Thermal phase fluctuations in optically pumped dual-frequency vertical external-cavity surface-emitting lasers for cesium clocks based on coherent population trapping

Abstract

A fully analytical model is established for the thermal fluctuations of the beatnote phase of an optically pumped dual-frequency vertical-external-cavity surface-emitting laser (VECSEL). This model starts with the resolution of the heat equation inside the semiconductor chip structure and follows with the evaluation of the induced thermo-optic phase shift. Both the fluctuations of the heat induced by the optical pumping and the thermodynamic fluctuations at room temperature are considered. On the one hand, the thermal response of the structure is investigated and a significant thermal lens effect caused by the pump is deduced. On the other hand, the power spectral density of the frequency noise is calculated in the presence of diffusion spatial anisotropy. The present model is in very good agreement with the phase noise measured for a dual-frequency VECSEL at 852 nm for application to metrology and the validity of the usual low-pass filter model is discussed.