Abstract

Coupled-mode analyses of surface-emitting, distributed-feedback lasers with concentric-circle diffraction gratings have described coupling between the waveguide modes, neglecting radiation.¹ In this paper we discuss a model of the radiation characteristics of the concentric-circle grating. A boundary perturbation technique is applied to describe the interaction of the waveguide modes with the radiation field. A radiation coupling coefficient describes this interaction and relates the strength and shape of the radiated fields to those of the guided modes. The perturbation technique also predicts the far-field radiation patterns. We explore issues such as the effect of the additional radiative coupling on mode frequencies, threshold gain, and longitudinal mode profiles. An understanding of these radiation field effects is crucial for interpreting the relationship of beam quality to grating parameters such as period, depth of grating, and grating shape.

© 1992 Optical Society of America