Use of the Epstein dielectric model to describe modes of planar stripe-geometry heterojunction lasers

The Epstein model of a dielectric layer having a smooth profile is used to describe the complex permittivity $varepsilon$ in the plane of the active layer of the three-dimensional wave-guide structure in a planar stripe-geometry laser. A three-layer model generally suitable for a double heterostructure is used along the normal to the plane of the active layer. Aspects associated with the description of properties of hybrid modes are analyzed and solutions are obtained for a non-Gaussian angular distribution caused by bending of the wavefront under the influence of the $Im\varepsilon$ profile (in a waveguiding or “antiwaveguiding” structure). A comparison is made between the spontaneous emission intensity profiles in various types of planar stripe-geometry heterojunction lasers and the characteristic $Im\varepsilon$ profile in the assumed Epstein model. It is shown that the theoretical model can be applied to calculations of the mode profile in heterojunction lasers with stripe contact widths of approximately 15 $\mu m$.