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Optics Letters

Line narrowing and hole burning within the homogeneous linewidth: a new wave-mixing effect in two-level systems

Jens Förstner, A. Knorr, Markus Lindberg, S. W. Koch

Published Oct 15, 2002• 1 citation
Publisher

Abstract

The interaction of strong low-area pulses with two-level systems shows absorption line narrowing and hole burning within the homogeneous linewidth as a result of nonlinear wave mixing. The wave mixing results from the two-level electronic saturation nonlinearity and occurs, depending on the sign of the pulse area, as a strong absorption enhancement or gain at the transition frequency of the two-level system for resonant excitation.

DOI
10.1364/ol.27.001830

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The interaction of strong low-area pulses with two-level systems shows absorption line narrowing and hole burning within the homogeneous linewidth as a result of nonlinear wave mixing. The wave mixing results from the two-level electronic saturation nonlinearity and occurs, depending on the sign of the pulse area, as a strong absorption enhancement or gain at the transition frequency of the two-level system for resonant excitation.
Features reminiscent of spectral hole burning in a homogeneous line are predicted to result from the interaction of small area pulses with the semiconductor exciton resonance. The small area pulses may be designed through pulse shaping or evolve naturally in bulk semiconductors via polaritonic effects. The spectral features exhibit signatures that are characteristic for the underlying material nonlinearity and should occur in any system with isolated spectral resonances and coherent nonlinearities.
The nonlinear response of a two-level system interacting with two pump beams of different frequencies is studied with a view to examine several recent experiments on nonlinear mixing of high orders, instabilities in homogeneously broadened lasers, and holes in homogeneous lines. Such a nonlinear response is calculated with use of the continued fractions given in our earlier work [J. Opt. Soc. Am. B1, 164 (1984)]. Saturation effects lead to the appearance of many structures at submultiples of the Rabi frequency. The origin of these subharmonics in nonlinear-response functions is explained. It is shown that collisions not only lead to hole burning at the line center for weak fields but can also lead in moderate fields to the appearance of structures at subharmonics of the Rabi frequency. Existence of collision-induced coherences similar to those in four-wave mixing is shown in six-wave mixing. Exact results for the degenerate nonlinear mixing of arbitrary order are presented for arbitrary values of field strengths. Saturating fields create holes at the line center of such nonlinear mixing signals. Gain profiles of two modes symmetrically displaced from line center are also given. Numerical results, with complete account of saturation and collisions, for a variety of nonlinear-response functions are presented.
The nonlinear response of a two-level system interacting with two pump beams of different frequencies is studied with a view to examine several recent experiments on nonlinear mixing of high orders, instabilities in homogeneously broadened lasers, and holes in homogeneous lines. Such a nonlinear response is calculated with use of the continued fractions given in our earlier work [J.Opt. Soc. Am. 81, 164 (1984)]. Saturation effects lead to the appearance of many structures at submultiples of the Rabi frequency. The origin of these subharmonics in nonlinear-response functions is explained. It is shown that collisions not only lead to hole burning at the line center for weak fields but can also lead in moderate fields to the appearance of structures at subharmonics of the Rabi frequency. Existence of collision-induced coherences similar to those in four-wave mixing is shown in six-wave mixing. Exact results for the degenerate nonlinear mixing of arbitrary order are presented for arbitrary values of field strengths. Saturating fields create holes at the line center of such nonlinear mixing signals. Gain profiles of two modes symmetrically displaced from line center are also given. Numerical results, with complete account of saturation and collisions, for a variety of nonlinear-response functions are presented.
We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 , ∓ω1{\mp}\omega_{1}∓ω1​, ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.
The two-step persistent spectral hole burning (PSHB) of a hole in the inhomogeneous distribution function (IDF) of the optical transition frequencies in a three-level system by two successive light pulses, in the case of an exponentially increasing and decreasing first coherent pulse and an infinitely short second pulse is calculated. The compensation effect of the natural linewidth of the first excited level and the parameter describing the exponential decrease of the intensity of the first burning pulse is shown. The time-dependent zero-phonon line (ZPL) in luminescence spectrum in the recording scheme containing the time gate in front of the spectrometer with high resolution in the case of exponential opening and closing of the time gate is calculated. The effect of the compensation of the natural linewidth of the excited level and the parameter describing the exponential increase of the transparency of the time gate is shown.
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.