# Organic Crystals for THz Photonics
## 3 THz-Wave Generation and Detection via NLO Processes
### Phase-Matching Characteristics for THz-Wave Generation in Organic NLO Crystals
In a broader THz frequency range up to about 10 THz (for which the THz refractive index data is available), DSTMS shows similar THz velocity-matching properties compared to DAST. OH1 crystal is a non-ionic crystal and has even higher figure of merit for THz-wave generation (see Table 2) compared to the stillazoium salts DAST and DSTMS. OH1 has optimum velocity-matching between 1200 nm and 1460 nm for 0.3-2.5 THz, and has no absorption at about 1 THz but at about 3 THz [85]. Above 3 THz, the optimal phase matching conditions for OH1 are shifted to longer wavelengths, which is less optimal considering the available pump laser sources. Laser sources at around 1550 nm are not best suitable for OH1 due to a smaller absorption band in the optical range at this wavelength (see Figure 5b). In any case, OH1 has the highest efficiency among presently known organic crystals, at least in the lower THz frequency range below 3 THz [85]. Figure 8: (**a**) optical group index \(n_{g}(\lambda)\) as a function of wavelength for selected organic crystals; (**b**) optical properties in the THz range: the refractive index \(n_{\text{THz}}(f)\) (red solid curves) and the absorption coefficient \(\alpha_{\text{THz}}(f)\) (blue dotted curves, right scale) as a function of frequency \(f=\omega/(2\pi)\). The corresponding properties are given for selected organic crystals along their polar axis, which is most often employed in THz applications. The \(n_{g}(\lambda)\) are obtained from the dispersions \(n(\lambda)\) shown in Figure 5a. The THz properties \(n_{\text{THz}}(f)\) and \(\alpha_{\text{THz}}(f)\) are according to the following references: DAST [126, 127, 128], DSTMS [129], OH1 [91], HMQ-TMS [53, 83]. For the quinolinium salt HMQ-TMS, see Figure 9d, the best phase-matching range is shifted towards shorter wavelengths compared to DAST and DSTMS, which is an advantage for using certain widely pump-wavelength sources at around 1000 nm [53; 84; 83]. Note that the measurements of material parameters required for evaluating \(l_{c}\) may be very time consuming and often also have a limited precision, therefore these figures only give a first approximation for the coherence length and are only available for a few organic NLO crystals. Some other organic NLO crystals, for which phase matching has been studied in more detail, are OHQ-T [131], BNA [103] and COANP [109]. BNA and COANP are, for example, interesting, although having somewhat lower nonlinearity, because their absorption is considerably blue shifted (see Figure 5a for BNA) and therefore they allow for velocity matching at around the Ti:Sapphire laser wavelength of 800 nm [103; 107; 109]. The velocity-matching evaluation based on the coherence length \(l_{c}\) as presented in Figure 9 does not take into account the influence of the optical and the THz-wave absorption. Based on the analytical solution for the THz electric field given by Equation (22), an equivalent parameter \(l_{\text{opt}}\) has been defined, the so-called optimum crystal length \(l_{\text{opt}}\)[112], which considers both optical/THz absorption and optical/THz group/refractive indices. The corresponding plots of \(l_{\text{opt}}\) as a function of \(f\) and \(\lambda\) for DAST, DSTMS, OH1 and HMQ-TMS can be found in Ref. [15]. The main conclusions about the best velocity-matching ranges remain, however, very similar to those resulting from Figure 9.  
It is usually assumed that the NLO coefficient for THz-wave generation \(d_{\text{THz}}\), which is important for the THz-wave generation efficiency beside phase matching (see Equations (16) and (22)), is approximately constant in the THz frequency range. This may not be the case due to the phonon and vibrational modes in this range and the NLO susceptibility in this range can be also considerably frequency dependent similarly to the linear optical properties shown in Figure 8b.