## Abstract

The nonlinear optical coefficients of ${\mathrm{YCa}}_{4}\mathrm{O}({\mathrm{BO}}_{3}{)}_{3}$ (YCOB) have been calculated for the first time to the authors’ knowledge by use of the revised Gaussian 92 program on the basis of the anionic group theory. The ${d}_{11},$
${d}_{12},$
${d}_{32},$ and ${d}_{33}$ coefficients of the crystal were determined by the Maker fringes method at $\mathrm{\lambda}=1064\mathrm{nm},$ and ${d}_{13},$ and ${d}_{31}$ were also evaluated by measurement of the Maker fringes. The coefficients determined by the Maker fringes are in agreement with the theoretical values. On the basis of the ${d}_{\mathit{ij}}$ coefficients and the Sellmeier equations, the effective second-harmonic generation (SHG) coefficient ${d}_{\mathrm{eff}}$ of YCOB as a function of phase-matching angles *θ* and Φ was determined. It is interesting that the maximum effective SHG coefficient ${d}_{\mathrm{eff}}$ of YCOB is not in the principal plane but is located out of the $X\u2013Z$ plane in the positions $\theta =65.9\xb0,$
$\mathrm{\Phi}=36.5\xb0$ and $\theta =66.3\xb0,$
$\mathrm{\Phi}=143.5\xb0.$ It is also worth noting that the largest ${d}_{\mathrm{eff}}$ of YCOB in the region of $0\xb0<\theta <90\xb0,$
$90\xb0<\mathrm{\Phi}<180\xb0$ is larger than that in $0\xb0<\theta <90\xb0,$
$0\xb0<\mathrm{\Phi}<90\xb0.$ These calculated results have been proved by the effective SHG coefficient measurements of YCOB and conversion-efficiency measurements of frequency-doubling experiments on Nd:YCOB.

© 2000 Optical Society of America

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