Download Advances in Chemical Physics, Vol.119, Part 1. Modern by Myron W. Evans, Ilya Prigogine, Stuart A. Rice PDF

By Myron W. Evans, Ilya Prigogine, Stuart A. Rice

The recent variation will give you the sole finished source on hand for non-linear optics, together with exact descriptions of the advances during the last decade from world-renowned specialists.

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Extra info for Advances in Chemical Physics, Vol.119, Part 1. Modern Nonlinear Optics (Wiley 2001)

Example text

11a. while the Q function does not suffer from such problems. When the initial state of the fundamental mode is a coherent state, the initial distribution is a Gaussian, and the result of simulation is pretty good. The method of classical trajectories has been used by Bajer et al. to explain the sub-Poissonian photon statistics in the second harmonic generation [36] as well as the third harmonic generation [37] in the no-energy-exchange regime. They have found that in this regime it is possible to obtain the steady-state solutions exhibiting subPoissonian photon statistics, and, surprisingly, they have shown that this quantum effect can be explained within the classical trajectories approach.

In Fig. 6 we present both solutions for the initial mean number of photons Na ¼ 100, which gives E0 ¼ 0:01. Both solutions are almost identical up to the first maximum, but subsequent maxima are substantially damped with respect to the approximate solution. The approximate solution correctly predicts the transition from the second harmonic regime to the downconversion regime, which is the physical reason for starting oscillations. The quantum noise really induces macroscopic revivals, but subsequent maxima are smaller and smaller and the second harmonic intensity asymptotically approaches a certain value.

The latter products appeared as a result of application the bosonic commutation relations (4) for the operators of the two modes, and these terms represent purely quantum contributions that would not appear if the fields were classical. For classical fields, only the highest-order products survive. The quantum noise contributions appear in terms $ t3 and higher in the expansion (94) for the fundamental mode operators and in terms $ t2 and higher in the expansion (95) for the second harmonic mode operators.

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