# 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  
For efficient THz-wave generation by NLO processes (such as difference-frequency generation and optical rectification), it is essential to achieve phase matching (velocity matching) \(n_{\text{THz}}\simeq n_{g}\) between the fundamental optical and the generated THz waves, as discussed in Section 3. Because of the dispersion of the refractive indices in both ranges, the phase matching condition is strongly dependent on the wavelength \(\lambda\) of the pump optical beam(s) and the frequencies \(\omega\) of the generated THz beams. The dispersion of the optical group indices \(n_{g}=n-(\partial n/\partial\lambda)\lambda\) is shown in Figure 8a next to the dispersion of the refractive indices \(n(\omega)\) in the THz range (see Figure 8b) for selected organic NLO crystals. For different materials, there are different ranges where the velocity matching condition \(n_{\text{THz}}\simeq n_{g}\) is reasonably well satisfied and is roughly marked by the shaded thick lines in Figure 8. DAST for example has a stronger phonon resonance near 1.1 THz resulting in roughly two different regions: good velocity matching can be realized either for pump wavelengths between ca. 1000 nm and 1200 nm, yielding THz waves between 0.2 THz and 1 THz, or for pump waves with wavelengths between 1200 nm and 1700 nm for the generation of THz waves above 1.5 THz [125; 112]. For crystals with a blue shifted visible absorption edge such as HMQ-TMS, the best velocity matching ranges are also blue shifted, which is very important when selecting an organic THz generator that should be optimized for a certain pump laser source. The optical phonon resonances and molecular vibrations that occur in the THz frequency range (see Figure 3) induce some absorption of the generated THz radiation in organic NLO crystals (see the graphs for \(\alpha_{\text{THz}}(f)\) in Figure 8b), which is also very important when optimizing these crystals for different desired frequency ranges. Note also that the properties in Figure 8 are only given along the polar axis of the selected NLO crystals. Several crystals also have notable off-diagonal \(\chi^{(2)}\) components (see Table 1). Although these coefficients may be lower compared to the diagonal susceptibility coefficients (employed when both optical and THz beams are polarized along the polar axis), they may allow other velocity matching ranges. For DAST, for example, using the pump beams polarized along the crystalline \(b\) axis (see Figure 4) generates THz radiation along the polar \(a\) axis based on the off-diagonal \(\chi^{(2)}_{122}\) susceptibility, which is velocity matched for the pump wavelengths close to 800 nm [75; 112], an important wavelength of available high-power Ti:Sapphire fs laser sources. Best conditions for velocity matching can be straightforwardly evaluated if the relevant optical parameters given in Figure 8 are known. The simplest figure-of-merit for the velocity matching is the coherence length \(l_{c}(\lambda,f)\) given by Equation (15) and is shown in Figure 9 for selected organic materials obtained using the parameters in Figure 8 as a function of the pump optical wavelength \(\lambda\) and the generated THz frequency \(f=c/\lambda_{\text{THz}}\). For highly nonlinear organic NLO crystals DAST and DSTMS presented in Figure 9, the best pump wavelength range is at around telecommunication wavelengths, which is very interesting given the availability of very compact and relatively low-cost fs fiber lasers [125]. The generation of THz waves with frequencies at around 1.1 THz is in DAST limited due to a strong optical phonon vibration [130]. In DSTMS (DAST derivative with an isomorphic structure), the optical phonon absorption near 1 THz is suppressed (see Figure 8b), most probably due to a heavier counter anion, and therefore this material is superior to DAST within this frequency range [72].