Theory of a vertical-cavity surface-emitting semiconductor laser with an external mirror

High-power lasing in a single spatial mode of a vertical-cavity surface-emitting semiconductor laser (VCSEL) can be achieved by controlling the mode composition by means of an external cavity. Among the important factors which affect the mode composition is the interference of the fields inside the VCSEL and the field which returns after reflection from the external mirror. An approximate theoretical analysis of the optical modes is performed for a VCSEL with an external mirror. The mode frequencies and the degree of longitudinal mode discrimination are determined in a plane wave approximation. A condition for the existence of a single longitudinal mode is obtained. A two-dimensional equation for the effective refractive index is derived in the explicit form, which describes the transverse field distributions. Explicit expressions are obtained for the fields of transverse modes in a VCSEL with a plane external mirror and a parabolic profile of the gain.