Application of linear prediction and singular value decomposition for the analysis ofperiodic oscillations in coherent excitation spectra of condensed media and solidinterfaces

Abstract

The observation of periodic responses after absorption of ultrashort laser pulses incondensed media and at solid interfaces is a common phenomena in various time-resolvedspectroscopic methods using laser pulses shorter than the period of the coherently excitedvibrations. Normally these signals have to be separated from strong slowly decayingbackgrounds related to the creation of nonequilibrium carriers. The recording normallyrequires either a small period of time or lacks temporal resolution to obtain thegood signal-to-noise ratio necessary for the observation of the vibrations. Thestandard method used for the analysis of the data is a curve-fitting routine to thetime-domain data. However, the disadvantage is the necessity to estimate the numberof spectral components before fitting. This paper will introduce under whichconditions linear prediction and singular value decomposition in combination withan iterative nonlinear fitting in the time and spectral domain may extract anunknown number of spectral components including amplitude, lifetime, frequency andphase. Such information is essential to unambiguously evaluate the dominantoptical excitation process, the phase of the initial displacement, the symmetryof the excited vibrational mode and the specific vibration generation process.