Lasing modes in equilateral-triangular laser cavities

Abstract

We report the study of lasing modes in broad-area, equilateral-triangular laser cavities. An alternative approach is proposed to study optical modes in equilateral triangular cavities in an analytical form. The modes were obtained by examining the simplest optical paths inside the cavity, which yields the final solution with the boundary conditions. The cavities can be fabricated from semiconductor heterostructures grown on ͑111͒oriented substrates, which can be easily cleaved into equilateral triangular shapes. Such a design takes advantage of total internal reflection at the cleaved facets of the cavity for circulating modes. Experimental results are obtained from cavities fabricated from a superlattice structure of In 0.13 Ga 0.87 As/GaAs grown on a ͑111͒ GaAs substrate.

Electromagnetic modes in dielectric equilateral triangle resonators

“…The DBC approximation applied previously [2,14] clearly does not describe the fields correctly at a dielectric-dielectric boundary. The goal here is to use the general knowledge of the modes from the DBC analysis, but do the correct matching of plane wave fields inside the cavity with evanescent fields on the outside.…”

“…Eqs. (17) and (18) merely give some sums of the ∆ l phase factors, whereas, we actually need to determine each one separately, and more importantly, we need to find the wavevector magnitude k. This is accomplished by using their definitions (12) together with the corresponding y-components of the wavevectors, obtained from (2). The necessary components are…”

“…Using values n 5 ≥ 0 and evaluating the possible quantum numbers, the well-known solutions for DBC are recovered [2,9,15], in terms of shifted quantum numbers,…”

“…To this end, various twodimensional (2D) geometries have been considered for their different influence on the mode properties, including disks, [1] cleaved [2] and etched [3] semiconductor triangles, squares, [4,5,6] and zeolite ALPO 4 -5 hexagonal crystals. [7,8] The problem of equilateral triangle resonators (ETR) considered here is particularly interesting, because the symmetry present allows for a considerable simplification of the analysis.…”

“…Chang et al [2] analyzed the ETR wavefunctions under the assumption of Dirichlet boundary conditions (DBC), using an exactly known solution [9], for transverse magnetic (TM) polarization only. In the presence of a dielectric-dielectric boundary, however, the fields do not go to zero on the boundary, instead, the field confinement can be provided by TIR, assuming a refractive index in the cavity, n, greater than that of the surroundings, n ′ .…”