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

ISBN-10: 0471389307

ISBN-13: 9780471389309

The hot version will give you the sole finished source on hand for non-linear optics, together with particular descriptions of the advances over the past 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)

Example text

It is true, for example, for the initially squeezed state of the fundamental mode. quantum noise in nonlinear optical phenomena 37 It is interesting to consider one particular initial state of the field in which there are only two photons at the fundamental mode and no photons in the second-harmonic mode: j2; 0i. With this initial state the only state that can be created in the process is the state j0; 1i with one photon in the second-harmonic mode and zero photons in the fundamental mode. Next, the second-harmonic photon can be downconverted into two photons of the fundamental mode, and we observe fully periodic evolution.

At a later time, t ¼ 1, a single, well-resolved peak of the distribution is visible, signifying a relatively well defined phase of the second-harmonic mode in conjunction with the phase of the fundamental mode.

There is a quantity that is conserved during this motion, and we can write "   # d 1 dnb 2 2 0 À2nb ½ð1 À nb Þ À E Š ¼ 0 dt 2 dt ð109Þ where E0 ¼ 1=C0 is the term representing the quantum noise contribution (it comes from application of the commutation rules to the field operators). The quantity in the square brackets can be considered as the total energy of a ‘‘particle’’ at position nb , with the kinetic energy 12 ðdnb =dtÞ2 and the potential energy V ¼ À2nb ½ð1 À nb Þ2 À E0 Š. The potential energy is shown in Fig.

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