Thermal noise in optically pumped DF-VECSELs

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 identified: (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 first sources of noise are well modeled and understood. But in [2] a simple second-order low-pass filter behaviour is assumed for the thermal contribution to the frequency noise power spectral density (PSD) spectra. Yet, defining unequivocally a cut-off frequency is not obvious since different time scales are actually involved. Moreover, this over-simplified 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.