Flicker noise in frequency fluctuations of lasers.

Abstract

Measured frequency fluctuation spectra ${S}_{\ensuremath{\delta}f}$ in ring lasers show that ${S}_{\ensuremath{\delta}f}=\frac{{h}_{\ensuremath{-}1}}{\ensuremath{\nu}}+\frac{{h}_{\ensuremath{-}2}}{{\ensuremath{\nu}}^{2}}$ at low Fourier frequencies $\ensuremath{\nu}$, while white noise prevails at higher frequencies. Experimentally, ${S}_{\ensuremath{\delta}f}=(\frac{\overline{A}{f}_{0}^{2}}{{Q}^{4}})(\frac{1}{\ensuremath{\nu}})$ has been found for the dependence of the $\frac{1}{\ensuremath{\nu}}$ noise (flicker noise) on the quality factor $Q$, with $\overline{A}\ensuremath{\approx}4$ (${f}_{0}=\mathrm{laser}\mathrm{frequency}$). The ${Q}^{\ensuremath{-}4}$ dependence is readily explained by loss (or gain) fluctuations, through use of a Van der Pol oscillator.