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Additional info for Coherent Nonlinear Optics: Recent Advances
Field is a vacuum. 13). t; o(x-x ') <,E(x,O)t(x ' ,0» = 0 . 17b) In addition, for large N even moments of higher order can be expressed as sums of products of the corresponding second-order moments in a way characteristic of Gaussian statistics. Thus, each pulse behaves as if it were initiated by a random classical fluctuating source which follows Gaussian statistics. 17 Either choice of ordering may, of course, be used. When normal ordering is chosen, as in the Glauber-Haake treatment, pulse evolution appears to be triggered by the initial uncertainty in the atomic polarization.
These problems ca~ be circumvented by using indirect excitation methods such as three-level pumping and two-photon excitation with a nonresonant intermediate state. All observations of superradiance up to now have employed such schemes. However, the problem remains that when the pump radiation is turned off, a large residual polarization could be left at the pump transition. This can result in superradiance at this transition, which could deplete the population available for superradiance at the desired wavelength.
18) with 1. the identity operator, the operator equations of motion become linear. Their solution is then formally identical to that of the linearized semiclassical Maxwell-Schrodinger equations. Furthermore, once the atomic polarization becomes large compared to its initial fluctuations, the behavior of the system becomes completely semiclassical. 3, this occurs after a few TR, and long before nonlinear behavior due to decreasing inversion density sets in. Based on these considerations, Polder, Schuurmans and Vrehen developed a stochastic variable description to model the pulse evolution process, considering the initiating fluctuations as arising from a classical fluctuating field source.