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Journal of Physics B Atomic Molecular and Optical Physics

Resonant Rayleigh-type optical mixing spectra of homogeneously and inhomogeneously broadened two-level systems

O. Arístides Marcano, Isaac Reif, José Luis Paz, Héctor J. Franco

Published Apr 14, 1990• 3 citations
Publisher

Abstract

Resonant Rayleigh-type optical mixing spectra for homogeneously and inhomogeneously broadened two-level systems are calculated. Differences in the forms of the spectra, such as symmetry, saturation and AC Stark splitting are presented. The observed differences can be used to discriminate whether the spectrum is homogeneously or inhomogeneously broadened.

DOI
10.1088/0953-4075/23/7/021

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Resonant Rayleigh-type optical mixing spectra for homogeneously and inhomogeneously broadened two-level systems are calculated. Differences in the forms of the spectra, such as symmetry, saturation and AC Stark splitting are presented. The observed differences can be used to discriminate whether the spectrum is homogeneously or inhomogeneously broadened.
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.
The influence of the high-pump-field intensity saturation and dynamic Stark effects on the resonant nearly degenerate four-wave-mixing signal (${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$) is studied in a frequency space defined by the pump- and probe-field frequencies, ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, respectively. Variable inhomogeneous widths have been considered ranging from extremely narrow (homogeneous distribution) to extremely wide. Remarkable differences between nearly homogeneously broadened systems and extreme inhomogeneous ones are exhibited. It is shown, for the situation of homogeneous broadening, that the spectra carried on with fixed probe and fixed pump frequency values have substantial differences in shape. These differences disappear in the situation of extreme inhomogeneous broadening. Fixed-pump-frequency resonant and fixed-probe-frequency nonresonant spectra are proposed as very convenient tools to yield useful evidence about the width of the inhomogeneous molecular distribution.
The dependence of the Rayleigh-type optical mixing signal intensity on the incident pump and probe frequencies for different values of T1/T2 is shown in a three-dimensional plot for a homogeneously broadened line. The symmetry properties of the signal in this space and of the nonlinear process that generates the line are related. These properties are used to show the dependence of the measured spectra on the way in which the frequencies of the incident fields are varied. Furthermore, this plot in frequency space yields information that may be used for the determination of the relaxation times T1 and T2.
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
The formulation of phase conjugation via nondegenerate four-wave mixing in a homogeneously broadened resonant medium is generalized to include saturating pump waves. An ultrahigh-Qoptical filter is predicted, showing both gain and a bandwidth less than the homogeneous linewidth of the atom. The dependence of the filter function on the ac Stark effect and on the use of asymmetric pump wave intensities is discussed. In addition, several new phenomena are shown which manifest themselves as a dip in the degenerate reflectivity at line center.