By Myron W. Evans, Ilya Prigogine, Stuart A. Rice
The hot version will give you the sole accomplished source to be had for non-linear optics, together with targeted descriptions of the advances over the past 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)
This kind of comparison has been done for second-harmonic process by Nikitin and Masalov . Since it is really impressive to see how good the quantum Q function contours are reproduced by a cloud of points that undergone classical evolution starting from the initial conditions described by the Gaussian distribution, we show in Fig. 12 clouds of 1000 points for the same values of the evolution time as in Fig. 11 for Na ¼ 10. Why is the Q function reproduced so well with the classical trajectories?
K¼0 k0 ¼0 0 Â ð141Þ The two functions can be evaluated numerically for a not-too-large mean number of photons Na . In Fig. 11 we have shown the contour plots of the Q function for the fundamental mode (Fig. 11a) and the second-harmonic mode (Fig. 11b) for the initial mean number of photons of the fundamental mode Na ¼ 10. It is seen that the centroid of the distribution, in case of the fundamental mode, moves to the left along the Re a axis showing squeezing along this axis at initial stages of the evolution, and next it becomes a two-peak structure first noticed by Nikitin and Masalov .
1 0 0 2 4 6 8 τ (b) 10 12 14 16 Figure 5. Intensity of the second-harmonic: (a) initial coherent state with Na ¼ 2 (solid line) and initial number state with two photons (dashed line); (b) initial coherent state with Na ¼ 10 (solid line), Na ¼ 40 (dashed line), and Na ¼ 100 (dashed–dotted line). Dotted line marks the classical solution. ity Na ) 1. The curves are plotted for Na ¼ 10 (solid line), Na ¼ 40 (dashed line), and Na ¼ 100 (dashed-dotted line). For reference, with the dotted line the classical solution is marked on both figures.