1. Introduction

Rapid development of terahertz (THz) science allows us to generate intense THz laser pulses with extremely high efficiency [1, 2]. A pulse energy of 125 μJ [1] and an electric field of 1.2 MV/cm [3] have been achieved by table-top laser sources and open the way for nonlinear THz spectroscopy in solids [4, 5], liquids [6], gases [7], and nanoparticles [8]. The nonlinear interaction between THz light and matter has recently been of interest not only for its characteristics but also for its availability to control molecular motion in the gas phase [7, 9, 10] and carrier dynamics in solids [4, 11]. Theoretical studies have suggested that arbitrarily shaped THz pulses can precisely control the dynamics of matter; for instance, the chirality of molecules [12], the displacement of ions in ferroelectric crystals [13]. However, pulse shaping in the THz region is not yet well developed because of the lack of the basic components to manipulate the THz light.

The laser pulse train, which is a pulse sequence with equal time spacing between the neighboring pulses, is one of the essential shaped pulses and has been realized in the THz region by shaping the optical pulse that pumps a nonlinear crystal to generate THz light [14–16]. However, since the shaped optical pulse is significantly stretched, the conversion efficiency to THz light is much smaller than that of compressed optical pump pulses. Therefore, directly generating a pulse train from THz light would be ideal. For this purpose, we must develop multiple interferometers or an etalon that can operate in the THz region. The former, composed of a large number of interferometers to generate a long pulse train, is not realistic as an optical device. On the other hand, a single and small etalon device can realize a THz pulse train. Jewell et al. have demonstrated a Fabry–Perot etalon for obtaining frequency-tunable THz light [17]. They constructed their etalon using an indium-tin-oxide (ITO)-clad liquid crystal. The ITO layer reflects THz light with high reflectivity [18] and acts as a good Fabry–Perot reflector. The frequency was tuned by the voltage applied to the liquid crystal. However, the significant problem with the etalon is that a large part of the incident THz pulse is reflected by the highly reflective input coupler of the etalon, and thus is not introduced into the etalon.

In this study, we developed an etalon with an optical shutter to obtain a THz pulse train with high efficiency. A schematic of the proposed etalon device is shown in Fig. 1 . The etalon is composed of a high-resistivity silicon (Si) plate as an input coupler and an ITO-coated glass plate as an output coupler. Initially, the input surface of the Si plate is irradiated with a THz pulse. Since the Si plate is transparent to THz light, the input THz pulse is introduced into the etalon cavity except for Fresnel reflection losses. The THz pulse propagates through the air and arrives at the ITO layer. The major part of the THz pulse is reflected by the ITO layer, whereas only a small portion of the pulse passes through the ITO-coated glass plate. Before the reflected THz pulse arrives at the Si plate again, the optical pulse irradiates the etalon from the opposite direction. Since the ITO is transparent to optical light of wavelengths longer than 400 nm [19], the optical light can excite the Si surface to generate a plasma layer that strongly reflects THz light. The lifetime of the photoinduced carriers in the plasma layer is a few microseconds, which is much longer than the round-trip time of the THz pulse in the etalon. Therefore, the optical pulse acts as the optical shutter to trap the THz pulse in the etalon cavity. This is the key to generating the THz pulse train with high efficiency. In each round trip, a small part of the THz pulse transmits through the ITO output coupler. The sequence of the transmitted pulses forms the THz pulse train.

 

Fig. 1 Schematic diagram of the etalon with an optical shutter. The time sequence of the THz and optical shutter pulses and their propagation in the etalon are shown from top to bottom. The vertical thick red lines represent the conductive layers that strongly reflect THz light.

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2. Experimental setup

Figure 2(a) shows a schematic of our experimental apparatus to demonstrate the THz etalon with the optical shutter. A 1 kHz pulse train centered at 800 nm with a pulse duration of 45 fs and a pulse energy of 1.2 mJ was split into three parts for THz generation, the optical shutter, and THz detection. The THz pulse was generated by optical rectification in an LiNbO₃ prism with pulse front control [20]. The optical shutter pulse was frequency doubled by a 1-mm-thick β-BBO crystal to generate an ultraviolet (UV) pulse with energy of 80 μJ. The THz and shutter pulses were delivered to the etalon by the use of counter propagation geometry. The THz pulse was focused on the Si plate to ensure that the spot size was smaller than that of the shutter pulse on Si. The transmitted THz pulse from the etalon was detected by free-space electro-optic (EO) sampling [21, 22] in a ZnTe crystal. Since a scan of long temporal length was required to measure the long THz pulse trains, a combined (100)-(110) ZnTe crystal was employed to avoid influencing the back reflection inside the ZnTe crystal [23]. Figure 2(b) shows the THz spectrum generated by this setup without the etalon. The available frequency range was up to 2 THz.

