Modal reflection of quarter-wave mirrors in vertical-cavity lasers

Abstract

Very high plane-wave reflection coefficients can be obtained with practical semiconductor quarter-wave mirrors, but for beams of finite width, the reflection coefficient of a mirror with no lateral guiding and hence the finesse of cavities that use such structures will be limited by diffraction loss. The authors analytically and numerically study the modal reflection of practical semiconductor quarter-wave mirrors. They introduce a quantity called the diffraction range of a quarter-wave mirror as a means of exact analytical comparison between infinite lossless mirrors (and approximate comparison for finite mirrors) in the Fresnel diffraction limit. The exact modal reflection coefficient for an arbitrary incident mode pattern is determined by vector plane-wave decomposition. The modal reflection coefficients of two representative semiconductor quarter-wave mirrors used in vertical cavity laser technology, AlAs/GaAs and InGaAsP/InP, are studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>