Publications

A methodology is presented that allows the derivation of low-truncation-error finite difference equations for photonics simulation. This methodology is applied to the case of wide-angle beam propagation in two dimensions, resulting in finite difference equations for both TE and TM polarization that are quasi-fourth-order accurate even in the presence of interfaces between dissimilar dielectrics. This accuracy is accomplished without an appreciable increase in numerical overhead and is concretely demonstrated for two test problems having known solutions. These finite difference equations facilitate an approach to the ideal of grid-independent computing and should allow the simulation of relevant photonics devices on personal computers.

Recent advances in Vertical-Cavity Surface-Emitting Laser (VCSEL) technology that have led to higher efficiencies and lower thresholds have opened up a new realm of applications for these devices. In particular, phase-locked arrays of VCSELs1, previously thought to be impractical due to thermal considerations, now look extremely attractive as high-power and highbrightness sources. In addition, a new understanding of waveguiding in VCSELs2 has led to practical methods for designing phase-locked arrays employing either evansecent or leaky-mode (antiguided) coupling. The latter type of coupling is particularly attractive in light of previous calculations1 that predict especially strong mode discrimination against higher-order lateral modes. In this paper we report the first detailed simulation of leaky-mode coupling between two VCSEL pixels performed without the use of simplifying assumptions such as the effective index model. The results of this simulation are, however, found to be in good agreement with previously-developed simple theories3 of leaky-mode coupling.

Vertical-cavity surface-emitting lasers (VCSELs) are presently the subject of intense research due to their potential as compact, efficient, astigmatic laser sources for a number of important applications. Of special interest are the selectively-oxidized VCSELs that have recently set records for threshold current and wall-plug efficiency. The onset of higher-order modes at powers of a few milliWatts, however, presently limits the wide utilization of these devices and indicates the need for improvements in design. Unfortunately, their complexity precludes optimization based solely upon empirical methods, and points instead to the need for better numerical models. Modeling the optical field in a vertical-cavity laser, however, is especially difficult due to both the high Q of the optical cavity and the distributed reflectivity of the mirrors. Our approach to this dilemma has been the development of modeling techniques on two complexity scales. We first derived an effective- index model that is numerically efficient and thus can be included together with carrier transport and thermal models to make up a self-consistent modeling package. In addition to its use in the overall VCSEL model, this simplified optical model has been extremely valuable in elucidating the basic principles of waveguiding in VCSELs that in turn have led to new ideas in device design. More specifically, the derived expression for the effective index shows clearly that index guiding in a VCSEL depends only on variations in optical cavity length, and thus can be engineered without the need to alter the material index of refraction. Also, we have designed index- guided and antiguided devices whose cavity lengths are modified in certain regions by etching of the cavity material prior to growth of the second mirror. Fabrication of these new device designs is presently in progress.

We present a comprehensive numerical model for vertical-cavity surface-emitting lasers that includes all major processes affecting cw operation of axisymmetric devices. In particular, our model includes a description of the 2-D transport of electrons and holes through the cladding layers to the quantum well(s), diffusion and recombination of these carriers within the wells, the 2-D transport of heat throughout the device, and a multilateral-mode effective index optical model. The optical gain acquired by photons traversing the quantum wells is computed including the effects of strained band structure and quantum confinement. We employ our model to predict the behavior of higher-order lateral modes in proton-implanted devices and to provide an understanding of index-guiding in devices fabricated using selective oxidation.