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Fluctuation-induced resonances in nonlinear optics

Yehiam Prior, Peter Stern

Published Jun 9, 1986• 0 citations
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Abstract

Recently,1 a detailed analysis was given for the role played by laser phase fluctuations in the interaction of radiation with a resonant molecular system. 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.

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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
The effect of stochastic laser phase fluctuations on nonlinear optical phenomena are investigated within the phase-diffusion model. Averaged equations of motion are derived in the limit of infinitely short correlation times and the results are applied to multiphoton absorption and to four-wave mixing. The effect of the stochastic phase fluctuations is shown to be equivalent to a T2{T}_{2}T2​ dephasing process, and a procedure is described for the inclusion of this equivalence in many nonlinear-optical problems. When a given mode contributes n photons to a multiphoton absorption process, its contribution to the width of the multiphoton transition is n2{n}^{2}n2 times its own stochastic width. When correlated lasers are used as the excitation sources in four-wave-mixing experiments, (new) stochastic-fluctuation-induced extra resonances in four-wave mixing (SFIER4) will be observed, in complete analogy to the extra resonances induced by collisions [pressure-induced extra resonances in form-wave mixing (PIER4)].
The influence of the laser fluctuations on resonance fluorescence is treated exactly within the framework of multiplicative stochastic processes. For the phase diffusion model of the laser, I find that, in the limit of strong fields, the ratios of the width and height of the central peak to the side peak are, respectively, 23x\frac{2}{3x}3x2​ and 3x3x3x, where $x=\frac{(\ensuremath{\gamma}+{\ensuremath{\gamma}}_{c})}{(\ensuremath{\gamma}+2{\ensuremath{\gamma}}_{c})}$. The envelope of the intensity correlations is found to decay at the rate $\frac{(3\ensuremath{\gamma}+{\ensuremath{\gamma}}_{c})}{2}$.