The amplitude and phase noises of a dual-frequency vertical-external-cavity surface-emitting laser (DF-VECSEL) operating at telecom wavelength are theoretically and experimentally investigated in detail. In particular, the spectral behavior of the correlation between the intensity noises of the two modes of the DF-VECSEL is measured. Moreover, the correlation between the phase noise of the radio-frequency (RF) beatnote generated by optical mixing of the two laser modes with the intensity noises of the two modes is investigated. All these spectral behaviors of noise correlations are analyzed for two different values of the nonlinear coupling between the laser modes. We find that to describe the spectral behavior of noise correlations between the laser modes, it is of utmost importance to have a precise knowledge about the spectral behavior of the pump noise, which is the dominant source of noise in the frequency range of our interest (10 kHz to 35 MHz). Moreover, it is found that the noise correlation also depends on how the spatially separated laser modes of the DF-VECSEL intercept the noise from a multi-mode fiber-coupled laser diode used for pumping both the laser modes. To this aim, a specific experiment is reported, which aims at measuring the correlations between different spatial regions of the pump beam. The experimental results are in excellent agreement with a theoretical model based on modified rate equations.
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