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

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

ISBN-10: 0471389307

ISBN-13: 9780471389309

ISBN-10: 0471466131

ISBN-13: 9780471466130

The recent variation will give you the sole complete source to be had for non-linear optics, together with specified descriptions of the advances during the last decade from world-renowned specialists.

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

Example text

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. (110) the nonzero value of E0 comes from the quantum noise. We can interpret this fact in the following way.

For reference, with the dotted line the classical solution is marked on both figures. The solutions are oscillatory but the oscillations are damped rather quickly when the pump mode is strong. The higher is the intensity of the pump mode, the longer the solution sticks to the classical solution before the process is reversed from the second-harmonic 40 ryszard tanas´ generation into the downconversion. The maximum reached by the second harmonic intensity increases, as the intensity of the pump mode increases, giving better efficiency of conversion of the fundamental mode field into the second harmonic.

B. Linearized Quantum Equations Assuming that the quantum noise is small in comparison to the mean values of the field amplitudes, one can introduce the operators Á^a ¼ ^ a À h^ ai ; Á^ b ¼ ^b À h^bi ð79Þ 22 ryszard tanas´ which describe the quantum fluctuations. On inserting the fluctuation operators (79) into the original evolution equations (56) and keeping only the linear terms in the quantum fluctuations, we get the equations d bi þ h^aþ iÁ^bÞ Á^ a ¼ À2ikðÁ^ aþ h ^ dt d ^ Áb ¼ À2ikh^ aiÁ^a dt ð80Þ where h^ ai and h^ bi are the solutions for the mean fields and can be identified with the classical solutions.

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Advances in Chemical Physics, Vol.119, Part 1. Modern Nonlinear Optics (Wiley 2001) by Myron W. Evans, Ilya Prigogine, Stuart A. Rice

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