By Myron W. Evans, Ilya Prigogine, Stuart A. Rice
The recent version will give you the sole finished source on hand for non-linear optics, together with specified descriptions of the advances during the last decade from world-renowned specialists.
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Additional info for Advances in Chemical Physics, Vol.119, Part 1. Modern Nonlinear Optics (Wiley 2001)
5. In Fig. 5a we have plotted the normalized second-harmonic intensity ^ b i=Na , where Na is the initial mean number of photons of the coherent nb ¼ 2hN state of the fundamental mode, against the scaled time t for the initially coherent state with the mean number of photons equal to 2 (solid line) and compared it with the corresponding intensity obtained for the initial state of the fundamental mode being the Fock state with two photons [Eq. (132)]. In the latter case we see the perfectly periodic behavior with complete transfer of energy between the fundamental and second-harmonic modes.
4. The potential represents a well in which the particle will oscillate exhibiting fully periodic behavior. From Eq. (109) we get qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ dnb ð110Þ ¼ 2 nb ð1 À nb Þ2 À nb E0 dt Comparing Eq. (110) with Eq. (66), we find that both equations have extra terms (the E or E0 terms) which make the solutions oscillatory, but the physical reason for oscillations is different in both cases. In Eq. (66) different from zero E comes from the nonzero initial value of the second-harmonic mode intensity, while in Eq.
The linearized results are in good agreement with the exact numerical results roughly up to the scaled time t ’ 1. The long-time evolution (t > 1) of the quadrature variances is principally different from their linearized approximation counterparts because the linearization fails to predict the quantum noise induced revival in the evolution. It is also clear from Fig. 8a that the degree of squeezing that can really be obtained is much smaller than that predicted from the linearized theory. The long time behavior of the quadrature variances is presented in Fig.