An electron-hole transport model for the analysis of thephotorefractive harmonic gratings

摘要

The steady-state exact solution for the higher harmonic gratingsnthat synthesize the space-charge field is derived without restrictionsnwithin an electron-hole transport model which allows the behavior ofnthese harmonic gratings to be determined rigorously in terms of the mainnphotorefractive parameters. The model predicts the independence of thenfundamental and harmonic amplitudes on the average excitation intensity.nWith respect to the modulation depth m, the dependence of eachnΝ-harmonic order is established as mΝ which is thenresult obtained in the single-level model. In terms of the gratingnspacing, three regions of quite different behavior are identified as thenlinear, transition, and nonlinear regions. The extent of each region innterms of Λ strongly depends on the acceptor density relative tonthe donor density. If the acceptor density is much greater or smallernthan the donor density, the linear region spreads out toward the lowestnspacing, the nonlinear region extends toward the highest spacing, andnthe intermediate region is located in-between, as in the Kukhtarevnmodel. But, for similar concentrations, the nonlinear region is shiftedntoward smaller spacing with respect to the linear region. On the othernhand, the electron-hole competition can be deleterious for recording thengrating, due to the charge compensation produced by the additionalncharge carrier that screens the internal space-charge field. Also, thenrelative importance of the higher harmonics is apparent for the smallestnvalues of the external field as in the single-level model