1. Introduction

A terahertz (THz) wave has been considered useful for applications such as molecular spectroscopy, noninvasive imaging, and homeland security [1–4] etc. To date, THz-wave radiations are mostly generated in the form of either broad-band electromagnetic pulses or narrow-band electromagnetic waves. The latter is a laser-like coherent radiation and is the focus of this paper. Among various methods for generating THz radiations, nonlinear frequency mixing is known to offer an effective means to obtain coherent THz-wave radiations at room temperature. In particular, in the past 10–15 years Ito et al. [5–10] have demonstrated several promising THz-wave parametric amplifiers and oscillators using lithium niobate (LiNbO₃) as the parametric gain medium. The THz wave emits at about 64° from the pump direction of an optical wave in the LiNbO₃ crystal. The non-collinear phase-matching configuration and fast diffraction of the THz wave in the bulk LiNbO₃ crystal exacerbate the poor parametric efficiency due to strong absorption of the THz wave in LiNbO₃. Recently Edward et al. were able to lower the threshold energy of the LiNbO₃ THz-wave parametric oscillator (TPO) to about 1 mJ by installing a LiNbO₃ TPO in a pump-laser cavity [11]. A narrow linewidth is also often desirable for a coherent radiation source. Although a conventional TPO is known to start from the amplification of spontaneous noise, Imai et al. demonstrated a single-frequency pumped TPO with a 200-MHz output linewidth by using a MHz-linewidth seeding signal [5]. To the best of our knowledge, all the previously reported LiNbO₃ TPOs without signal seeding had an output linewidth larger than 20 GHz [8, 9]. The aim of our work is to demonstrate an externally pumped LiNbO₃ TPO starting from spontaneous noise while having both the lowest threshold [12] and the narrowest linewidth to date.

A THz waveguide is known to confine the THz radiation and enhance the parametric conversion efficiency of a TPO [12, 13]. It has also been demonstrated in the optical-frequency regime that an intra-cavity grazing-incidence grating can greatly narrow down the linewidth and offer wavelength tunability of a laser [14–16]. By taking advantage of the THz waveguide in our previous work [12] and the intra-cavity grazing-incidence grating, we demonstrate in this paper a low-threshold and narrow-line TPO in a LiNbO₃ planar waveguide.

2. Experimental setup

Figure 1 shows the schematic of the grazing-incidence TPO (GITPO) with an intra-cavity grating. The pump laser is an injection-seeded actively Q-switched Nd:YAG laser, producing 5.8-ns laser pulses at 1064 nm with a 310-MHz linewidth. The seed laser to the pump is a homemade, single-longitudinal-mode, continuous-wave, diode-pumped Nd:YVO₄ laser with an intra-cavity Littman grating. To improve the overlap between the pump and the THz waves in the LiNbO₃ crystal, we cut the Gaussian tail of the TEM₀₀ pump mode by transmitting a well collimated, 3.6-mm-diameter pump beam through a 0.8-mm-diameter aperture before the GITPO. After the aperture, the pump beam was focused to the center of a congruent LiNbO₃ crystal with dimensions of 45, 15, and 1 mm along the crystallographic x, y, and z directions. The 1-mm thick crystal can accommodate many THz-wave modes, but the TM₀ mode has the largest overlap integral with a well aligned pump mode and is the mode most likely to grow [12]. The x surfaces of the crystal were optically polished and an anti-reflection coated film at the pump (1064 nm) and signal (~1071 nm) wavelengths. The polarization of the pump laser was aligned along the z direction so that the highest nonlinear coefficient, d₃₃, can be used for parametric wave mixing. We constructed the GITPO by using two flat mirrors highly reflecting at the signal wavelength (M1 and M2, reflectance >99.5% @~1071 nm) and an intra-cavity gold-coated grating (Edmund Scientific NT55-263, 1200 grooves/mm, blaze angle =36°52’). The resonant cavity of the GITPO, formed by mirrors M1 and M2, has a length of 13 cm. At the 85° grazing-incidence angle for a TM wave at the signal wavelength, the single-pass resolution of the intra-cavity grating is 24.5 GHz and the diffraction efficiency of the 1^st-order beam is 57.5%. Since the signal wave reflects twice on the grating for each round-trip propagation in the cavity, the effective resonator loss is about 67%. Fine tuning of the THz-radiation wavelength can be achieved by rotating the angle of mirror M2. In our experiment, we can remove the grating-M2 assembly to study the experiment for a THz-wave parametric generator (TPG). When comparing the GITPO with a conventional TPO, we replaced the grating-M2 assembly with a flat mirror (50% transmittance @ 1071 nm) as the output coupler. The TPO in our comparison study has a cavity length the same as that of the GITPO.

