The grating decomposition method: A new approach for understanding polarization-selective transient grating experiments. I. Theory

Fourkas, John T.; Trebino, Rick; Fayer, M. D.
July 1992
Journal of Chemical Physics;7/1/1992, Vol. 97 Issue 1, p69
Academic Journal
In this paper and the following Paper (II) we introduce a new method of viewing transient holographic grating experiments in which the gratings are formed by laser beams of orthogonal linear or circular polarizations (or one of each). In this paper, we show that the two traditional methods of modeling these gratings, electric-field pictures and diagrammatic perturbation theory, may be augmented. We demonstrate that any grating can be decomposed into component intensity gratings that are related to the polarizations in its electric-field picture. Each of these component gratings may be analyzed separately (with or without diagrammatic perturbation theory), facilitating the incorporation of secondary effects (such as transport and heat deposition) into the grating calculation. The grating decomposition method (GDM) illuminates spatial structure that is not evident in standard perturbative calculations; it also provides a physical description that makes qualitative insights more readily obtainable, while at the same time making the electric-field approach rigorous and quantitative. Furthermore, the GDM reduces the complexity of many diagrammatic perturbation theory calculations. We also introduce effective two-interaction matrix elements (ETIMEs), which can be used to greatly simplify perturbative grating calculations. We show that ETIMEs, when considered in conjunction with the symmetry properties of the third-order susceptibility (χ(3)), can often be used to prove that some of the component gratings in a decomposition do not contribute to the signal and therefore need not be considered. In II, we apply this theory to two grating problems.


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