Anisotropic optical responses of sapphire (α-Al2O3) single crystals

Anisotropic dielectric functions of sapphire have been determined by both reflection and transmission variable angle spectroscopic ellipsometry. The measurements were made on a-plane (2 (1) over bar (1) over bar 0) sapphire substrates in the energy range of 0.75-6.5 eV at room temperature. The orientation of the optic axis of the a-plane sapphire sample was determined by polarized Raman scattering based on which the Euler angles are set for the fitting model. Two pairs of Cauchy user-defined functions were constructed to describe the optical constants of both ordinary n(perpendicular to) (omega) and extraordinary n(parallel to)(omega) rays, respectively. As a result the optical constants from the generalized ellipsometry analysis are in good agreement with the reported data. The Kramers-Kronig (KK) relation between the real and the imaginary part have been carefully checked for both ordinary and extraordinary rays. The perfect fitting between the calculated and experimental epsilon(1)(omega) function indicates that both functions of ordinary and extraordinary rays are KK consistent. The refractive index difference between the ordinary and extraordinary rays is close to a constant (+0.008), which is determined mainly by the off-diagonal signal of the transmission ellipsometry data. The extinction coefficients are zero below 6 eV, and increase rapidly above 6 eV. (C) 1999 American Institute of Physics. [S0021-8979(99)01409-7].