Demodulation of intensity and shot noise in the optical heterodyne detection of laser interferometers for gravitational waves

Demodulation of intensity noise in the optical heterodyne detector is analyzed for application in interferometric gravitational-wave detectors. The correlation function and the power spectral density of the demodulated intensity noise are derived, taking into account the effect of bandpass filtering at the photodiode and an arbitrary demodulation waveform. The analysis includes demodulation of the rf-modulated shot noise as a special case of the intensity noise. For shot-noise-limited detection, the signal-to-noise ratio is found as a function of the modulation parameters, and the optimization of the signal-to-noise ratio with respect to the demodulation phase is described.