[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Thermal Noise in Optically Pumped DF-VECSELs

摘要： Over the last decades, the low noise properties of Vertical–External–Cavity Surface–Emitting Lasers (VECSELs) have aroused interest for various applications. The dual–frequency (DF) VECSELs can generate a very low noise RF signal resulting from the beatnote of two orthogonal linear polarizations as sketched in Fig.1(a). For example, the very high spectral purity and class–A operation of DF–VECSELs are of interest for ultrastable atomic clocks [1] or microwave electronics for optically-carried RF signal processing or wide-band RADARs. The sources of noise of optically pumped VECSELs are well identi?ed : (i) the intensity noise induced by the pump through the laser dynamics, (ii) the spontaneous emission contribution, (iii) technical noises such as mechanical vibrations, and (iv) the thermal noise. The two ?rst sources of noise are well modeled and understood. But in [2] a simple second–order low-pass ?lter behaviour is assumed for the thermal contribution to the frequency noise power spectral density (PSD) spectra. Yet, de?ning unequivocally a cut–off frequency is not obvious since different time scales are actually involved. Moreover, this over–simpli?ed model fails at low frequencies in [3] as displayed in Fig.1(b). Indeed, below 200 kHz the slope of the beatnote phase–noise spectrum of a DF–VECSEL at 852 nm obeys a f ?3 scaling law instead of the f ?4 expected behaviour. The aim of the present work is to microscopically model the thermal noise contribution. First, we describe the layers of the optically pumped emitting–surface, which is glued to a Peltier cooler. The heat equations take into account transverse and longitudinal diffusion processes. Assuming a gaussian pro?le for the pump, we obtain the temperature ?eld inside the structure using Hankel transformation formalism and we investigate the transient thermal response. The pump intensity ?uctuations induce heat ?uctuations inside the structure leading to changes of the refractive index and the material thermal–expansion, which are responsible for frequency ?uctuations of the laser mode. We ?nd an analytical expression of the frequency noise PSD induced by these thermo-optic effects, which allows to model the beatnote phase noise PSD of DF-VECSELs. We ?nd a very good agreement with the f ?3 slope of the experimental datas and we evidence the fundamental thermal ?uctuations contribution at room temperature. Such thermodynamics ?uctuations were already investigated for VCSEL structures in [4], starting from a stochastic heat equation. We extend it to a full study of the frequency noise PSD spectrum for DF-VECSELs. We obtain a fully analytical expression and discuss its validity.