Non-Lorentzian spectral lineshapes near a Hopf bifurcation

The effects of additive white noise upon the dynamics of a system described by its normal form are investigated, with particular reference to the well-known model of a detuned mode laser. The power spectrum corresponding to the laser amplitude is determined finite-difference solution of a partial differential equation, and analytical formulas are determined in asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.