Calculation of microcavity VCSEL field modes using a doubly iterative weighted index method

Michael J. Noble; John P. Loehr; James A. Lott

doi:10.1117/12.275571

6 June 1997 Calculation of microcavity VCSEL field modes using a doubly iterative weighted index method

Michael J. Noble, John P. Loehr, James A. Lott

Proceedings Volume 2994, Physics and Simulation of Optoelectronic Devices V; (1997) https://doi.org/10.1117/12.275571
Event: Photonics West '97, 1997, San Jose, CA, United States

Abstract

We generalize the weighted index method for analysis of modal structure in various devices, including vertical cavity surface emitting lasers. Our model uses a doubly iterative process to calculate the bound modes for any dielectric device with an azimuthally symmetric geometry. In order to calculate the modes we assume a separable form for the electric and magnetic vector potentials. The scalar wave equation is then solved for the axial components of electric and magnetic vector potentials. Assuming a functional form of A_z equals F((rho) )G(z) and F_z equals P((rho) )Q(z) we form coupled differential equations between F((rho) ) and G(z). These equations are then iteratively solved using the coupled boundary conditions for A_z and F_z. Convergence by tracking the change in the eigenfrequency for the radial and axial eigenvalue equations. Our method allows rapid calculation, compared to an analogous finite element approach, and will handle any azimuthally-symmetric geometry with piecewise-constant indices of refraction. This model is particularly well suited to the calculation of bound modes in microcavity and oxidized structures where field confinement effects can be very important. The model can also, in principle, be adapted to obtain radiative modes, and should provide a valuable tool to analyze field behavior and quantum optics effects in microcavity devices.

Citation Download Citation

Michael J. Noble, John P. Loehr, and James A. Lott "Calculation of microcavity VCSEL field modes using a doubly iterative weighted index method", Proc. SPIE 2994, Physics and Simulation of Optoelectronic Devices V, (6 June 1997); https://doi.org/10.1117/12.275571

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