Specific features in the band structure and linear and nonlinear optical susceptibilities of ${\mathrm{La}}_2\mathrm{Ca}{\mathrm{B}}_{10}{\mathrm{O}}_{19}$ crystals

The electronic and optical properties have been calculated for monoclinic ${\mathrm{La}}_2\mathrm{Ca}{\mathrm{B}}_{10}{\mathrm{O}}_{19}$ (LCB) crystal using the state-of-the-art full potential linear augmented plane wave method. We present results for the band structure, density of states, birefringence, imaginary and real parts of the frequency dependent linear and nonlinear optical response. We have found that LCB is a semiconductor with an indirect energy band gap of about $4.45\mathrm{eV}$. A simple scissor operator is applied to adjust the band energy gap from the calculations to match the experimental value $\left(5.4\mathrm{eV}\right)$. The calculated birefringence of the LCB crystal has positive sign in agreement with the experimental data. Calculations are reported for the frequency-dependent complex second-order nonlinear optical susceptibilities ${\chi }_{abc}^{\left(2\right)}\left(\omega \right)$ up to $6\mathrm{eV}$ and for zero-frequency limit ${\chi }^2\left(0\right)$. LCB exhibits second harmonic generation efficiency about two times larger than KDP crystal $\left(\mathrm{K}{\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4\right)$.

Figure 1

(Color online) (A) The ${\mathrm{B}}_5{\mathrm{O}}_{12}$ group. (B) Oxygen coordination to the La and Ca atoms. (C) Brillouin zone of the $C2$ group.

Figure 2

(Color online) Band structure and total density of states (states /eV unit cell), along with $\mathrm{La}\text{−}s∕p∕d∕f$, $\mathrm{Ca}\text{−}s∕p$, $\mathrm{B}\text{−}s∕p$, and $\mathrm{O}\text{−}s∕p$ partial densities of states. The optical transitions depicted on a generic band structure.

Figure 3

Calculated ${\epsilon }_2^{\perp }\left(\omega \right)$ (dark curve) and ${\epsilon }_2^{\Vert }\left(\omega \right)$ (light curve).

Figure 4

Calculated ${\epsilon }_1^{\perp }\left(\omega \right)$ (dark curve) and ${\epsilon }_1^{\Vert }\left(\omega \right)$ (light curve).

Figure 5

Calculated $\Delta n\left(\omega \right)$.

Figure 6

(First panel) Calculated $\mathrm{Im}{\chi }_{123}^{\left(2\right)}\left(\omega \right)$ (dark curve) and $\mathrm{Im}{\chi }_{112}^{\left(2\right)}\left(\omega \right)$ (light curve). (Second panel) Calculated $\mathrm{Im}{\chi }_{211}^{\left(2\right)}\left(\omega \right)$ (dark curve) and $\mathrm{Im}{\chi }_{233}^{\left(2\right)}\left(\omega \right)$ (light curve). (Third panel) Calculated $\mathrm{Im}{\chi }_{222}^{\left(2\right)}\left(\omega \right)$ (dark curve) and $\mathrm{Im}{\chi }_{231}^{\left(2\right)}\left(\omega \right)$ (light curve). (Fourth panel) Calculated $\mathrm{Im}{\chi }_{332}^{\left(2\right)}\left(\omega \right)$ (dark curve) and $\mathrm{Im}{\chi }_{312}^{\left(2\right)}\left(\omega \right)$ (light curve). All $\mathrm{Im}{\chi }^{\left(2\right)}\left(\omega \right)$ are multiply by ${10}^{-7}$, in esu units.

Figure 7

(Color online) Calculated $\mathrm{Im}{\chi }_{123}^{\left(2\right)}\left(\omega \right)$ along with the intraband $\left(2\omega \right)$ and interband $\left(2\omega \right)$ contributions. All $\mathrm{Im}{\chi }^{\left(2\right)}\left(\omega \right)$ are multiply by ${10}^{-7}$, in esu units.

Figure 8

Calculated $\mathrm{Re}{\chi }_{211}^{\left(2\right)}\left(\omega \right)$ (dark curve) and $\mathrm{Re}{\chi }_{233}^{\left(2\right)}\left(\omega \right)$ (light curve). $\mathrm{Re}{\chi }_{211}^{\left(2\right)}\left(\omega \right)$ and $\mathrm{Re}{\chi }_{233}^{\left(2\right)}\left(\omega \right)$ multiply by ${10}^{-12}\mathrm{pm}∕\mathrm{V}$, in SI units.