Terahertz (THz) waves are electromagnetic waves that exist in the spectrum between radio waves and light. If THz waves are regarded as light, their oscillation frequency is the lowest among all types of light. We can observe this oscillation directly by THz time-domain spectroscopy (TDS), which is widely used for spectroscopic measurement [1], tomography [2], and topography [3]. These applications utilize information on both the amplitude and phase of the THz wave. The easy acquisition of phase data by THz-TDS is a striking feature of recent THz measurements. This feature makes THz-TDS suitable for research dealing with the polarization of light because the polarization state is described by the phase relation between two orthogonal electric field oscillations.

Recently, several studies related to THz wave-polarization have been reported [3–6]. Even so, progress in polarization research using THz waves has not been so rapid. The main reason for this is a lack of suitable polarization control optics for THz waves, particularly in the case of THz-TDS. A recent development in THz technology involves use of a femtosecond-laser-based technique for THz pulse emission and detection. Using this technique, the emitted THz pulse has a spectral range covering two orders of magnitude, e.g., 0.1–10 THz. In principle, a conventional wave plate utilizing optical birefringence can be used for monochromatic THz waves but is not adequate for broadband THz pulses. There have been some proposals for making achromatic wave plates for THz pulses [7–9]; however, their spectral range is still restricted. Additionally, neither half-wave plates nor quarter-wave plates have been realized in the foregoing examples. In addition, although several techniques for emitting arbitrarily polarized THz pulses have been developed [10,11], an achromatic broadband wave plate is still needed for controlling THz waves.

In this Letter, we demonstrate broadband THz half- and quarter-wave plates utilizing phase retardation by internal total reflection in a prism. The prism-type wave plate exhibited achromatic characteristics over a large THz spectral region. The broadband properties of this prism-type wave plate were evaluated by comparing phases between two THz pulse waveforms obtained by setting the wave plate in two orthogonal positions. We employed two novel prism designs for minimizing lateral walk-off and allowing use with a large-aperture THz beam. To illustrate the validity of our approach, real-time polarization imaging of two crossed bunches of hairs was demonstrated using a large-aperture THz beam.

Fresnel showed that phase retardation takes place in total internal reflection. The phase difference between s-polarized light and p-polarized light due to total internal reflection is determined by the boundary condition at a discontinuous surface between two media. The phase difference $\delta$ due to total internal reflection is given by [12]

 

Fig. 1. (a) Calculated incident-angle dependence of phase retardation due to a single total internal reflection. The case of Si is represented by the black line and that of a plastic (ZEONEX; cyclo-olefin polymer) is represented by the gray line. Side views of (b) a three-reflection type prism and (c) a four-reflection type prism. The gray line shows the light path. The angles $\alpha$, $\beta$, and $\gamma$ are the prism parameters shown in Table 1. (d) Perspective view of the MSP wave plate.

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A rhomb-prism designed to produce circularly polarized light from linearly polarized light is called Fresnel’s rhomb [12,13]. Fresnel’s rhomb is designed to attain a phase retardation of $\lambda /4$ via two total internal reflections, or in other words, a phase retardation of $\lambda /8$ by a single reflection. It is therefore possible to attain an arbitrary phase retardation by several total internal reflections. We designed a half-wave plate using a three-reflection prism [Fig. 1(b)] and a quarter-wave plate using a four-reflection prism [Fig. 1(c)]. Here, the prism medium was silicon (refractive index, $n_{\mathrm{Si}}=3.42$), with an effective aperture of 5 mm. Si is a suitable material for a prism-type wave plate because it has high transparency for THz waves and has a flat refractive index characteristic across a broad THz spectral range (up to 4.5 THz as long as published) [14].

To use the phase retarder prism as a wave plate, we designed the prism to be rotatable so as to arbitrarily change the polarization state of the THz pulse. As opposed to Fresnel’s rhomb, our prism is designed so that the incident and exit light beams are coaxial. The characteristic parameters are summarized in Table 1.

Table 1. Parameters of Prisms

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The phase retardation of our quarter-wave plate is $3\lambda /4$; in other words, it is actually a $-\lambda /4$ wave plate. If the phase retardation of the quarter-wave plate were set to $\lambda /4$, the angle $\gamma$ (Fig. 1) would become 78.2°. Such a grazing incidence angle would cause elongation of the quarter-wave plate. By adopting a phase retardation of $3\lambda /4$ for the quarter-wave plate, the length can be reduced to less than 1/3, and lateral walk-off caused by misalignment can be reduced. Unlike a conventional wave plate that utilizes optical birefringence, a temporal delay does not occur in this case because the phase retardation of our prism-type wave plate is caused by a phase jump due to total internal reflection. Therefore, the functions of a $\lambda /4$ wave plate and a $-\lambda /4$ wave plate are exactly the same, except for the rotation direction. To realize a phase retardation of $3\lambda /4$ with a four-reflection prism, a $3\lambda /16$ phase retardation has to be achieved in a single reflection. This leads to the condition that the lower limit of the refractive index of the prism media is 1.87, from Eq. (1).

Figure 2 shows the phase retardation of prism-type half- and quarter-wave plates measured by using THz-TDS. We measured two THz temporal waveforms with the wave plate placed in orthogonal orientations and evaluated the phase difference. The THz emitter and detector were ZnTe crystals with a thickness of 1.0 mm. The effective spectral range of our system was restricted to 2.5 THz by the coherence length. Large retardation stability over the whole spectral range was observed. The measured phase retardations, namely, $1.0\pi$ (half-wave plate) and $-0.5\pi$ (quarter-wave plate), were as designed, and the wide retardation stability showed that our prism can be used as an achromatic wave plate for broadband THz pulses.