 

Fig. 1 The schematic of the GITPO pumped by an injection-seeded Q-switched Nd:YAG laser. It is a conventional TPO when the grating-M2 assembly is replaced by an output coupled at the signal wavelength. Without the grating-M2 assembly, the setup can be used for studying a TPG. (HR: high reflection, FP: Fabry-Perot)

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One of the y surfaces of the LiNbO₃ crystal is optically polished. As shown by the phase-matching configuration at the upper-right corner of Fig. 1, the THz wave emits at ~65° from the signal beam direction and is incident on the y surface at a ~26° angle. We attached a 240-µm-thick silicon-grating coupler to the optically polished y surface to avoid total internal reflection and extract the energy of the THz wave [7]. The grating period, groove depth, and the groove width of the silicon grating are 125, 50, and 65 µm, respectively. The grating formula governs the relationship between the incidence and diffraction angles of the THz wave, given by sinθ_m=n_Sisinθ_si -mλ/Λ, where Λ is the grating period, and θ_m is the m ^th-order diffraction angle, θ_si=sin^-1(n_T/n_Si sinθ_i) is the incident angle of the THz wave in the silicon grating with θ_i~26° being the incident angle of the THz wave in the LiNbO₃, and n_T (~5.25) and n_Si (~3.4) are the refractive indices of the LiNbO₃ and the silicon wafers at THz frequencies, respectively. For the 164-µm THz wavelength in our experiment, the 1^st-order and 2^nd-order diffraction angles are nearly 90° and 18° from the surface normal of the grating.

Following the silicon-grating coupler, a set of off-axis parabolic mirrors (f=152-mm, 2″-aperture) collects and collimates the THz-wave radiation into the 4K Si bolometer. The silicon grating is placed at the front focal plane of the first off-axis parabolic mirror. The spectrum of the infrared signal wave was measured by a typical 1/2-m grating monochromator (CVI DK480). We measured the THz wavelength by using a scanning Fabry-Perot (FP) etalon inserted between the two off-axis mirrors. The etalon was made from two parallel wire meshes containing 45 µm×45 µm square apertures with a 54% filling factor. The transmittance of the wire mesh is 20% for an incident THz wave at 164 µm, yielding finesse of 14 for the scanning etalon spectrometer.

3. Experimental results and discussions

Figure 2 shows the output signal-wave energy versus pump energy of the TPG, TPO, and GITPO. The pump thresholds of the TPO and GITPO were found to be 1.9 mJ (60 MW/cm² pumping intensity) and 2.2 mJ (70 MW/cm² pumping intensity), respectively, which are, to the best of our knowledge [8, 10], the lowest oscillation thresholds ever reported for an externally pumped LiNbO₃ TPO [12]. At the maximum pump energy 4.4-mJ (140MW/cm²), the overall parametric conversion efficiencies of the TPG, TPO, and GITPO were 1.9%, 10.0%, and 5.0%, respectively. Since the round-trip optical loss at the grating is 67%, which is higher than the 50% output-coupling loss of the TPO, the pump threshold of the GITPO is slightly higher than that of the TPO. The low pump threshold and high efficiency were made possible from waveguide confinement of the THz wave and thus better spatial overlap between the pump and THz waves in the parametric gain region.

 

Fig. 2 Signal versus pump energy of the TPG (green dots), TPO (red dots), and GITPO (blue dots) using a 1-mm-thick, 45-mm-long LiNbO₃ planar waveguide. The pump threshold intensities of the TPO and GITPO are shown in the plot.

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Figures 3(a) and (b) show the temporal and spectral measurements for the signal wave, respectively, at 4.4-mJ pump energy. As expected, the signal-wave pulse width of the GITPO is slightly longer than that of the TPG in Fig. 3(a), because the parametric oscillation enhances the energy conversion in the trailing part of the signal pulse. In Fig. 3(b), the measured signal spectra of the TPG, TPO, and GITPO are 213, 134, and 12 GHz, respectively. It can be seen that the signal linewidth of the GITPO is greatly reduced from that of the TPG by ~18 times and TPO by ~11 times. Since the linewidth of the pump laser was measured to be 310 MHz, the THz-wave linewidth can be inferred from the frequency relationship of parametric conversion

with a known signal linewidth, where ω is the angular frequency of the mixing wave, and the subscripts p, s, and THz, denote the quantities associated with the pump, signal, and THz waves, respectively. From Eq. (1), the linewidth of the THz wave is approximately 12 GHz. Given the specifications of the grating, it can be calculated that the single-pass grating bandwidth is 24.5 GHz at an 85° grazing-incidence angle [16]. In theory, the signal and thus the THz-wave output linewidth of the GITPO is the single-pass grating bandwidth divided by the square root of the number of the round-trip propagations of the signal wave in the cavity [16]. With the 13-cm cavity length and 3.5-ns signal-wave pulse width, the number of the round-trip propagations is 4. Therefore the theoretical value of the THz-wave linewidth of the GITPO is 12.5 GHz, which is in good agreement with the value deduced from Fig. 3(b) and the frequency relationship (1). In Fig. 3(b), the spectrum of the signal wave or the frequency of the THz wave is tuned over a 130-GHz range by simply rotating the angle of mirror M2 by 0.6 mrad. In this GITPO, the grating-M2 assembly offers excellent spectral stability to the output THz wave, which is usually not available from a conventional TPO.

