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

ISBN-10: 0471389307

ISBN-13: 9780471389309

ISBN-10: 0471466131

ISBN-13: 9780471466130

The recent version will give you the sole complete source to be had for non-linear optics, together with distinct 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)

Example text

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.

Comparison of the fully quantum numerical solution (solid line) and the approximate solution (112) (dashed line) for the initial mean number of photons Na ¼ 100ðE0 ¼ 0:01Þ. Classical solution is marked by dotted curve. quantum noise in nonlinear optical phenomena 41 the photon statistics when the evolution is restricted to the two-state subspace. Even in this simple case the fundamental mode evolved from the sub- to superPoissonian photon statistics. The numerical method presented above is suitable for answering questions about photon statistics and squeezing equally well as the question about the mean intensity.

We can thus expect from the short-time approximation that quantum noise does not significantly affect the classical solutions when the initial pump field is strong. We will return to this point later on, but now let us try to find the shorttime solutions for the evolution of the quantum noise itself—let us take a look at the quadrature noise variances and the photon statistics. Using the operator ^ solutions (94) and (95), one can find the solutions for the quadrature operators Q 2 2 ^ ^ ^ and P as well as for Q and P .

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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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