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Annual Meeting Optical Society of America

Multiwave mixing in semiconductor media

Murray Sargent, Stephan W. Koch

Published Jan 1, 1988• 0 citations
Publisher

Abstract

We consider an intrinsic semiconductor medium subject to an injection current, an arbitrarily intense electromagnetic wave, and one or two non-saturating waves. We assume that the saturating wave intensity is constant throughout the interaction region and ignore transverse variations. We further assume that the carrier–carrier scattering is sufficiently fast that the carriers are described approximately by Fermi-Dirac distributions. We find that the probe-wave propagation is described by Beer’s law or coupled-mode equations. These equations are determined by a Fourier expansion technique highly developed for two-level atoms. The absorption and coupling coefficients experience asymmetric dips generated by pump scattering off carrier-density pulsations induced by the pump–probe interference. These effects are reminiscent of coherent-dip phenomena well-known in two-level systems but differ significantly in form.

DOI
10.1364/oam.1988.fb3

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We consider an intrinsic semiconductor medium subject to an injection current, an arbitrarily intense electromagnetic wave, and one or two non-saturating waves. We assume that the saturating wave intensity is constant throughout the interaction region and ignore transverse variations. We further assume that the carrier–carrier scattering is sufficiently fast that the carriers are described approximately by Fermi-Dirac distributions. We find that the probe-wave propagation is described by Beer’s law or coupled-mode equations. These equations are determined by a Fourier expansion technique highly developed for two-level atoms. The absorption and coupling coefficients experience asymmetric dips generated by pump scattering off carrier-density pulsations induced by the pump–probe interference. These effects are reminiscent of coherent-dip phenomena well-known in two-level systems but differ significantly in form.
This paper analyzes the interaction of a strong wave and one or two probe waves with an intrinsic semiconductor medium which is partially inverted by an injection current. The many-body interactions of the electron-hole excitations are described using recently developed generalized Bloch equations for semiconductors. Coupled-mode equations for the different light fields are derived and solved, and predict that the gain and the coupling coefficients experience asymmetric dips. These dips are generated by scattering of the strong field off carrier-density pulsations induced by the pump-probe interference.
We investigate the resonance fluorescence spectrum of a bulk semiconductor subject to an injection current and an arbitrarily intense electromagnetic wave. We assume that the electronhole system is in quasiequilibrium due to the rapid carrier-carrier intraband scattering. The analysis is based on the generalized Bloch equations1 for semiconductors. Although the fast carrier scattering heavily damps the electronic coherence, it nevertheless allows the medium to follow adiabatically the relatively slowly varying field fluctuations. As a consequence, the resonance fluorescence spectra reveal asymmetric dips generated by pump scattering off carrier-density pulsations induced by the interference between the pump and vacuum mode. Similar to the two-level resonance fluorescence and probe absorption, the semiconductor probe absorption coefficient equals the difference between the resonance fluorescence and reabsorption coefficients. The results are important for nonlinear semiconductor spectroscopy and semiconductor laser instabilities.
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 semiclassical two-level multiwave coefficients are presented in the limit that the population-difference lifetime T1, is much greater than the dipole lifetime T2. These coefficients are easy to understand analytically and show how pump-probe detuning shifts the phase and the amplitude of pump scattering off induced population pulsations. In particular, a simple formula is found that shows how energy can be exchanged by two waves in an apparently pure-index regime. An FM wave is shown to propagate unchanged through such a medium, and the beat-note component of an AM wave is shown to be unmodified by a thin medium. Simple formulas for T1 of the order of T2 are given that reveal intense pump-dispersive and Lorentzian features at a glance. The results are of use in saturation spectroscopy, modulation spectroscopy, optical instabilities, and phase conjugation.
We investigate the resonance fluorescence spectrum of a bulk semiconductor subject to an injection current and an arbitrarily intense electromagnetic wave. We assume that the electron-hole system is in quasiequilibrium due to the rapid carrier-carrier intraband scattering. The analysis is based on the generalized Bloch equations for semiconductors. Although the fast carrier scattering heavily damps the electronic coherence, it nevertheless allows the total carrier density to adiabatically follow the relatively slowly varying field fluctuations. As a consequence, the resonance fluorescence spectra reveal an asymmetric peak generated by pump scattering from carrier-density pulsations induced by the interference between the pump and a vacuum mode. Similar to the two-level fluorescence and probe absorption, the semiconductor-probe absorption coefficient equals the difference between the resonance fluorescence and reabsorption coefficients. The results are important for nonlinear semiconductor spectroscopy and semiconductor laser instabilities.
We investigate the interplay of multiwave-mixing processes with the microscopically coupled spatiotemporal light field and charge carrier dynamics in broad-area semiconductor laser amplifiers. Our theoretical description is based on extended spatially resolved Maxwell-Bloch equations including on the microscopic level spatiotemporal multiwave-mixing processes. Performing a third-order expansion in terms of the microscopic carrier distribution, we include in our description both the effects of population pulsations of the total carrier density at the beat frequency and the spatiospectral interactions of the light fields leading to gain nonlinearities as well as spatial and spectral hole burning. Our simulations show that in a broad-area semiconductor laser amplifier, spatiotemporal wave-mixing processes occur in both transverse and propagation directions of the multifrequency optical beams employed in a typical excite-probe configuration.