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Optics Express

Enhanced four-wave mixing efficiency in four-subband semiconductor quantum wells via Fano-type interference

Shaopeng Liu, Wen‐Xing Yang, You-Lin Chuang, Ai-Xi Chen, Ang Liu, Yan Huang, Ray‐Kuang Lee

Published Nov 14, 2014• 36 citations
Publisher

Abstract

We propose and analyze an efficient way to enhance four-wave mixing (FWM) signals in a four-subband semiconductor quantum well via Fano-type interference. By using Schrödinger-Maxwell formalism, we derive explicitly analytical expressions for the input probe pulse and the generated FWM field in linear regime under the steady-state condition. With the aid of interference between two excited subbands tunneling to the common continuum, the efficiency to generate FWM field is found to be significantly enhanced, up to 35%. More interestingly, a linear growth rate in the FWM efficiency is demonstrated as the strength of Fano-type interference increases in presence of the continuum states, which can be maintained for a certain propagation distance (i.e., 50μm).

DOI
10.1364/oe.22.029179

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We propose and analyze an efficient way to enhance four-wave mixing (FWM) signals in a four-subband semiconductor quantum well via Fano-type interference. By using Schrödinger-Maxwell formalism, we derive explicitly analytical expressions for the input probe pulse and the generated FWM field in linear regime under the steady-state condition. With the aid of interference between two excited subbands tunneling to the common continuum, the efficiency to generate FWM field is found to be significantly enhanced, up to 35%. More interestingly, a linear growth rate in the FWM efficiency is demonstrated as the strength of Fano-type interference increases in presence of the continuum states, which can be maintained for a certain propagation distance (i.e., 50μm).
We propose an efficient four-wave mixing (FWM) scheme in asymmetric semiconductor quantum wells (SQWs) via two-photon resonance. By using the coupled Schrödinger–Maxwell formalism, we derive explicitly the corresponding analytical expressions of the inter-probe pulse and generated FWM field in the linear regime under the steady-state condition. With the aid of cross coupling between one ground state and two closely adjacent excited states, the efficiency of the generated FWM field is found to be significantly enhanced, up to 60%. More interestingly, a wide region of the maximum FWM efficiency is demonstrated as the ratio of transition dipole moments is within the values ranging from 1.1 to 1.3, which can be maintained for a certain propagation distance (i.e. 100 μ m).
In this article, we use spatially modulated control fields to increase the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, motivated by similar works in atomic systems. Using a simplified version of the propagation equations, we show analytically that for control fields with a constant amplitude and linearly varying mixing angles with the propagation distance, a conversion efficiency close to unity can be achieved even for relatively short propagation distances. Subsequently, we confirm these results by numerically simulating the full set of propagation equations.
We perform a time-dependent analysis of the formation and stable propagation of an ultraslow optical soliton pair, and four-wave mixing (FWM) via tunable Fano interference in double-cascade type semiconductor multiple quantum wells (SMQWs). By using the probability amplitude method to describe the interaction of the system, we demonstrate that the electromagnetically induced transparency (EIT) can be controlled by Fano interference in the linear case and the strength of Fano interference has an important effect on the group velocity and amplitude of the soliton pair in the nonlinear case. Then, when the signal field is removed, the dynamic FWM process is analyzed in detail, and we find that the strength of Fano interference also has an important effect on the FWM's efficiency: the maximum FWM efficiency is ~28% in appropriate conditions. The investigations are promising for practical applications in optical devices and optical information processing for solid systems.
In the present article, we derive optimal spatially varying control fields, which maximize the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, following analogous works in atomic systems. The control fields coherently prepare the medium, where a weak probe pulse is propagated and eventually converted to a signal pulse at the output. The optimal fields, which maximize the conversion efficiency for a given propagation length, are obtained by applying optimal control theory to a simplified form of propagation equations but are tested with numerical simulations using the full set of Maxwell–Schrödinger equations, which accurately describe the propagation of light pulses in the medium. For short propagation distances, the proposed optimal scheme outperforms a simpler spatially changing control protocol that we recently studied, while for larger distances, the efficiency of both protocols approaches unity. The present work is expected to find application in frequency conversion between light beams, conversion between light beams carrying orbital angular momentum, and nonlinear optical amplification.
The time-dependent four-wave mixing (FWM) is analyzed in a four-level double semiconductor quantum well. The results show that both the amplitude and the conversion efficiency of the FWM field are enhanced with increasing the strength of two-photon Rabi frequency. Interestingly, when the one-photon detuning becomes stronger the control field corresponding to the maximum efficiency increases. Such a controlled enhanced FWM may be used to generate coherent short-wave length radiation, and it can have potential applications in quantum control and communications.
We present an experimental study of the coherent dynamics in quantum wells for the simultaneous excitation of Lorentzian excitons below the band edge and structured exciton Fano continua corresponding to higher-order subband transitions. Spectrally resolved transient four-wave mixing (FWM) experiments with 100 fs pulses were performed on a 500 \AA{} broad GaAs/${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum well over a wide range of carrier densities. At lower carrier densities, the dephasing times of the different exciton transitions were determined from the width of the narrow resonances in the distinctly structured FWM spectra. These data demonstrate that the decay of the FWM signal from exciton Fano continua in the time-delay domain is not determined by dephasing at the lowest carrier densities. This is indicative of quantum interference which has its origin in many-body exciton-continuum coupling. At higher carrier densities, the FWM spectra are much less structured due to stronger dephasing, quantum interference effects lose their importance, and the structured exciton Fano continua show properties similar to unstructured continua without embedded exciton transitions.