General formula for the natural width of optical parametric oscillator spectral lines

A new approach to the quantum analysis of the spectral linewidths of optical parametric oscillators (OPOs) is proposed. The approach is based on introducing a Hermitian frequency deviation operator. The spectral linewidths in the triply resonant OPO above-threshold regime have been calculated. It has been found that the width of the generated spectral line depends on the loss at all interacting frequencies, the photon number of frequency under study, and the threshold photon number of pump. The formula obtained for the spectral width is general; in particular cases, it yields the well-known results. The developed simple approach can be applied to the quantum analysis of the spectra of various oscillatory systems, for example, the multifrequency parametric and non-linear optomechanical interactions and lasers.