Resonant-wavelength control and optical-confinement analysis for graded SCH VCSELs using a selfconsistent effective-index method

We report novel design considerations for graded separate confinement heterostructure (SCH) cavities of oxideconfined vertical-cavity surface-emitting lasers (VCSELs). Using a self-consistent effective-index method, we have analyzed ungraded, linearly and exponentially graded SCH cavities of an 850-nm VCSEL. An ungraded SCH gives the best optical-confinement factor, while linear and exponential gradings reduce the factor by 18% and 9%, respectively. Grading the SCH cavities of oxide-confined VCSELs leads to both a shift in the resonant wavelength as well as a decrease in the optical-confinement factor. The resonant-wavelength shifts in graded SCH cavities are attributed to two competing effects: the formation of an effective-index step that redefines the (lambda) cavity, and larger optical-field leakage, which relaxes the confinement. We have also demonstrated that wavelength shifts can be easily compensated by optimized width extensions of the aperture layers which sandwich the graded SCH cavity, without further reducing the optical-confinement factor. Based on a revised understanding of the resonances for graded SCH cavities, we can therefore control the design of graded SCH VCSELs to obtain a desired resonant wavelength with great precision.