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As X-ray measurements have shown, domain walls in LiNbO$_3$ exhibit the structure of compressed bulk material [1]. Hence, knowledge of the optical response of LiNbO$_3$ as a function of compression can help to characterize the domain walls of LiNbO$_3$ and yields information about their optical signatures.
In our work, we model linear and non-linear optical properties of LiNbO$_3$ in dependence on uniaxial compressive strain in x-, y- and z-direction from first principles using time-dependent density functional theory (TDDFT) [2]. This includes the calculation of the energy dependent second (SHG) and third harmonic generation (THG). We find changes for all components of the second- and third-order polarizability tensor $\chi^2$ and $\chi^3$. In particular, for |$\chi_{\mathrm{zzz}}^2$| we obtain a linear increase with applied compression in z-direction. Due to the threefold rotational symmetry, LiNbO$_3$ has four independent $\chi^2$ elements [3]. However, compression in x- and y-direction reduces the symmetry, lifting the degeneracy of identical $\chi^2$ components. Additionally, from the calculated dielectric tensor the refractive index and birefringence as a function of compression is obtained. Knowledge of both these properties under compression is particularly important for the application of Ti waveguides.
[1] M. Rüsing et al., Phys. Rev. Mat. 2, 103801 (2018).
[2] C. Attaccalite and M. Grüning, Phys. Rev. B 88, 235113 (2013).
[3] A. Riefer et al., Phys. Rev. B 87, 195208 (2013).
