# Organic Crystals for THz Photonics
## 2 Second-Order Organic Nonlinear Optical (NLO) Crystals
### Organic Single Crystalline Materials  
To achieve a macroscopic second-order NLO response in organic materials with non-zero \(\chi^{(2)}\), the constituting asymmetric NLO chromophores have to be distributed non-centrosymmetrically. This is by far not trivial because these molecules usually possess a high permanent dipole moment and they tend to orient antiparallel, as illustrated in Figure 1c, which cancels the macroscopic \(\chi^{(2)}\) response. There have been many possibilities proposed to achieve a macroscopic non-centrosymmetric order of NLO molecules. Most commonly, a non-centrosymmetric order is achieved by incorporating NLO chromophores in a polymer matrix and then pole the material by applying a very strong static electric field (just below the electric breakdown) above the glass transition temperature to align these molecules, based on their relatively high permanent dipole moment \(\mu\). The advantage of this approach is that it is in principle applicable for all chromophores with a permanent dipole moment, including those with the highest first hyperpolarizabilities \(\beta\)[6]. On the other hand, it is  
Figure 3: Schematics of the material linear polarization response as a function of frequency of the external electric field. For organic materials, the contributions of \(e^{o}\) and \(e^{d}\) to the static relative permittivity \(\epsilon^{T}\) are much less important compared to inorganic materials, which is an important advantage for high-speed electro-optic modulation and THz-photonics applications (see text). The scale below shows the THz frequency range in frequency \(f\), wavelength \(\lambda\), and spectroscopic wavenumber \(1/\lambda\). extremely challenging to achieve a desired long-term orientational stability of the non-centrosymmetric order at room temperature [6]. For THz photonics applications, the achievable material thickness of polymer-based materials is also very limited [27]. For highly-efficient THz-wave generation, the thickness of the THz generation material (organic or inorganic) in the range of 0.1-1 mm is required [28]. Another possibility to obtain an efficient macroscopic second-order active NLO organic material is by crystallization, offering the highest possible chromophore density, the best possible long-term orientational stability and sufficient sample thickness (\(\sim\) 0.1-1 mm range), which is the approach discussed in this review. Additional to the much superior temporal stability of crystals compared to poled polymers, their photochemical stability may be better by several orders of magnitude [29], which is particularly important for THz-wave applications, where high optical power densities are used and therefore a high damage threshold is required. On the other hand, only a very small ratio of known chromophores can crystallize in a non-centrosymmetric crystalline space group and there seems to be a limit in the conjugation length (i.e., the first hyperpolarizability strength \(\beta\)) that can still lead to a non-centrosymmetric alignment [15; 30]. The chromophores, besides having a large \(\beta\), need to be usually specially designed to promote a non-centrosymmetric alignment [15; 30]. In addition, even for the chromophores that naturally self assemble into a non-centrosymmetric structure, the growth of high optical quality crystals large enough and with desired morphology may be too challenging to allow for practical applications. For all these reasons, although there are endless possibilities for molecular engineering to obtain organic NLO crystals, there have been only a few identified that lead to crystals that can be potentially used for practical NLO applications and some of these are presently commercially available.