Influence of Carrier Transport on Diffraction Efficiency of Steady-State Photocarrier Grating

A two-dimensional theoretical model of a diffractive steady-state photocarrier grating (SSPCG) has been developed. The carrier diffusion equation with a spatially periodic excitation source was solved, and an analytical expression of the carrier density distribution was obtained. Based on the band-filling theory and the Kramers–Kronig relation, the carrier-induced refractive index change of SSPCG was estimated, and the refractive index profile was determined. The diffraction efficiency of the SSPCG was calculated by multilevel rigorous coupled-wave analysis. Simulations were carried out to investigate the influence of the carrier transport properties on the diffraction efficiency of the SSPCG. The results show that a semiconductor material with a longer lifetime and a smaller diffusivity will have a higher diffraction efficiency. The spatial amplitude of the carrier density and the grating strength of the SSPCG are closely related to the grating period. For an InP-based SSPCG, the diffraction efficiency of the +1st\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+1\mathrm{st}$$\end{document} transmitted wave reaches its maximum value (25 %) when the grating provides a π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} phase shift. The theoretical analysis and conclusions are helpful for material selection and experimental parameter determination of a diffractive SSPCG.