Optical properties of the langasite family crystals: La$_3$Ga$_5$SiO$_{14}$, La$_3$Ga$_{5.5}$Ta$_{0.5}$O$_{14}$, Ca$_3$TaGa$_3$Si$_2$O$_{14}$

Optical properties of lanthanum-gallium silicate (La$_3$Ga$_5$SiO$_{14}$), lanthanum-gallium tantalate (La$_3$Ga$_{5.5}$Ta$_{0.5}$O$_{14}$), calcium-tantalum-gallium silicate (Ca$_3$TaGa$_3$Si$_2$O$_{14}$) crystals in the near ultraviolet (UV) and visible wavelength ranges (200–800 nm) have been studied. For the first time the angles of deviation of the moments of the dipole transition spectral dependences $\theta(\lambda)$ were used to characterize the absorption processes in these crystals. These dependences make it possible to reveal absorption bands that are weakly noticeable on the transmission coefficients spectral dependences, and to estimate the degree of deviation of the dispersion dependence $\theta(\lambda)$ from the value $\theta$ = 45$^\circ$ corresponding to an ideal ordered crystal. Analysis of $\theta(\lambda)$ dependencies showed that in the studied wavelength range, the lowest deviation from $\theta$ = 45$^\circ$ is observed in Ca$_3$TaGa$_3$Si$_2$O$_{14}$, and the highest in La$_3$Ga$_5$SiO$_{14}$. The coefficients of the specific rotation angle of the polarization plane $\rho$ were obtained by the spectrophotometric interference method in polarized light. The measured values are best approximated by the Vyshin equation. For the first time, dependences of the modified Drude formula $1/\rho=f(\lambda^2)$ were calculated for these crystals. These dependences should be linear in case of an ideal crystal. The largest deviation from the linear dependence is observed for La$_3$Ga$_5$SiO$_{14}$ crystals, and the lowest for Ca$_3$TaGa$_3$Si$_2$O$_{14}$. The discrete values of the refractive coefficients $N_o$ and $N_e$ were measured by the prism method. La$_3$Ga$_{5.5}$Ta$_{0.5}$O$_{14}$ crystals have the highest refractive coefficients, Ca$_3$TaGa$_3$Si$_2$O$_{14}$ crystals have the lowest. The obtained values are approximated by the Sellmeier equation.