Terahertz (THz) wave generation based on nonlinear frequency conversion is a promising method for realizing a tunable monochromatic high-power THz-wave source. Unfortunately, many nonlinear crystals have strong absorption in the THz frequency region. This limits efficient and widely tunable THz-wave generation. The Cherenkov phase-matching method is one of the most promising techniques for overcoming these problems. Here, we propose a prism-coupled Cherenkov phase-matching (PCC-PM) method, in which a prism with a suitable refractive index at THz frequencies is coupled to a nonlinear crystal. This has the following advantages. Many crystals can be used as THz-wave emitters; the phase-matching condition inside the crystal does not have to be observed; the absorption of the crystal does not prevent efficient generation of radiation; and pump sources with arbitrary wavelengths can be employed. Here we demonstrate PCC-PM THz-wave generation using the organic crystal 4-dimethylamino-N-metyl-4-stilbazolium tosylate (DAST) and a Si prism coupler. We obtain THz-wave radiation with tunability of approximately 0.1 to 10 THz and with no deep absorption features resulting from the absorption spectrum of the crystal. The obtained spectra did not depend on the pump wavelength in the range 1300 to 1450 nm. This simple technique shows promise for generating THz radiation using a wide variety of nonlinear crystals.
©2010 Optical Society of America
The THz frequency range is extremely attractive for applications including, but not limited to, biomedical analysis and large-stand-off-distance detection of hazardous materials. The development of monochromatic and tunable coherent THz sources is of great importance for use in these applications. Recently, a parametric process based on second-order nonlinearities was used to generate tunable, monochromatic, coherent THz sources using nonlinear optical (NLO) crystals [1–4]. In general, however, NLO materials have high absorption coefficients in the THz region, which prevents the efficient generation of THz radiation. NLO crystals also have a difference in refractive index between the optical and THz frequencies, and this inhibits effective collinear frequency conversion. Quasi-phase matching methods can address this problem, but the tunable range is limited due to the periodicity of the device. Surface-emitting THz generation can overcome these problems ; absorption is minimized because the THz-frequency wave is generated at the crystal surface: Cherenkov-type radiation is generated as surface emission [6–11]. We have previously demonstrated a Cherenkov phase-matching method for monochromatic THz generation via difference frequency generation (DFG) using lithium niobate crystals [12–15]. We were able to generate monochromatic THz radiation with wide tunability, in the range 0.1–7.2 THz. The lithium niobate crystal has a strong absorption line at 7.5 THz, and the refractive index changes considerably around the line. The Cherenkov condition would break down slightly above 7.5 THz because the refractive index of lithium niobate would become smaller than in the near-infrared region. On the other hand, the Cherenkov radiation angle, including refraction at the interface between the surface of the crystal and the cladding material, is not dependent on the refractive index of the crystal in the THz region, but rather on that of the cladding material . This means that the THz wave can be out-coupled by the use of a suitable cladding material, in which nTHz < nopt, where nTHz and nopt are refractive indices of the crystal in the THz region and optical region, respectively. However, this effect was not observed in the device described in . That device was 3.8 µm thick, and the high-frequency limit of the emitted radiation was 7 THz, as the thickness of the crystal corresponded to half of the wavelength. Here, we demonstrate the Cherenkov phase-matching condition using a DAST crystal and a Si prism coupler  to obtain THz radiation.
2. Cherenkov phase matching with prism coupler
Cherenkov THz radiation is generated inside a nonlinear crystal when the velocity of the polarization excited by a DFG process is greater than the phase velocity of the radiated wave. In general, many nonlinear crystals have strong dispersion between the optical and THz regions, and the refractive index at THz frequencies is larger than that at optical frequencies. This may result in behavior that satisfies the Cherenkov-type phase matching condition, i.e.
The organic nonlinear crystal DAST is attractive material for THz generation  because the crystal has a very large nonlinear coefficient. DAST is also strongly absorbing in the THz region, which has so far prevented efficient THz generation. The PCC-PC method, however, allows efficient THz generation with very high nonlinear efficiency. DAST has very similar refractive indices in the near infrared and THz-frequency regions, and this means that collinear phase matching can be achieved. Figure 1 shows phase-matching vectors under the following conditions: kTHz > k1 - k2, kTHz = k1 - k2, and kTHz < k1 - k2. Perfect phase matching in a collinear configuration is satisfied when kTHz = k1 - k2. Cherenkov phase matching is also satisfied when kTHz > k1 - k2. However, when kTHz < k1 - k2, phase matching cannot be achieved.
Figure 2 shows the relative wave vectors in the DAST crystal during THz generation. The dispersion relation data in the calculation were taken from Ref. 18 in the optical region  and from Ref. 19 in the THz region . Although the Cherenkov phase-matching condition cannot be satisfied when kTHz < k1 - k2 in the bulk, the PCC-PM condition can be satisfied by applying a Si cladding layer, as follows from Eq. (2).
Figure 3 shows the calculated Cherenkov angles between light propagating in the DAST crystal and Si cladding layer. The angle inside the crystal strongly depends on the dispersion characteristics of the DAST crystal; this means that the pump wavelength influences the angle. As shown in the figure, the Cherenkov phase-matching condition cannot be satisfied across the whole THz-frequency region when the wavelength of the pump is 1300 nm.