 

Fig. 2. Measured phase retardation of the half-wave plate (black line) and quarter-wave plate (gray line). To emphasize that the phase retardation of our quarter-wave plate is $3\lambda /4$, the signs of these results are opposite.

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Thanks to the ability of THz-TDS to directly observe the electric field of a THz wave, we can easily distinguish between right- and left-handed circular polarizations. Figure 3 shows 2D distributions of a THz pulse temporal waveform that we obtained by rotating the quarter-wave plate to $+45°$ (clockwise) and $-45°$ (counterclockwise). It was clearly observed that the rotation direction of the THz electric-field polarization changed depending on the rotation direction of the quarter-wave plate. In the case of a half-wave plate, the polarization direction of a linearly polarized THz pulse was changed arbitrarily according to the rotation angle of the wave plate (data not shown). From these results, we verified that the polarization of a THz pulse could be satisfactorily controlled by our wave plate.

 

Fig. 3. Temporal waveform of THz pulses plotted in 3D space defined by X amplitude, Y amplitude, and time when the quarter-wave plate was rotated to (a) $+45°$ and (b) $-45°$.

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For practical applications, a prism-type wave plate has the drawback of a large size when applied to a large-aperture THz beam, which is essential for 2D THz imaging and collimated propagation of long-wavelength light. For instance, when a prism designed for a THz beam diameter of 5 mm is scaled up to handle a 30 mm diameter beam, the prism length increases from 29 to 122 mm, and the turning radius increases from 8.2 to 55.6 mm. To avoid such problems, we employed a novel design using a multistacked prism-type (MSP) wave plate. Figure 1(d) shows a perspective view of the MSP wave plate. This MSP wave plate consisted of several stacked tile-like prisms, each having the same shape as that of a four-reflection prism as viewed from the side (Fig. 1(c)). The incident THz beam was divided into several parts in the stacked prism; their polarizations were individually changed, and they were combined again into one beam. For a 30 mm diameter beam, we made six tile-like prisms from a plastic (ZEONEX, refractive index of 1.51). The phase retardation was $\lambda /2$. The characteristic parameters of the prisms are summarized in Table 1. The gap length $g$ [Fig. 1(d)] is 0.81 mm. It is several times longer than the penetration depth of THz waves [15]. Therefore the coupling effect in the reflection is negligible.

To show the performance of the MSP wave plate, we demonstrated THz real-time polarization imaging of two crossed bunches of hair.

Figure 4(a) shows the measured sample: two bunches of hair (about 180 hairs each) were crossed over each other and fixed to a holder. The experimental setup was similar to that in [16] except that a wire-grid polarizer at an angular position of 45° was installed behind the sample. The THz pulse emitter and detector were ZnTe (110) crystals. The femtosecond laser used for pumping and probing the THz pulse was a Ti:sapphire laser based on the chirped pulse amplification technique (Legend, Coherent Inc.), which provided laser pulses with a central wavelength of 800 nm, a pulse duration of 50 fs, a pulse energy of 2.5 mJ, and a repetition rate of 1 kHz. The emitted THz pulses passed though the MSP wave plate, where their polarization was modulated. Then the THz pulses passed through the sample and formed an image of the sample on a ZnTe detector. Since the wire-grid polarizer restricts the polarization to 45°, 45° linearly polarized components of both vertical- and horizontal-polarization THz pulses were extracted. Therefore, this optical system could acquire both vertical- and horizontal-polarization THz images without changing the setup, even though the ZnTe detector has polarization dependence.

 

Fig. 4. (a) Photograph of imaging sample (two crossed bunches of hairs). Real-time THz transmission images obtained with (b) a vertically polarized THz pulse and (c) a horizontally polarized THz pulse.

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We acquired two images obtained by changing the polarization of the THz pulse to horizontal or vertical polarization. Figures 4(b) and 4(c) show THz images acquired by using a vertical-polarization THz pulse and a horizontal-polarization THz pulse, respectively. The sign of the THz electric field is represented by pseudo color. Obviously, there is a considerable difference between the two images. This difference appears in the color, not in the intensity of the signal. Analysis of the temporal waveform (data not shown) revealed that the difference originated from the difference in the delay of the THz pulse. This polarization dependence of the delay is explained by the wire-grid-like behavior of the bunches of hairs. When the directions of the THz electric field and the hairs are orthogonal, the THz pulse passes through the hairs with no change, like the case of a wire-grid polarizer. In contrast, when the directions of the THz electric field and the hairs are parallel, the THz pulse “feels” the hairs and experiences a temporal delay according to the refractive-index difference between air and the hairs. Consequently, an image of the hairs appears only when setting them in the same direction as the THz electric field. In addition, there are no unnecessary artifacts in the THz image introduced by stacking the prisms, since the manufacturing accuracy of the prisms was better than the wavelength of the THz wave. From these result, we confirmed that the MSP wave plate functions effectively with a large-aperture THz beam.

In conclusion, we designed and characterized a half-wave plate, a quarter-wave ($3\lambda /4$) plate, and an MSP wave plate for arbitrary polarization control of a broadband THz pulse. The phase retardation of the half- and quarter-wave plates was measured using THz-TDS. These prism-type wave plates have a large bandwidth covering the spectral region in which broadband THz pulses exist. In addition, real-time polarization imaging of crossed bunches of hairs was performed to characterize the MSP wave plate. We found that the hairs acted like a permeable wire-grid polarizer. In practice, the large Fresnel reflection loss occurring when the THz pulse enters and exits the prism-type wave plate will be an issue. A single-layer antireflection coating can suppress this loss to a certain degree [17]; however, research on broadband antireflection coatings showing no polarization dependence is still required. Once such optical technology is developed for THz waves, a true THz wave optical system could be built in the near future.