E₁(t) from E₂(t).

 

Fig. 1. (a). Experimental scheme and achiral, right- and left-twisted gammadion grating structures. When the linearly polarized incident THz wave is transmitted through the sample, the transmitted wave is polarized elliptically. Definition of the elliptical polarization with the polarization azimuth rotation angle θ and ellipticity η, which are defined in this figure. (b) Schematic figure of sample structure. Cross section of left-twisted structure is shown. (c) The three measurement configurations of the THz polarimetry with three wire grid polarizers (WGP’s).

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From the first step measurement, we can measure E_x(t) with high sensitivity and from the second and third steps, we can determine E_y(t) without altering our basic experimental setup. This scheme is ideally suited to determine with a high sensitivity the x- and y-components the THz wave transmitted through the sample.

In addition to this, we measured the electric field of THz radiation without the sample, (E ^ref) as the reference signal of the incident wave. By performing a Fourier transform to the electric field in the time domain, the electric field vectors in the frequency domain (Ẽ^sam(ω) and Ẽ^ref(ω)) can be obtained as complex vectors. We evaluated the complex Jones matrix of the samples by comparing Ẽ^sam(ω) with Ẽ^ref(ω).

3. Result

The waveforms of the electric field obtained with the cross-Nichol configuration are shown in Fig. 2(a), and those obtained with the angle of WGP2 at -45°and +45°with x axis are shown in Figs. 2(b) and 2(c) respectively. The green curves show the signals without sample indicating the waveform of the incident wave, E ^ref. The relative delays between the signals with and without a sample correspond to the propagation delay times of the THz pulses during the propagation through the samples.

 

Fig. 2. Time domain THz waveforms of transmitted waves obtained in the cross-Nichol arrangement (a), with WGP2 -45°(b) and +45°(c). The green curves show a reference signal measured without sample. The red, blue and black curves show the signal for right- and left-twisted gammadion samples and cross-patterned samples, respectively. By Fourier transform, the x- and y- elements of the electric field in frequency domain are calculated and shown in (d) and (e). Absolute value of electric fields is shown in Fig. (d)

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In Fig. 2(a), the chiral samples show pronounced orthogonal components of the electric fields and the sign of the electric fields are opposite for right- and left-twisted gammadion samples. This means that the polarization rotation occurs for chiral patterns, and the rotation direction is reverted depending on the chirality of the unit cell pattern. The frequency domain spectra of the amplitude, Ẽ_x(ω)’s shown in Fig. 2(d), are almost the same for right- and left-twisted patterns, and much larger than that of the cross pattern. The slight difference observed between the spectra of left- and right-twisted patterns is mainly due to the limitation of reproducibility in the pattern fabrication. It should be noted that the crossed component shown in Fig. 2(a) shows a non-zero signal even without a sample or with the cross pattern. This is due to the imperfectness of the WGP’s. In the actual experiment, the transmitted THz wave from a wire grid polarizer does not show perfect linear polarization but a slightly elliptical one. Since such a leakage component is comparable to the signal of interest, we need to take into account this effect precisely. We evaluate the polarization characteristics of the WGP’s experimentally, model the Jones matrices of WGP’s and use them in our polarimetry analyses.

In our previous measurements of the visible region [20], the samples showed finite asymmetry due to a slight astigmatism of the electron beam. Therefore we extracted such a deviation of samples experimentally. In the present experiment, we also examined the anisotropy of the samples by rotating it along the normal to the grating plane. We did not detect any deviation within the accuracy of the measurements. Therefore, it is reasonable to assume a perfect four-fold symmetry of the sample in the analysis of this measurement.

We measured the electric field of THz radiation transmitted through the sample Ẽ^sam and the reference field Ẽ^ref in the frequency domain by the method we explained above. It should be noted that the electric field vector of the incident wave, Ẽ^ref, has both x- and y-components due to the imperfectness of WGP’s as mentioned above. These two vectors, Ẽ^sam and Ẽ^ref, are related by

where T̃ is the Jones matrix of the sample. Considering the four-fold rotation symmetry, this matrix is described as $\tilde{T}=\left[\begin{array}{cc}{\tilde{t}}_1& {\tilde{t}}_2\\ -{\tilde{t}}_2& {\tilde{t}}_1\end{array}\right]$. This matrix is constant under any rotation operation, so the polarization rotation does not depend on the orientation of the polarization of the incident wave. From the measured values of Ẽ^sam and Ẽ^ref, we solve Eq. (1) and obtain t̃₁ and t̃₂ as a function of frequency,

We performed such analyses in the frequency range between 0.2 and 2.5 THz. Figure 3(a) and (b) show the obtained values of |t̃₁| and |t̃₂|. The errors show the standard deviations for the statistical fluctuation after repeating the measurements eight times. The signal of achiral sample of the cross-Nichol configuration [Fig. 2(a)] is described as Ẽ^samx=t̃₁ Ẽ^ref _x.

The polarization azimuth rotation and ellipticity angle spectra for the incident linear polarization are calculated from the Jones matrix by the following relationships.

Figures 3(c) and 3(d) show the obtained spectra of polarization azimuth rotation θ and ellipticity angle η. Large rotations of about 1.5 degrees are observed at 0.4 THz and 1.2THz, about 1 degree at 0.8THz.