 

Fig. 2 (a) Schematic diagram of the experimental setup. BS1 and BS2, beam splitters with reflectivities of 3%, and 50%, respectively; G, grating with the groove density of 1800 L/mm; λ/2 and λ/4, half and quarter wave plates, respectively; LN, magnesium-doped stoichiometric LiNbO₃ crystal; L1, L2, and L3, plastic lenses for THz light (PAX, Tsurupica) with the focal length of 30, 100, and 100 mm, respectively; BBO, second harmonic crystal; W, Wollaston prism; PD, photodiode. (b) THz spectrum generated by this setup without the etalon. (c) Transmittance spectra of the silicon plate and the ITO-coated (sheet resistance of 15 Ω and 300 Ω) glass plates used in this study.

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The etalon was composed of a Si plate (2 kΩcm) of 1 mm thickness and an ITO-coated (with layer thickness of 150 nm) glass plate of 1.1 mm thickness. The spacing L between both plates is adjustable so as to control the temporal spacing between the neighboring pulses in the THz pulse train. When the Si plate is irradiated by UV light of wavelength 400 nm, a 0.1-μm-thick thin plasma layer is generated on the surface [24]. Since this layer is much thinner than 10 μm at 800 nm [25], the density of the carriers induced by the 400 nm light is 100 times higher than that induced by the 800 nm light. Therefore, the dense plasma layer, which acts as the metallic surface for THz light, can easily be generated with UV light. The UV light was focused to the diameter of 4 mm and the energy density of 640 μJcm⁻² on the Si surface. The density of carriers generated by this UV light was estimated to be 1.3 × 10¹⁹ cm⁻³ which corresponds to the plasma frequency of 23 THz. The plasma layer sufficiently acts as the metallic mirror for the THz light with the frequency lower than 1 THz.

Figure 2(c) shows the transmittance spectra of the unexcited silicon plate and the ITO-coated glass plates used in this study. The transmittance of Si was constant at 0.5, which indicates no significant absorption, considering the Fresnel reflection. On the other hand, the transmittance range of the ITO-coated glass plate was limited, up to 1 THz. Therefore, the available frequency range of the presented etalon was also up to 1 THz. As shown in Ref [18], the reflectance of the ITO layer does not strongly depend on the frequency lower than 2.5 THz. The limitation in the transmittance range shown in Fig. 2(c) comes from the highly absorbing glass plate. The transmittance of ITO also depended on the resistivity of ITO. Since carrier conductance increases with decreasing resistance of the ITO layer, an ITO layer with low resistance is more metallic-like than that with high resistance. Therefore, the transmittance of a layer with 15 Ω is much lower than that with 300 Ω.

3. Results and discussion

Figure 3(a) shows waveforms of the THz pulse trains transmitted from the etalon by the use of ITO with a sheet resistance of 300 Ω. The temporal spacing T between the neighboring pulses in the THz pulse train was changed by adjusting the spacing L in the etalon and was expressed by T = 2L/c, where c is the speed of light. Without applying the optical shutter, the pulse intensity rapidly decreased in each round trip and disappeared within three round trips. On the other hand, with the optical shutter, the pulse survived over four round trips, which indicates that the optical shutter successfully enhanced the reflectivity on the Si surface. The frequency spectra obtained from Fourier transforms of the corresponding waveforms are shown in Fig. 3(b). Since the optical shutter increases the total intensity of the pulse train, the spectral intensities were increased by the shutter. By applying the optical shutter, a comb shape clearly appeared in the spectra. The peak width became much narrower than that measured without the shutter.

 

Fig. 3 (a) Measured waveforms of the THz pulse trains transmitted through the etalon with ITO with a sheet resistance of 300 Ω. The spacings between the Si and ITO-coated glass plates in the etalon were 1 mm and 2 mm. The thick red and thin black lines show the waveforms measured with and without the optical shutter, respectively. (b) Frequency spectra obtained from the Fourier transforms of the corresponding waveforms shown in (a). The waveforms and the spectra measured with the etalon with 15 Ω ITO are shown in (c) and (d), respectively.

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When we used ITO with low-sheet resistance (15 Ω), the effect of the optical shutter was more clearly observed, as shown in Fig. 3(c). Without the shutter, since 70% of THz light was transmitted through the Si plate, the pulse intensity rapidly decreased even with low-resistance ITO. On the other hand, the number of pulses in the THz pulse train drastically increased with the shutter and was larger than 10. As shown in Fig. 3(d), the comb spectral shape also improved by applying the optical shutter and low-resistance ITO. At the spacing L = 2 mm of the etalon, the spectral width of the comb peaks was measured to be δν = 8.3 GHz (full-width at half-maximum), which is much narrower than the comb spacing (free spectral range) Δν of 75 GHz; thus, the finesse of the etalon with the optical shutter was evaluated to be F = δν /Δν = 9.04.

