Theoretical study on phase conjugation in weakly injected vertical-cavity surface-emitting lasers

This paper gives a detailed theoretical investigation on phase conjugation induced by nearly degenerate four-wave mixing in single mode vertical-cavity surface-emitting lasers (VCSELs) with weak optical injection. Considering VCSELs that can work in linearly polarized or elliptically polarized states, it derives the theoretical expression of the conjugated field by small signal analysis based on the vectoral rate equations---the spin-flip model. For linearly polarized state, VCSELs show similar conjugate spectra to edge-emitting semiconductor lasers. For the elliptically polarized state, dichroism and birefringence parameters as well as the spin-flip rate can change the conjugate spectra. Especially, when frequency detuning of the probe and pump waves is between the positive and negative relaxation oscillation frequency, changes are evident. For specific values of parameters, conjugate efficiency between 20\,dB to 40dB are obtained.