From the obtained complex Jones matrix of the sample, we can determine the complex effective dielectric tensor of the sample as a whole, including the Si substrate. Because of its symmetry, this tensor should have the form: $\left[\begin{array}{cc}\tilde{\epsilon }& \tilde{\delta }\\ -\tilde{\delta }& \tilde{\epsilon }\end{array}\right]$. Following the method of usual THz-TDS, the diagonal element $\tilde{\epsilon }$=ε₀ñ² is determined by solving with a Newton-Raphson method the equation

where L is the total thickness of the sample.

Then, the off-diagonal element $\tilde{\delta }$ is determined by the equation:

Figures 3(e)–3(h) shows the spectra of the elements of effective dielectric tensor calculated this way. A prominent resonant feature is observed in the vicinity of 0.4THz, which originates from the grating structure.

4. Discussion

We clearly observe the isotropic optical activity in symmetry-controlled quasi two-dimensional structures. Spectroscopic analyses of the visible region revealed that the optical activity in the quasi-two dimensional planar chiral nanogratings should be ascribed to the non-local light matter interaction caused by the three-dimensionality of the induced electric fields. The resonant excitation of surface plasmons at the air-metal and metal-substrate interfaces, induces a morphology-dependent non co-planar twisted electric field distribution. The broken mirror symmetry of chiral patterned samples brings the non-vanishing contribution averaged over the entire structures. In the visible experiments, the asymmetry of surface plasmon resonances at two interfaces plays a key role for the enhancement of such effects [20] [23].

In the case of a THz experiment, the skin depth d_skin of surface plasmons at 1 THz is $d_{\mathrm{skin}}=\sqrt{2{\epsilon }_0{c}^2⁄\sigma \omega }=74.6\left(\mathrm{nm}\right)$ using the value of the conductivity of gold σ=4.55×105 (Ωcm)^-1. This skin depth is comparable to the gold film thickness, which is 100 nm. Therefore, surface plasmon excitation affects the THz transmission of the samples covered with gold.

The transmission spectra shown in Fig. 3(a) clearly show a pronounced frequency dependence in the measured frequency range of 0.2 THz to 3.0 THz. Considering the surface plasmon dispersion of a uniform gold film and grating period, we may have resonances of surface plasmon excitation for normal incident THz wave in this range. The actual resonance frequencies depend on the detailed shapes of the structures. We compared the spectra for the samples with different grating periods and we found that the signals, found around 0.4 and 0.8 THz in Fig. 3, have a systematic shift depending on the period of gratings. This indicates a resonant excitation of surface plasmons assisted by the gratings. The right- and left-twisted gammadion structured samples have similar transmission spectra, while a deviation is found for the spectrum of the cross-patterned sample.

 

Fig. 3. Absolute values of diagonal (a) and off-diagonal (b) elements of the Jones matrix of the sample. Spectra of rotation angle (c) and ellipticity (d). Effective complex dielectric tensor of the sample for left (blue) and right-twisted (red) gammadion samples and cross-patterned sample (black). Green curves show the results of the Si substrate. ((e)–(h))

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Concerning the optical activity, we clearly reproduced the chirality dependence that we observed in visible experiments. Only samples which have patterns without mirror symmetry show a strong optical activity. A remaining issue to clarify is the mechanism of non-local interaction induced by the morphology of the present samples. For this purpose, we examine the samples that had a lift-off treatment, i.e., a single-layer chiral grating. Following the same procedures, we evaluate the optical activity and find that compared with the corrugated structures shown above, the effects are smaller by about one order of magnitude. This indicates that the coupling between two displaced metal layers with complementary shapes brings an enhanced non-local light interaction to induce polarization rotation. In such a situation, a breaking of the mirror symmetry is still a requirement for the appearance of the optical activity.

The enhancement of optical rotation in double-layered metal structures has been discussed for twisted chiral metal objects [18] [27] and multi-layered structures with magnetic metamaterials for visible light [19]. The structure that we propose here, a double layer with complementary patterns, is advantageous due to its simplicity in fabrication. We can easily fabricate such structures by conventional electron-beam lithography. Moreover, the two planar structures with complimentary patterns can have efficient electro-magnetic coupling for the following reasons. First, the morphology-sensitive electric fields pronounced at the edge of the structures always share the lateral positions for top and bottom layers. Second, the phase-sensitive resonances of upper and lower structures occur at same frequency due to the Babinet’s principle [28], as was experimentally demonstrated for THz waves [15]. Therefore the proposed double-layered complimentary structures have strong potential for the application to THz polarization optics.

5. Conclusion

In conclusion, we have demonstrated specific polarization rotation in the THz region when the THz wave is transmitted through two-dimensional gratings consisting of displaced double metal layers of complimentary chiral structures with four-fold symmetry. The rotation is independent of the incident polarization direction characteristics of the isotropic optical activity, which appeared by the chirality of the structure. Moreover, we observed this phenomenon with a structure whose thickness is much smaller than the wavelength of the electromagnetic radiation.

Our observation indicates that relatively thin structured samples with a step of only 100 nm leads to strong polarization effects for the THz wave. This will open new techniques to control polarization of THz waves by conventional micro printing techniques such as ink-jet printing. Furthermore, it may be possible to realize a THz polarization modulator in combination with MEMS technology.