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By Farhad H. M. Faisal (auth.)

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The three distinct third-order diagrams which provide the first correction to the one-photon absorption amplitude. 41 The Perturbation Theory Figure 11. The ten topologically distinct diagrams which provide the second correction to the one-photon absorption amplitude. 5. Two-Photon Absorption (Two-Mode Field) Let us denote the photons of two distinct modes by two distinct arrows, N'+ and~. In the lowest nonvanishing order (second order) there are four distinct diagrams, shown in Figure 12. We note that diagrams (c) or (d) correspond to absorption of two photons of the same mode, and therefore are of the same kind as in the monomode case in Figure 2.

22) By interpreting the energy-conserving delta functions as in the first-order case, we see that Eq. 22) contains: 34 Chapter 2 1. 23) 2. 24) 3. 25) is nonzero only when w, = wr. 25) gives the mixing amplitude between a degenerate pair of states, i) and f), due to the radiation field. 3. The Diagrammatic Method The preceding section contains some examples of the fact that an algebraic evaluation of a a given term of the perturbation series generates contributions to several distinct physical processes, not all of which may be of interest at the same time.

27), on the normalization volume of the laser field. , in a dilute gas) one may take the limit L 3 ~ oo, N. fixed, so that H" ? 0. , in a dense gas) where the effective electron number N. / L 3 = p (constant), one should expect a significant contribution from the polarization energy term H". 1. Introduction The essence of the theory of multiphoton processes proper lies in perturbation theory of one form or another. In this chapter we shall present a systematic development of perturbation theory and the relevant diagrammatic technique suitable for multiphoton processes.

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