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Physical Review A

Multiwave mixing in semiconductor laser media

Murray Sargent, Fenglei Zhou, S. W. Koch

Published Nov 1, 1988• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.38.4673

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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 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.
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.
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.
This dissertation considers multi-wave interactions in bulk semiconductors. Non-equilibrium Green's functions are used to derive an appropriate set of equations describing the interaction of a light field with a semiconductor. Many-body effects lead to the screening of the Coulomb potential in these equations, as well as, carrier-carrier scattering. The carrier-carrier scattering is studied within the context of the carrier Boltzmann equation which contains the dynamically screened Coulomb potential. The relation between carrier scattering and optical dephasing is also made. The carrier scattering rates are then used in the equations describing a two beam pump-probe experiment. The resulting equations are solved numerically for both passive and active systems, and effects such as spectral hole burning, coherent light scattering, and light induced band splitting are studied. Considering three CW beams (pump and two probes) allows for the study of four-wave mixing in semiconductors. By considering CW fields, the semiconductor may be treated in the quasi-equilibrium approximation allowing for greater detail in the treatment of the light field. The resulting probe absorption yields asymmetries which result in an asymmetric four-wave mixing spectrum. The four-wave mixing spectrum is then used to study the amount of squeezing in the light field exiting the cavity in a four-wave mixing experiment.
A theory of four-wave mixing in semiconductor laser media is developed by considering the contributions of both the gain and index gratings created by the carrier-density modulation occurring at the beat frequency of the pump and the probe waves. The general formalism can be applied to semiconductor lasers operating below or above threshold. As an illustration, we consider the case in which the semiconductor laser is operated as a traveling-wave amplifier. The results show that the dominant contribution to the four-wave mixing process comes from the index grating. Further, the index grating makes the probe transmission asymmetric with respect to the pump-probe detuning.