Transverse effects in coherently driven nonlinear cavities

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Abstract
We derive reduced field equations describing two cases of optical cavities driven by an external coherent field, taking into account the influence of transverse effects. For the passive-cavity case, we focus on the transistor characteristic and the onset of optical bistability. We prove that, depending on the sign of the detuning, different equations are needed. A global description of the field is possible in terms of a generalized Ginzburg-Landau equation, unless the detuning is finite and positive. That case requires a modal expansion. Furthermore, the good-cavity limit is regular, implying the same differentiation according to the sign of the detuning. For the active-cavity case, the same dependence on the sign of the detuning is found. A global description is obtained only for negative detunings. The good-cavity limit is described by a unique equation for all detunings.