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Analysis of complex multidimensional optical spectra by linear prediction



Ethan Swagel, Jagannath Paul, Alan Bristow, Jared Wahlstrand


We apply Linear Prediction from Singular Value Decomposition (LPSVD) to the analysis of two-dimensional complex optical spectra. LPSVD is a non-iterative procedure that fits time-domain complex data to the sum of damped sinusoids, or Lorentzian peaks in the spectral domain. Because the fitting is linear, it is not necessary to give initial guess parameters as in nonlinear fits. Although LPSVD is a one-dimensional algorithm, it can be performed column-wise on two-dimensional data. The method has been extensively used in NMR spectroscopy, where spectral peaks are typically nearly ideal Lorentzians, but to our knowledge has not been applied in the analogous optical technique, where peaks can be far from Lorentzian. We apply LPSVD to the analysis of zero, one, and two quantum electronic two-dimensional spectra from a semiconductor microcavity. The spectra consist of non-ideal, often overlapping peaks. We find that LPSVD achieves a very good fit even on non-ideal data. It reduces noise and eliminates discrete distortions inherent in the discrete Fourier transformation (DFT). We use it to isolate and analyze weak features of interest.
Optics Express


multidimensional spectroscopy, data analysis, optical spectroscopy


Swagel, E. , Paul, J. , Bristow, A. and Wahlstrand, J. (2021), Analysis of complex multidimensional optical spectra by linear prediction, Optics Express, [online],, (Accessed June 18, 2024)


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Created October 27, 2021, Updated November 29, 2022