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Physical Review B

Slow light using excitonic population oscillation

Shu‐Wei Chang, S. L. Chuang, C. C. Kuo, Connie J. Chang-Hasnain, Phedon Palinginis, Hailin Wang

Published Dec 1, 2004• 43 citations
Publisher

Abstract

We develop a theoretical model for slow light using excitonic population oscillation in a semiconductor quantum well. In a two-level system, if the resonant pump and the signal have a difference frequency within the range of inverse of the carrier lifetime, coherent population beating at this frequency will be generated. We analyze the excitonic population oscillation using an atomiclike model extended from semiconductor Bloch equations for both spin subsystems of the excitonic population and the electrical polarization density. The two spin subsystems are coupled by the excitation-induced dephasing rate, which depends on the net population difference in conduction and heavy hole quantized bands and the population exchange due to flip of the spins of electrons or holes. We present our theoretical results for the absorbance, the refractive index spectra, and the slowdown factor due to population oscillation at various pump intensities, and show very good agreement with experimental data. It is shown that a slowdown factor of $3.12\ifmmode\times\else\texttimes\fi{}{10}^{4}$ has been achieved for a semiconductor quantum-well structure. We also obtain analytical solutions from our theory and account for different response behaviors of the signal when its polarization is either parallel or orthogonal to that of the pump, which has also been confirmed by experiments.

DOI
10.1103/physrevb.70.235333

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We develop a theoretical model for slow light using excitonic population oscillation in a semiconductor quantum well. In a two-level system, if the resonant pump and the signal have a difference frequency within the range of inverse of the carrier lifetime, coherent population beating at this frequency will be generated. We analyze the excitonic population oscillation using an atomiclike model extended from semiconductor Bloch equations for both spin subsystems of the excitonic population and the electrical polarization density. The two spin subsystems are coupled by the excitation-induced dephasing rate, which depends on the net population difference in conduction and heavy hole quantized bands and the population exchange due to flip of the spins of electrons or holes. We present our theoretical results for the absorbance, the refractive index spectra, and the slowdown factor due to population oscillation at various pump intensities, and show very good agreement with experimental data. It is shown that a slowdown factor of 3.12\ifmmode×\else\texttimes\fi1043.12\ifmmode\times\else\texttimes\fi{}{10}^{4}3.12\ifmmode×\else\texttimes\fi104 has been achieved for a semiconductor quantum-well structure. We also obtain analytical solutions from our theory and account for different response behaviors of the signal when its polarization is either parallel or orthogonal to that of the pump, which has also been confirmed by experiments.
This is a detailed study of slow light based on quantum effects in semiconductor nanostructures. We propose to implement an optical buffer using semiconductor quantum dots and quantum wells based on coherent population oscillation and spin related electromagnetically induced transparency. We identify different pump-and-probe schemes and develop comprehensive theoretical models which include important physical mechanisms in semiconductors. Semiconductors have unique properties which are inaccessible to other slow light media, and these enable the possibilities of controlling the semiconductor-based optical buffer in addition to the optical method. We investigate how to electrically control group index (slowdown factor) in quantum dots by using reverse bias voltage and forward injection current. We also develop a model to use the anisotropy of the light-hole exciton to vary the slowdown factor via two different mechanisms (coherent population oscillation and spin related electromagnetically induced transparency). Finally, we propose an idea to use the strain to control the spin relaxation time in semiconductors, which can help spin-dependent slow light in semiconductors. This research shows that the semiconductor is a promising candidate to demonstrate an optical buffer and can provide more flexible control than other slow light materials.
Coherent population oscillation (CPO) is a successful method used to implement semiconductorbased slow light using the coherent pump-probe effect. The first demonstration was carried out in semiconductormultiple quantumwells (MQWs) [1-3] soon after the experimental demonstration of slow light in ruby crystal [4,5]. Later, slow light based on CPO in semiconductor QWs and quantum dots (QDs)was also successfully demonstrated at room temperature [6-10], and the slow-light regime was soon extended to the corresponding fast-light regime in semiconductor gainmedia [11-17] using a semiconductor optical amplifier (SOA) alone or combined with an electroabsorbtion (EA) section. The basicworking principle of slow light based onmost pump-probe schemes is to decrease the group velocity vg using the sharp variation of the refractive index ∂n′/∂ω within a narrow frequency range: vg = c ng = c n′ + ω ∂n′ , (2.1) where ng = n′ + ω∂n′/∂ω is the group index n′ is the real part of the refractive index n For the CPO case, the required sharp variation of the refractive index originates from the population oscillation induced by the pump and probe signals applied to a two-level system, as indicated in Figure 2.1. The induced population oscillation generates a new polarization component and changes the susceptibility and thus the refractive index experienced by the signal. In semiconductor quantum structures, this two-level system can be the heavy-hole (HH) exciton [1-3,6,18] of QWs and QDs, or the valence and conductionground states of QDs [18,19]. In principle, as long as the optical transition between the two states is dipole-allowed, the slow light based on CPO can be implemented.
Coherent population oscillations (CPO) in quantum dots (QDs) have been utilized in this article to achieve slow and fast light effects in a semiconductor optical amplifier. These phenomena have been achieved based on a pump-probe scheme and tuning the input current source. Coupled rate equations have been developed to determine the carrier dynamics and occupation probabilities. The effects of barrier, wetting layer and excited state densities have been included for CPO phenomenon occurring between the ground states. A quantum disc model embedded in another disc has been assumed for modeling the QDs and density matrix elements are used to obtain induced polarization at the signal frequency after determining the energy states and state probabilities. Tunable absorption dip, corresponding refractive index variation and group index, exhibit widely tunable slow and fast light characteristics by changing the bias condition.
We develop a model for slow light based on the coherent population oscillation of quantum dots at room temperature. With the absorption dip and corresponding variation of the refractive index due to the coherent population beating induced by the pump and probe signal, quantum dots can be used as a slow-light medium. Our theoretical model matches the experimental results very well. We also experimentally and theoretically demonstrate that both the forward-bias injection current and reverse-bias voltage can change the group index in a semiconductor quantum-dot waveguide. Our results indicate that quantum-dot devices can be potentially used as electrically and optically controllable slow light devices
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.