Slow light using excitonic population oscillation

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 $3.12\times {10}^4$ 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.

Figure 1

Schematic diagram of the pump and signal polarizations for the parallel $({\widehat{e}}_p\Vert {\widehat{e}}_s)$ and orthogonal $({\widehat{e}}_p\perp {\widehat{e}}_s)$ configurations.

Figure 2

The level configuration of the excitonic population oscillation. The positive-helicity components of the pump and signal as well as the spin-down C and HH bands consist of one subsystem while their counterparts form the other.

Figure 3

Parallel-polarization configuration between the signal and the pump polarization. (a) The calculated absorbance spectra and (b) the real part of the refractive indices of the optical signal are plotted as a function of the detuning frequency between the signal and pump.

Figure 4

Orthogonal-polarization configuration between the signal and the pump polarization. (a) The calculated absorption spectra and (b) the real part of the refractive indices of the optical signal are plotted as a function of the detuning frequency between the signal and pump.

Figure 5

Experimental results of the absorbance due to excitonic population oscillation in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wells, which should be compared with the theory curves in Fig. 3a.

Figure 6

(a) Experimental results of the polarization dependence of the absorbance spectrum in the presence of excitonic population oscillation. The experiment was done near the excitonic absorption peak. (b) Our theoretical results.

Figure 7

The slowdown factor of the excitonic population oscillation (a) when ${\widehat{e}}_s\Vert {\widehat{e}}_p$ and (b) when ${\widehat{e}}_s\perp {\widehat{e}}_p$ are plotted as a function of the detuning frequency between the signal and pump.

Figure 8

(a) Experimental results of the phase delay and absorbance due to excitonic population oscillation in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wells. (b) Our theoretical result. (c) The theoretical slowdown factor as a function of the detuning frequency between the signal and pump. The peak slowdown factor agrees with the value extracted from the experiment.

Figure 9

Peak slowdown factor as a function of pump intensity.