
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

Analysis of Modes in a Vertical Cavity Surface Emitting Laser with Multilayer Bragg Reflectors
Seiji MUKAI Masanobu WATANABE Hiroyoshi YAJIMA
Publication
IEICE TRANSACTIONS on Electronics
Vol.E77C
No.9
pp.14791488 Publication Date: 1994/09/25 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: PAPER Category: OptoElectronics Keyword: mode analysis, vertical cavity laser, diode laser,
Full Text: PDF(900.6KB)>>
Summary:
A numerical method is introduced which is suitable for mode analysis in an optical resonator with complicated refractiveindex variations such as vertical cavity surface emitting lasers (VCSELs). In this method, the optical field of a laser mode is expressed as a linear combination of component fields with their coefficents to be determined. After a hypothetical boundary is set surrounding the region to be analyzed, the component fields are obtained by numerically integrating the wave equation in the inside region using the conditions on part of the boundary as the initial values of the integration. The total field, which is a linear combination of these fields, satisfies the equation and the selected part of the boundary conditions regardless of the coefficients. The conditions imposed on the total field on the rest of the boundary lead to a matrix eigenvalue problem, from which the optical frequency and the coefficients are obtained. The matrix expresses only boundary conditions and, therefore, its size is much smaller than that of a matrix expressing bulk conditions, as appears in the finite element method or the finite difference method. At the same time, this method has the advantage of adaptability for gradedindex problems in contrast to conventional boundary formalisms such as the boundary element method and the mode matching method, because in the present method the component fields (or base functions) are calculated for individual index distributions while in these methods an inflexible set of base functions is used. As an example of the application of the method, mode properties in gainguided VCSELs are analyzed using this method based on a twodimensional model. This is the first model that takes into account the effects of standingwave formation in the resonator and of the incident angle and polarizationdependence of reflectivity. The ability to treat these effects makes the present method suitable for VCSELs equipped with a thin active layer and with multilayer reflectors. Basic properties including polarization, threshold gain, oscillation wavelegths, and deflection of farfield patterns have been predicted for various cavity sizes and for various gradients in gain distributions. The major results of the analysis are: TE modes have lower thresholds than TM modes; the laser beam can be steered by tailoring the gain distribution as with edgeemitting lasers.