Fortunately, Eq. (2) tells us that the Cherenkov condition inside the crystal does not have to be satisfied for THz generation using the PCC-PM method. The THz radiation experiences the refractive index of the cladding material at the interface, and so it can be coupled out from the cladding layer, regardless of the relative refractive indices within the nonlinear crystal, with an almost fixed angle. The calculated angles inside the crystal range from 0° to 40°, and the THz radiation is totally reflected at the interface with air, as predicted from Eq. (2). If the Si cladding functions only as an output coupler, it follows that the Si coupler will not work as a Cherenkov phase-matching component, and the THz radiation at the frequency where the phase matching condition is not satisfied cannot be out-coupled unless the Si cladding is formed into a prism.
3. Experiments and Results
We used a 100-µm-thick DAST single crystal in the experiment. The crystal was hexagonal, as illustrated in Fig. 4 , so that we could achieve b-axis propagation of two pump beams. A Si prism was coupled along the (001) plane of the DAST crystal because as-grown DAST has a very flat surface in the plane. A dual-wavelength potassium titanium oxide phosphate (KTP) optical parametric oscillator (OPO) with pulse duration of 15 ns, pulse energy of 1.5 mJ, and 1300–1600-nm tunable range was used as a pump, as in our previous work [12–15]. The polarizations of the two pumps were parallel to the a-axis of the DAST crystal, which has the highest nonlinear coefficient component, and THz radiation was generated parallel to the a-axis. The pump beam was focused to form a 46-μm diameter beam using a cylindrical lens with a 50-mm focal length, resulting in a power density of about 50 MW/cm2. The emitted THz radiation was detected using a liquid-helium-cooled Si bolometer with an electrical gain of 1000.
Figure 5 shows the collected THz output spectra under different pump wavelengths. THz radiation was generated at levels from less than 1 THz to more than 10 THz, with spectra that were almost independent of the pump wavelength. The dip at 8 THz was originated from the transmission character of a filter inside the Si-bolometer. When collinear phase matching is used to generate THz radiation, a deep dip in the spectra is observed at around 1.1 THz [17,20]. This is suppressed here because the Cherenkov method results in surface emission, and we successfully obtained about 100 times higher signal compare to noise level of the detector. Additionally, radiation was generated below 1 THz, which cannot be generated using collinear phase matching with 1300–1450-nm pumping . At frequencies above ~10 THz, the detection efficiency of the bolometer falls off, and this explains the low observed power at higher frequencies. However, the collected power extends to higher frequencies than were observed when using bulk lithium niobate in our previous works . Although THz radiation generated far from the crystal–cladding interface interferes with that generated near the interface, resulting in destructive interference, the radiation generated deep within the crystal is attenuated due to the large absorption coefficient of the crystal. The absorption coefficient of DAST crystal at around 2–10 THz is 100–200 cm−1. The beam diameter was approximately 50 µm, and so the intensity of a THz-wave that propagates this distance will be attenuated by 30–60%. The output voltage of the Si bolometer can be converted to energy by considering that 1 V ≈20 pJ/pulse for low-repetition-rate detection and that we have a gain of 1000 at the bolometer. The highest-energy THz pulse obtained was about 50 pJ (3.3 mW at peak). The obtained output energy was higher than that of obtained by collinear phase matching condition using DAST crystal under almost same power density [17,20].
We demonstrated the PCC-PM THz generation using a DAST crystal. The spectra were broadband and almost independent of the pump wavelength over a range 1300–1450 nm. The PCC-PM method has the advantage of suppressing the strong absorption due to the nonlinear crystal. The conversion efficiency using collinear and non-collinear phase matching methods is inversely proportional to square of the absorption coefficient, and the large nonlinearity in the crystal cannot be fully exploited due to the large absorbance. The great potential of organic nonlinear crystals can be effectively exploited using this method because surface emission is not influenced by absorption in the crystal. Hebling et al. described a figure of merit of several nonlinear crystals  from the viewpoint of the nonlinearity and absorption coefficient. GaSe had the highest figure of merit; however, DAST has a larger optical nonlinearity. Using the surface-emission method described here, the absorption coefficient ceases to be an issue, suggesting that DAST may be a more efficient material for generating THz radiation using DFG. The method described here has the advantage of relaxing the phase-matching condition. Many crystals require that a phase-matching condition (such as birefringence, non-collinear, and quasi phase matching) is satisfied, however, the PCC-PM method provides a much less stringent phase-matching condition. Furthermore, the method does not require a specific pump wavelength. This method could allow the realization of simple, compact, highly efficient, and ultra-broadband THz sources using a range of nonlinear crystals.
In conclusion, we propose a prism-coupled Cherenkov phase-matching (PCC-PM) method, in which a prism with a suitable refractive index at THz frequencies is coupled to a crystal. This has the following advantages. Many crystals can be used as THz-wave emitters; the phase-matching condition inside the crystal does not have to be observed; the absorption of the crystal does not prevent efficient THz-wave generation; and pump sources with arbitrary wavelengths can be employed. Here we demonstrate PCC-PM THz-wave generation using the DAST crystal. We obtain THz-wave radiation with wide-tunability with no deep absorption features. The obtained spectra did not depend on the pump wavelength. This simple technique shows promise for generating THz radiation using a wide variety of nonlinear crystals.
References and links
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