Figure 4 shows the relative intensities of the pulses in the pulse train. The intensity plotted in this figure was calculated by the square of the peak amplitude in each pulse in the pulse train, as shown in Figs. 3(a) and 3(c), and normalized to that of the first pulse. The relative intensity is independent of the spacing L in the etalon and is expressed by $I_n/I_1={\left(R_{\text{I}}{R}_{\text{S}}\right)}^{n-1}$, where I_n is the intensity of the n-th peak in the pulse train, and R_I and R_S are the reflectivities of the ITO layer and the silicon surface, respectively. The observed relative intensities were fitted by this equation to obtain the product of the reflectivities, R_IR_S, as shown in Fig. 4. The product of the reflectivities of the etalon without the optical shutter was 0.34 and 0.10 with the 15 and 300 Ω ITO, respectively. By using the Fresnel reflectivity, R_S = 0.30, we obtained the reflectivity of the ITO layer as R_I ~1 and 0.33 for 15 and 300 Ω ITO, respectively. When we applied the optical shutter, the product of the reflectivities was increased to 0.69 and 0.26 with the 15 and 300 Ω ITO, respectively. Then, the reflectivity of the photo-excited Si surface was determined to be R_S ~0.74, which was 2.5 times larger than the Fresnel reflectivity of Si. The quality of the etalon is determined by the reflectivity of the conductive layers on the both end mirrors of the cavity. By employing the optical shutter and the conductive ITO layer, we realized an etalon with a large finesse (F = 9.04) and large conversion efficiency from a single input pulse to the pulse train.

 

Fig. 4 Relative intensities of the pulses in the pulse train generated by the etalon with 300 Ω (upper figure) and 15 Ω (lower). The intensity is normalized to that of the first pulse. The filled and open dots are the observed data with and without the optical shutter. The solid lines are the fitted results explained in the text.

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The reflectivity of the photo-excited Si surface, R_S ~0.74, obtained in this etalon is smaller than that (R_S > 0.9) measured by the time-resolved reflection spectroscopy with the mid-infrared probe pulses [26]. The small reflectivity of the photo-excited Si limits the number of the pulses in the pulse train and the finesse of the etalon. One of the possible reasons for this small reflectivity is the spatial diffusion of the carrier from the photo-excited Si surface. When the carrier density is high, 10¹⁹ ~10²⁰ cm⁻³, the carriers rapidly diffuse in picosecond time scale. At 100 ps after the UV light excitation, the carrier density at the surface is 10 times smaller than that just after the excitation [26]. Due to the carrier diffusion, the plasma frequency shifts lower at the long delay time, and therefore, the reflection efficiency decreased with time after the excitation. To avoid influence of the diffusion, the transparent substrate deposited the silicon layer whose thickness is similar to the penetration depth of the UV light (0.1 μm) is desired for the input coupler.

The second reason for the small reflectivity is the breaking of the plane wave approximation for the THz light. In usual, the light with plane wave front has to be introduced to the etalon, since the light is ejected from the etalon after many round trips. In this study, however, the focused THz light is injected to the etalon in order to ensure that the beam diameter of the THz light is smaller than that of the UV light. When the THz light is assumed to be the Gaussian beam, the Rayleigh length is estimated to be 6 mm by using the measured beam diameter, 2 mm, at the focus point. Since the Rayleigh length is not much longer than the spacing L in the etalon, the plane wave approximation is not satisfied after several round trips. To satisfy the approximation, the parallel beam with the small diameter has to be prepared before injection to the etalon.

4. Summary

We demonstrated an etalon with an optical shutter that can generate a THz pulse train with high efficiency. The free spectral range can easily be controlled by the spacing between the Si and the ITO-coated glass plates. A finesse F of 9.04 was achieved at the free spectral range Δν of 75 GHz, when we applied the optical shutter. To improve the performance of the etalon, we must reduce the Fresnel losses on the input Si surface by employing the anti-reflection coating for THz light that has already been developed for Si optics [27, 28]. Furthermore, it is also important to increase the reflectivity of both end reflectors in the etalon by choosing the materials best suited for the semiconductor and conductive layers as the input and output couplers, respectively. Especially, since the transmittance spectrum of the conductive layer coated substrate for the output coupler determines the bandwidth of an etalon, a substrate with wide passband width is necessary to obtain a broadband pulse train.

When we are able to develop a high-finesse etalon, THz laser oscillation and amplification will be realized with the gain media and the Pockels cell operated in the THz region. Recently, amplified stimulated THz emission from optically pumped graphene has been reported [29]. This will be one of the candidates for the THz gain media.