Complex Raman amplitude recovery and dynamics from the Raman excitation profile: application to iodobenzene and azulene

Abstract

AbstractRecovering the complex amplitude or phase from an intensity, which is given as the modulus square of the amplitude, is a problem common to diverse physical areas. The focus of this paper is on the Raman excitation profile — the Raman intensity of a mode as a function of the excitation energy — which is given by the modulus square of the Raman amplitude. Three methods, with different principles, are presented for amplitude or phase recovery: the dispersion or energy‐frame method; the z‐transform or time‐frame method; and the maximum entropy method. A comparison function technique is introduced to address the usual situation where the measured intensity is band‐limited. There are two classes of problems, minimum phase and non‐minimum phase, and the mapping from the intensity to the complex amplitude may not be unique. The non‐minimum phase situation occurs when the analytically extended complex amplitude, with the energy E replaced by ξ = γ − iE, has zeros in the right‐half complex plane. These zeros have implications for the system dynamics. An algorithm is presented to search for the critical zeros. The characteristics of the zeros are studied with a two‐mode harmonic model, and the theory is applied to the Raman excitation profiles of iodobenzene and azulene. Copyright © 2001 John Wiley & Sons, Ltd.