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Optics and Spectroscopy

On experimental potentialities of correlation analysis of the inhomogeneously broadened spectra

Valerii S Zapasskii, G. G. Kozlov, V. V. Ovsyankin

Published Nov 1, 2002• 0 citations
Publisher

Abstract

The potentialities of the correlation technique with respect to extracting the homogeneous line profile from an inhomogeneously broadened spectrum are analyzed by computer simulation. The signal-to-noise ratio for autoconvolution of the homogeneous line profile, obtained by statistical processing of an array of realizations of the inhomogeneously broadened spectrum for different experimental conditions and different values of parameters of the system is calculated. A general form of the dependence of the signal-to-noise ratio on the magnitude of the accumulated signal is established. An interpolation formula that expresses this dependence in an analytical form is obtained and a simple procedure is proposed that allows one to plot this dependence for specific experimental situations.

DOI
10.1134/1.1523994

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The potentialities of the correlation technique with respect to extracting the homogeneous line profile from an inhomogeneously broadened spectrum are analyzed by computer simulation. The signal-to-noise ratio for autoconvolution of the homogeneous line profile, obtained by statistical processing of an array of realizations of the inhomogeneously broadened spectrum for different experimental conditions and different values of parameters of the system is calculated. A general form of the dependence of the signal-to-noise ratio on the magnitude of the accumulated signal is established. An interpolation formula that expresses this dependence in an analytical form is obtained and a simple procedure is proposed that allows one to plot this dependence for specific experimental situations.
It is shown that the lineshapes of inhomogeneously broadened spectra, due to the statistical nature of their formation, exhibit spectral fluctuations. Formulas are obtained that allow one, based on correlation analysis of different realizations of the inhomogeneously broadened line, to reconstruct its homogeneous lineshape and to evaluate the number of centers involved in its formation. The magnitude of these spectral fluctuations is estimated and it is shown that the proposed method can be efficiently used in practice.
Methods for detection of narrow spectral lines in the radiation emitted by a distant source, masked by a spatially inhomogeneous frequency shift, are considered. An analysis is made of the possibility of using, in principle, the Brown-Twiss correlation method and of the optical heterodyne method with independent heterodynes for this purpose. The normalized mutual correlation function is calculated in the plane of two receivers used to investigate a distant source characterized by a spatially inhomogeneous broadening of the spectrum. Estimates are given of the signal/noise ratio for both methods when applied to sources in the form of laser regions in a stellar atmosphere in the case of a strong rotation-induced spatial broadening of the spectrum.
Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.
Two-dimensional (2D) line shapes derived from four types of coherent third-order nonlinear spectroscopies as a function of two independent time or frequency variables are compared. The signals scattered into two wave-vector-matching directions in the limits of high-time or high-frequency resolution are calculated for an inhomogeneously broadened ensemble of two-level systems with phenomenological dephasing and population relaxation times. While one-dimensional (1D) line shape analysis for this model is ambiguous, the contours of these 2D line shapes are shown to be characteristic of the relative time scales of the three relevant line-broadening parameters. These broadening mechanisms are also apparent by comparing 2D spectral profiles along the diagonal and antidiagonal frequency axes. For time domain experiments, in analogy with NMR correlation spectroscopy, the radiated signal is observed as a function of the two coherence periods and is 2D Fourier transformed to obtain a line shape. For experiments based on the photon echo, the ellipticity of the absolute value 2D line shape is related to the ratio of the inhomogeneous width to the dephasing rate, whereas experiments based on the transient grating method are shown to be functionally 1D. For frequency domain experiments, the contours of the 2D line shape can yield information on static and both dynamic broadening mechanisms. While the addition of spectral diffusion to such calculations will modify these results for frequency domain experiments, characterizing these dynamics in the time domain naturally leads to a 3D experiment analogous to the spin diffusion experiment in NMR.