Theory and Modeling of Lasing Modes in Vertical Cavity Surface Emitting Lasers

The problem of obtaining the lasing modes and corresponding threshold conditions for vertical cavity surface emitting lasers (VCSELs) is formulated as a frequency-dependent eigenvalue problem in required gain amplitudes and corresponding fields. Both index and gain guiding are treated on an equal footing. The complex gain eigenvalues define necessary but not sufficient conditions for lasing. The actual lasing frequencies and modes that the VCSEL can support are then determined by matching the gain necessary for the optical system in both magnitude and phase to the gain available from the laser's electronic system. Examples are provided