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arXiv:2504.08297 · Optics Letters

Quantitative line shape analysis for arbitrary inhomogeneity in two-dimensional coherent spectroscopy

Bhaskar De, Pradeep Kumar, Krishna K. Maurya, Rishabh Tripathi, Rohan Singh

Published Jun 2, 2025• 1 citation
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Abstract

Two-dimensional coherent spectroscopy (2DCS) provides simultaneous measurement of homogeneous and inhomogeneous linewidths through quantitative line shape analysis. However, conventional line shape analysis methods assume Gaussian inhomogeneity, limiting its applicability to systems with non-Gaussian inhomogeneity. We present a quantitative line shape analysis method incorporating arbitrary inhomogeneity using a bivariate spectral distribution function in 2DCS simulations. An algorithm is developed to extract the homogeneous linewidth and arbitrary inhomogeneous distribution from an experimentally measured 2D spectrum. We demonstrate this framework for a quantum-well (QW)-exciton resonance with non-Gaussian inhomogeneity. This work broadens the scope of quantitative line shape analysis for studying materials with non-Gaussian inhomogeneity.

DOI
10.1364/ol.564956

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Two-dimensional coherent spectroscopy (2DCS) provides simultaneous measurement of homogeneous and inhomogeneous linewidths through quantitative line shape analysis. However, conventional line shape analysis methods assume Gaussian inhomogeneity, limiting its applicability to systems with non-Gaussian inhomogeneity. We present a quantitative line shape analysis method incorporating arbitrary inhomogeneity using a bivariate spectral distribution function in 2DCS simulations. An algorithm is developed to extract the homogeneous linewidth and arbitrary inhomogeneous distribution from an experimentally measured 2D spectrum. We demonstrate this framework for a quantum-well (QW)-exciton resonance with non-Gaussian inhomogeneity. This work broadens the scope of quantitative line shape analysis for studying materials with non-Gaussian inhomogeneity.
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Correlated electron-hole pairs, or excitons, in semiconductor nanostructures have been studied extensively over the past few decades. The optical response of excitons is complicated due to inhomogeneous broadening, presence of multiple states, and exciton-exciton interactions. In this work we bring new perspectives to exciton physics in semiconductor quantum wells (QWs) through two-dimensional coherent spectroscopy (2DCS).\nThe effect of QW growth direction on the optical properties of excitons is explored by studying (110)-oriented GaAs QWs. The homogeneous and inhomogeneous linewidths of the heavy-hole exciton resonance are measured. By probing the optical nonlinear response for polarization along the in-plane crystal axes [1-10] and [001], we measure different homogeneous linewidths for the two orthogonal directions. This difference is found to be due to anisotropic excitation-induced dephasing, caused by a crystal-axis-dependent absorption coefficient. The extrapolated zero-excitation density homogeneous linewidth exhibits an activation-like temperature dependence.\nSpectral diffusion of excitons in (001)-oriented QWs has been studied. We show that the spectral diffusion characteristics depend strongly on the sample temperature. Spectral diffusion is generally assumed to follow the strong-redistribution approximation, partly because of lack of any evidence to the contrary. We find that this assumption is violated at low sample temperatures for excitons in QWs; high-energy excitons preferentially relax due to a negligible phonon population at low temperatures. The frequency-frequency correlation function is measured through a numerical fitting procedure to quantify spectral diffusion for sample temperatures >20>20>20 K.\nExciton-exciton interactions affect the light-matter interactions in QWs significantly. We present an intuitive and simple model for these interactions by treating excitons as interacting bosons. We show that the polarization-dependent exciton dephasing rate in GaAs quantum wells is due to the bosonic character of excitons. We fit slices from simulated spectra to those from the experimentally measured spectra and show that interference between two different quantum mechanical pathways results in a slower dephasing rate for co-circular and co-linear polarization of optical excitation pulses. This interference does not exist for cross-linearly polarized excitation pulses resulting in a faster dephasing rate. Additionally, we were able to separately quantify inter- and intra-mode interactions between excitons through exciton-density-dependent measurements.
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.
As an extension to powerful two-dimensional coherent spectroscopy, optical three-dimensional (3D) coherent spectroscopy has been experimentally implemented and found beneficial in studying various systems in physics and chemistry. A critical challenge is how to interpret 3D spectra and extract useful quantitative information, given the richness and complexity of 3D data. Here, we demonstrate how the information of a system's optical response is manifested in 3D spectra by theoretical simulations of a few representative examples including a homogeneous three-level V system, an inhomogeneous three-level V system, and an inhomogeneous three-level ladder system. These examples show that important parameters of the system can be extracted from the spectral pattern, peak positions, amplitudes, and line shapes. The method developed here can be used to analyze 3D spectra of more sophisticated systems which might be a generalization or combination of the three examples, contributing to develop a general approach for the interpretation of 3D spectra.
The interplay between disorder and Coulomb interactions ubiquitously affects the properties of condensed matter systems. We examine its role in the nonlinear optical response of semiconductor quantum wells. In particular, we investigate the coherent coupling strength between exciton resonances that are spectrally split by interface fluctuations. Previous studies yielded conflicting results. In light of rising interest in semiconductor devices that rely on spatial and/or temporal coherence, we revisit this problem by applying a newly developed spectroscopy method: electronic two-dimensional Fourier transform spectroscopy (2DFTS). 2DFTS is a powerful technique for revealing the presence of coupling and for distinguishing the (coherent or incoherent) nature of such coupling, especially in complex systems with several spectrally overlapping resonances. Even the most basic information about such complex systems, including the homogeneous and inhomogeneous linewidths of various resonances, cannot be extracted reliably using conventional spectroscopic tools. In these new 2DFTS measurements, we did not observe any clear cross peaks corresponding to coherent couplings between either heavy-hole or light-hole excitons. These measurements allow us to place a quantitative upper bound on the possible coupling strength in this prototypical system. A modified mean-field theory reveals a simple yet important relation that determines how the coherent coupling strength depends on the disorder correlation length and Coulomb interaction length. © 2010 Copyright SPIE - The International Society for Optical Engineering.