Flicker Noise in Frequency Fluctuations of Lasers

Measured frequency fluctuation spectra $S_{\delta f}$ in ring lasers show that $S_{\delta f}=\frac{h_{-1\mathrm{}}}{\nu }+\frac{h_{-2\mathrm{}}}{{\nu }^2}$ at low Fourier frequencies $\nu$, while white noise prevails at higher frequencies. Experimentally, $S_{\delta f}=\left(\frac{\overline{A}{f}_0^2}{Q^4}\right)\left(\frac{1}{\nu }\right)$ has been found for the dependence of the $\frac{1}{\nu }$ noise (flicker noise) on the quality factor $Q$, with $\overline{A}\approx 4$ ($f_0=\mathrm{laser}\mathrm{frequency}$). The $Q^{-4\mathrm{}}$ dependence is readily explained by loss (or gain) fluctuations, through use of a Van der Pol oscillator.