Application of linear prediction and singular value decomposition for the analysis of periodic oscillations in coherent excitation spectra of condensed media and solid interfaces

Abstract

The observation of periodic responses after absorption of ultrashort laser pulses in condensed media and at solid interfaces is a common phenomena in various time-resolved spectroscopic methods using laser pulses shorter than the period of the coherently excited vibrations. Normally these signals have to be separated from strong slowly decaying backgrounds related to the creation of nonequilibrium carriers. The recording normally requires either a small period of time or lacks temporal resolution to obtain the good signal-to-noise ratio necessary for the observation of the vibrations. The standard method used for the analysis of the data is a curve-fitting routine to the time-domain data. However, the disadvantage is the necessity to estimate the number of spectral components before fitting. This paper will introduce under which conditions linear prediction and singular value decomposition in combination with an iterative nonlinear fitting in the time and spectral domain may extract an unknown number of spectral components including amplitude, lifetime, frequency and phase. Such information is essential to unambiguously evaluate the dominant optical excitation process, the phase of the initial displacement, the symmetry of the excited vibrational mode and the specific vibration generation process.

Coherent optical phonon generation in Bi3Ge4O12

“…Originally developed for the analysis of NMR free induction decay signals, this numerical technique can reveal the amplitude, frequency, and lifetime of a series of exponentially decaying sinusoidal waves without a priori knowledge of the oscillatory modes. Recently, this technique has been extended to time-domain optical signals with very good results [28][29][30].…”