Relationship of the Second Order Nonlinear Optical Coefficient to Bandgap in Inorganic Non-Centrosymmetric Crystals
The purpose of this paper, is to provide a means of estimating and comparing the wavelength conversion efficiency (figure of merit, FOM) of new nonlinear materials knowing only their bandgap. The approach for the estimates is trend analysis of existing data1-28 for the second order nonlinear coefficient, x(2)ijk, or dij =x(2)ijk/2, the index of refraction n, and the bandgap E. No underlying physical basis for the result will be presented. The result of this trend analysis, in the form of plots of x(2) vs E and FOM vs E and the associated fit equations, will be used to estimate x(2) and the FOM for wavelength conversion efficiency for some new materials. The accuracy goal agrees within a factor of 2-5 with the experimental values, which is quite good considering the values range over four to seven orders of magnitude.
In this paper, following the usual conventions, the x(2) values are treated as having constant values in the region of high transparency between the bandgap and the onset of multiphonon absorption, and the full x(2) values are used, which means the impact of the phase matching angle is ignored. The requirement to phase match often reduces significantly the effective x(2) values below those of the full values. The distinction between direct, indirect, or pseudodirect bandgaps is ignored and the minimum room temperature gap is used in all cases.
Jackson, A. G.,
& Leclair, S. R.
(1995). Relationship of the Second Order Nonlinear Optical Coefficient to Bandgap in Inorganic Non-Centrosymmetric Crystals. .
Report # WL-TR-95-4098