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Journal of the Optical Society of America B

Analysis of χ^2 for inhomogeneously broadened intersubband transitions

William S. Rabinovich, Guy Beadie

Published Aug 1, 2001• 1 citation
Publisher

Abstract

We examine the effects of inhomogeneous broadening on second-order nonlinearities in intersubband-based quantum-well systems. In particular, we study the case of difference-frequency generation in a doubly resonant system, providing, to our knowledge, the first analysis of conversion efficiencies. For even modest amounts of inhomogeneous broadening both the peak conversion efficiency and the optimum interaction length may vary by more than a factor of 3 from that predicted by homogeneous theories.

DOI
10.1364/josab.18.001119

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We examine the effects of inhomogeneous broadening on second-order nonlinearities in intersubband-based quantum-well systems. In particular, we study the case of difference-frequency generation in a doubly resonant system, providing, to our knowledge, the first analysis of conversion efficiencies. For even modest amounts of inhomogeneous broadening both the peak conversion efficiency and the optimum interaction length may vary by more than a factor of 3 from that predicted by homogeneous theories.
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The effect of the depolarization field on the doubly resonant frequency mixing due to resonant intersubband transitions in asymmetric quantum wells, with only the ground subband occupied, is discussed. Calculations are performed in the framework of the perturbative density matrix formulation with relaxation time approximation. The results show that in the considered system the depolarization effect can be included by simple replacement (in the one-electron expression for the nonlinear susceptibility) of the intersubband energy by the depolarization shifted intersubband energy.
The interband sum frequency generation process due to three-wave interaction of interband and intersubband coupling lights has been investigated in a semiconductor quantum well using the perturbational density matrix approach. The origin of the nonlinear process lies in the second-order susceptibility /spl chi//sub c2-h1//sup (2)/ arising due to the optical transition between the second conduction subband and the first heavy hole state. Both the sign and the magnitude of the second-order susceptibility of the well may be controlled by the carrier density level and the frequency of the intersubband field.
Three wave mixing is investigated with respect to its spectroscopic applications under fully resonant conditions. A theoretical study of the appropriate second order susceptibility χ(2) reveals interesting features both for sum and difference frequency generation. For difference frequency generation two different mechanisms are possible one of which allows the observation of resonances between excited states and the study of dephasing induced coherent emission. The coherence decay rate between the two excited states may be measured and also its pure dephasing rate. The line-narrowing characteristics of the fully resonant χ(2) are studied with respect to correlation between the inhomogeneous distribution for different levels. The line-narrowing capabilities are found to be partly complementary for the sum—and the two difference frequency resonance configurations. This leads to the suggestion of new line-narrowing techniques which could provide information about type and amount of correlation in inhomogeneously broadened systems.
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.