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

Abstract

Recovering 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. © 2001 John Wiley & Sons, Ltd.