Nonlinear optical characterization of LiNbO3. I. Theoretical analysis of Maker fringe patterns for x-cut wafers

Marker fringe analysis was adapted to x-cut LiNbO3 wafers to examine variat ions in birefringence, thickness, and photoelastic strain. The pump beam wa s polarized parallel to the crystalline gamma axis and produced e- and o-po larized Maker fringes, owing to d(31) and d(22), respectively, by rotation of the sample about they y axis. Fitting our model to the o-polarized data enabled computation of the sample thickness to an uncertainty of approximat ely +/-0.01 mu m. The accuracy was limited by an implicit +/-2 x 10(-4) unc ertainty in n(o) that exists in the commonly used Sellmeier equation of G. J. Edwards and M. Lawrence, Opt. Quantum Electron. 16, 373 (1984). For a pu mp wavelength lambda(p) = 1064 nm, fitting the model to the e-polarized fri nges revealed that n(e) at 532 nm deviated from the Sellmeier result by typ ically -1.58 x 10-4. The uniformity of n(e) over a wafer 10 cm in diameter was approximately +/-4 x 10(-5). This result is consistent with that expect ed from compositional variations. Our model included multiple passes of the pump and second-harmonic waves. The effects of photoelastic strain in prod ucing perturbations and mixing of the e- and a-polarized fringes was invest igated. This was restricted to two experimentally motivated cases that sugg ested that strains produce rotations of the optic axis by typically +/-0.05 degrees about the x axis and y axis with the former assigned to an indeter minant combination of S-1, S-2, and S-4 and the latter to an indeterminant combination of S-5 and S-6. In both cases the magnitude of the collective s trains is of the order of 10(-4). The birefringence variations that are due to strain are of the same magnitude as those expected from compositional v ariations. The formalism developed here is used in the subsequent mapping s tudy of x-cut wafers. (C) 1998 Optical Society of America [S0740-3224(98)00 412-3] OCIS codes: 160.3730, 160.4330, 190.1900, 190.4400.