Generalized transfer function of nonlinear active semiconductor microring resonators

Abstract

The spectral properties of a single-mode active microring resonator are investigated in the frame of the extended transfer matrix formalism. Spontaneous emission, looked upon as the driving source of the radiation, is described in a semi-classical way in the spectral domain. The internal and emitted fields are filtered into the resonance modes of the whole structure; the spectral density of power is described by the generalized transfer function, which contains all essential mechanisms at work in a laser oscillator: gain, losses and sources. The active zone is saturated through Amplified Spontaneous Emission, integrated over its whole spectral range. Continuously valid across threshold, the method enables one to derive in a simple way the main steady-state properties of the laser oscillation, with the pumping rate as the only external parameter. In this approach, the optical properties of the active medium (the gain, the source and the refractive index) are supposed to be uniquely determined by the steady-state value of the carrier density, obtained within the framework of the rate equation formalism and assumed uniform along the active zone.