Phase Fluctuations

Albert D. Wheelon

Yehiam Prior, Peter Stern

Recently1 a detailed analysis was given for the role played by laser phase fluctuations in NL optics. In that work, the existence of new extra resonances induced by stochastic fluctuations was predicted, based on a derivation starting from the phase diffusion model. In this work we present the results of numerical simulations of laser phase fluctuations. The optical Bloch equations are solved numerically for a phase fluctuating laser. A model of a piecewise constant phase jumping at random between all values is treated, and other models are discussed. Molecular collisions are simulated and compared to phase fluctuations. The collisions give rise to the pressure-induced extra resonance (PIER4), while the phase jumps give rise to stochastic fluctuations-induced extra resonance (SFIER). These simulations show clearly that phase fluctuations may be analogous to real collisions and may cause extra resonances, and indeed, the SFIER4 resonance has recently been observed experimentally.2

Michael J. W. Hall

Aleksandr V. Belinsky, Alex A. Granovsky

It has been found that a nonlinear beam splitter is an interesting object for investigation for the following reasons. First, the classical and quantum descriptions of this object give opposite results for the behavior of phase fluctuations: according to the classical theory, the phase remains unchanged, whereas the quantum theory predicts that phase fluctuations increase or decrease in correlation with a decrease or increase in amplitude fluctuations. Second, quantum fluctuations of the input mode can be separated into amplitude and phase fluctuations, so that phase fluctuations are directed predominantly into one output mode, say the reflected mode, whereas amplitude fluctuations are directed predominantly into the other (transmitted) mode.

C. R. Willis

We derive and analyze the master equation for absorptive and dispersive optical bistability in the high-Q cavity limit where the driving laser has both amplitude and phase fluctuations which are larger than the small amplitude and phase fluctuations caused by incoherent spontaneous emission in the cavity. We treat the amplitude and phase fluctuations of the driving laser as independent time dependent Gaussian processes. The causes of jitter and amplitude fluctuations will vary from laser to laser and the fluctuations need not be Gaussian. However, we use Gaussian processes for mathematical tractability and because we expect them to be qualitatively correct. Recently,1 we have shown in the case of absorptive optical bistability when the driving laser has phase fluctuations the fundamental process which determines the statistical properties of the internal field is the competition between locking of the internal field phase to the phase of the driving laser and the diffusion of the phase of the internal field as a consequence of the driving laser fluctuations. The driving laser fluctuations have little effect if the phase locking rate is larger than the phase diffusion rate caused by the driving laser’s fluctuations. However, when the diffusion rate becomes comparable to the locking rate we find the amplitude of the 2 internal field is reduced and the dimensionless parameter2 measuring the importance of transitions from one branch of the OB curve to the other due to fluctuations takes on a value which leads to an appreciable transition rate due to fluctuations.

S. Werner