Dependence of Second Harmonic Generation on Crystal Inhomogeneity

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Abstract
Effect of the nonuniformity of the natural birefringence in a nonlinear crystal on second harmonic generation (SHG) is theoretically and experimentally studied. The second harmonic power at the phase‐matching temperature, the second harmonic power vs temperature, and the temperature bandwidth are calculated in terms of the gradient of the natural birefringence and compared with those from the SHG experiment using a cw Nd:YAG laser and Ba2NaNb5O15 single crystal. It is found that the second harmonic peak power is much depressed by the nonuniformity of the natural birefringence in a crystal. The oscillations in the second harmonic power vs temperature curve become broad and the temperature bandwidth increases with decreasing crystal homogeneity. Satisfactory agreement was obtained between theory and experiment. By analytical calculation the dependence of SH power on crystal length l, is expressed in terms of the inhomogeneity length li, which is defined as a measure of the length beyond which SHG is limited by the crystal inhomogeneity. It is found that in an inhomogeneous crystal the SH power does not vary with length as l2 but decreases by the factor (1−l2/6li2).