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Optics Letters

Analytical calculation of two-dimensional spectra

Joshua D. Bell, Rebecca Conrad, Mark E. Siemens

Published Mar 13, 2015• 36 citations
Publisher

Abstract

We demonstrate an analytical calculation of two-dimensional (2D) coherent spectra of electronic or vibrational resonances. Starting with the solution to the optical Bloch equations for a two-level system in the 2D time domain, we show that a fully analytical 2D Fourier transform can be performed if the projection-slice and Fourier-shift theorems of Fourier transforms are applied. Results can be fit to experimental 2D coherent spectra of resonances with arbitrary inhomogeneity.

DOI
10.1364/ol.40.001157

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We derive an analytical form for resonance lineshapes in two-dimensional (2D) Fourier transform spectroscopy. Our starting point is the solution of the optical Bloch equations for a two-level system in the 2D time domain. Application of the projection-slice theorem of 2D Fourier transforms reveals the form of diagonal and cross-diagonal slices in the 2D frequency data for arbitrary inhomogeneity. The results are applied in quantitative measurements of homogeneous and inhomogeneous broadening of multiple resonances in experimental data.
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