 

Fig. 3 (a) The signal pulse width of the GITPO (blue curve) is slightly longer than that of the TPG (green curve). (b) The linewidths of the TPG (green color), TPO (red color), and GITPO (blue and pink colors) were measured to be 213, 134, and 12 GHz, respectively. The signal-wave spectrum of the GITPO was tuned over 130 GHz by rotating a 0.6-mrad angle in mirror M2.

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While keeping the pump energy at 4.4 mJ and signal wavelength at 1071.45 nm, we measured the THz wavelength by using the scanning Fabry-Perot etalon between the two off-axis parabolic mirrors. Figure 4 shows the THz wave detected by the 4K Si bolometer versus the etalon gap. The solid curve is an Airy function fitted to the experimental data. Although the finesse of the spectrometer is not high enough for directly resolving the actual linewidth of the THz wave, the characteristic period of the transmission curve clearly shows a THz wavelength of 164 µm.

 

Fig. 4 The measured THz-wave transmission power (filled dots) versus the etalon gap. The solid curve is an Airy function fitted to the experimental data. A THz wavelength of 164 µm can be determined from periodicity of the fitting curve.

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The diffraction angle of the THz wave in the LiNbO₃ planar waveguide is about 10°. Therefore the 1-mm thick, 45-mm long LiNbO₃ crystal indeed served as a waveguide for the THz wave. In a slab waveguide, the maximum number of THz modes can be estimated from the expression m _max=2t(n ² T-1)^1/2/λ_T, where t andλ _T are the waveguide thickness and the THz wavelength, respectively [17]. The maximum number of the waveguide modes in the 1-mm-thick LiNbO₃ waveguide is 63 for n_T=5.25 at the 164-µm wavelength. However, not all waveguide modes but only those phase-matched ones with mode field distributions well overlapped with the pump mode can grow to some appreciable energy level [12]. Since the TM₀ mode has the largest overlap integral with the filtered TEM₀₀ pump beam, it is most likely that the TM₀ mode extracts most the parametric gain and is the dominant mode in such a multimode waveguide.

To estimate the THz-wave conversion efficiency of the GITPO inside the LiNbO₃ planar waveguide, we consider the pump intensity of 140 MW/cm² and the output signal-wave energy of 219 µJ at 4.4-mJ pump energy. In the theoretical limit [18], the optical-to-THz-wave conversion efficiency of the GITPO can be calculated to be ~2.8×10^-5, corresponding to ~123 nJ THz-wave energy in LiNbO₃. In the calculation, we have used the absorption coefficient and the nonlinear coefficient of 30 cm^-1 and 228 pm/V, respectively, for LiNbO₃ at 164 µm. Given the large absorption coefficient of LiNbO₃, most THz-wave energy did not exit the LiNbO₃ crystal. Since the purpose of this work is to demonstrate the low threshold and narrow linewidth of a TPO, we simply used an existing Si grating and detected the THz wave along the more convenient 2^nd-order diffraction direction. We estimated ~1.2-pJ THz-wave energy entering the detection cone of out Si bolometer. With a more optimized output coupling scheme, the extraction of the THz-wave energy could be greatly improved [8].

4. Conclusions

We have demonstrated low pump thresholds for an externally pumped TPO and a GITPO by using a LiNbO₃ planar waveguide as the parametric gain medium. The low pump threshold resulted from waveguide confinement of the generated THz wave and thus better overlap between the mixing waves. The GITPO shows an additional advantage of a greatly narrowed spectral output. The measured threshold energy and intensity of the GITPO were 2.2 mJ and 70 MW/cm², respectively, which are approximately 10 times lower than the previously reported values [8, 10]. At the pump energy of 4.4 mJ (two times above threshold), the overall parametric conversion efficiency of the GITPO is about 5%. The intra-cavity grazing-incidence grating of the GITPO effectively reduced the signal and thus the THz-wave linewidth by 11 times from the value of the TPO. We measured a 12-GHz output linewidth for the GITPO. By rotating the angle of the resonator mirror next to the grating of the GITPO, we were able to fine tune the output frequency of the GITPO by 130-GHz without changing the pump direction relative to the crystal orientation. Our scanning Fabry-Perot etalon confirmed a THz wavelength of 164 µm from the GITPO. The accomplishment of this work is a major step toward realizing low threshold and narrow-linewidth THz-wave sources.