Optical modeling of certical-cavity surface-emitting lasers

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