Nonlinear incoherent spectroscopy

Abstract

Two-dimensional (2D) time-domain CW spectroscopy is a form of non-linear incoherent spectroscopy, where the Fourier transform of a 2D spectrum is scanned in a pointwise fashion in the time domain. This is an alternative approach to the frequency domain data treatment used in stochastic N.M.R. spectroscopy. It is investigated for its use in 2D E.S.R. spectroscopy. A linear variant of the technique is applied in FTIR spectroscopy, where the auto-correlation function of the response is sampled as a function of a time delay introduced by a mirror displacement. In nonlinear incoherent spectroscopy nonlinear cross-correlation functions of excitation and response are recorded as functions of multiple delays. Their Fourier transforms are the nonlinear susceptibilities. The explicit time domain cross-correlation method dealt with is compared to the frequency domain data evaluation of stochastic 2D N.M.R. It is illustrated by 1D and 2D N.M.R. interferograms derived from numerical third order cross-correlation of experimental excitation and response records. The concept of an analog third order cross-correlator for use in E.S.R. spectroscopy is outlined. Given enough hardware, each time delay can be hardwired, so that a complete data matrix is obtainable in one shot. In contrast to pulsed 2D spectroscopy the method possesses a multi-dimensional multiplex advantage. However the measurement time needed in practice is determined by the systematic noise inherent to all correlation based methods.