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Magnitude and dispersion of Kleinman forbidden nonlinear optical coefficients

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1 Author(s)
Levine, B. ; Bell Laboratories, Murray Hill, NJ, USA

Starting with a perturbation expansion for the Kleinman forbidden nonlinear optical coefficientd_{ijk^{F}}and for Miller'sDelta_{ijk^{F}}, and making several approximations, we arrive at a simple result for the ratio of forbidden to allowed mixing nonlinearities (omega_{1} + omega_{2} = omega_{3}), namelyDelta_{ijk^{F}}/Delta_{ijk^{A}} propto (omega_{3}^{2} + 2omega_{1}omega_{2}). For second-harmonic generation (SHG) this can be expressed asDelta_{ijk^{F}}/Delta_{ijk^{A}} simeq (omega/chi)(partialchi/partialomega), which clearly shows the close connection betweenDelta_{ijk^{F}}and the linear dispersion. These expressions are shown to give good agreement with literature experimental values, as well as for our measurements on TeO2for various input frequencies ω1and ω2(i.e.,omega_{3} = 1.88, 2.33, 2.82, 3.50, and 3.76 eV).

Published in:

Quantum Electronics, IEEE Journal of  (Volume:9 ,  Issue: 9 )