Linear and nonlinear pulse propagation in a multiple-quantum-well photonic crystal

We investigate the temporal and spectral properties of subpicosecond pulses transmitted on the heavy-hole exciton transition through a multiple-quantum-well Bragg structure, exhibiting a one-dimensional photonic band gap. At low light intensities, a temporal propagation beating is observed. This beating is strongly dependent on the optical dephasing time $T_2$ which is dominated by the radiative interwell coupling. In an intermediate intensity regime, the Pauli-blocking nonlinearity leads to gradual suppression of the photonic band gap and vanishing of the linear propagation beating. For highly nonlinear excitation, we find signatures of self-induced transmission due to Rabi flopping and adiabatic following of the carrier density. Numerical simulations using the semiconductor Maxwell-Bloch equations are in excellent agreement with the experimental data up to intensities for which higher many-particle correlations become more important and self-phase modulation occurs in the sample substrate.

Figure 1

Schematic picture of the model configuration.

Figure 2

(a) Linear transmission spectra calculated for Bragg-periodic $\left(\mathrm{In},\mathrm{Ga}\right)\mathrm{As}∕\mathrm{GaAs}$ $\mathrm{MQWs}$ with $N=1$ (short-dashed line), 60 (solid line), and 200 (long-dashed line). (b) Linear transmission spectra calculated for $N=60$ $\left(\mathrm{In},\mathrm{Ga}\right)\mathrm{As}∕\mathrm{GaAs}$ $\mathrm{QWs}$ with $n_{b}d=0.5{\lambda }_{\mathrm{ex}}$ (solid line) and $n_{b}d=0.475{\lambda }_{\mathrm{ex}}$ (short-dashed line).

Figure 3

(a) Linear extinction spectra and (b) linear reflection spectra of the antireflection-coated $N=60$ $\left(\mathrm{In},\mathrm{Ga}\right)\mathrm{As}∕\mathrm{GaAs}$ $\mathrm{MQW}$ structure at $T=9\mathrm{K}$ for $n_{b}d=0.5{\lambda }_{\mathrm{ex}}$ (solid line) and $n_{b}d=0.479{\lambda }_{\mathrm{ex}}$ (short-dashed line). Marked are heavy-hole ($\mathrm{hh}$), light-hole ($\mathrm{lh}$), and continuum transitions.

Figure 4

Experimental setup using high-repetition $100\mathrm{fs}$ pulses tunable around $830\mathrm{nm}$. The shaped and propagated pulses are spectrally recorded and time resolved by cross correlation in a fast-scan sampling scheme. $\mathrm{PS}$: pulse shaper, $\mathrm{BBO}$: $\beta$-barium-borate crystal, $\mathrm{PMT}$: photomultiplier tube.

Figure 5

Propagation of a low-intensity $560\mathrm{fs}$ input pulse (short-dashed lines) resonant to the $\mathrm{hh}1s$ exciton through the Bragg-periodic $\mathrm{MQW}$ structure (solid lines). (a) Normalized cross-correlation traces and (b) transmitted spectra.

Figure 6

(a),(b) Propagation of low-intensity $560\mathrm{fs}$ pulses resonant to the $\mathrm{hh}1s$ exciton through the $\mathrm{MQW}$ structure for Bragg-periodic and detuned interwell spacing. (a) Normalized cross-correlation traces and (b) transmitted spectra. (c),(d) Numerical simulations based on the semiconductor Maxwell-Bloch equations. (c) Normalized transmitted intensities ${\mid E\left(t\right)\mid }^2$ and (d) ${\mid E\left(\Delta \lambda \right)\mid }^2$. In experiment and theory, the lowest curves represent the input pulses.

Figure 7

Propagation of low-intensity $560\mathrm{fs}$ pulses through the Bragg-periodic $\mathrm{MQW}$ structure for different laser detuning around the $\mathrm{hh}1s$ exciton resonance. (a) Normalized cross-correlation traces and (b) transmitted spectra. The lowest curves represent the input pulse tuned to resonance.

Figure 8

(a),(b) Propagation of $560\mathrm{fs}$ pulses resonant to the $\mathrm{hh}1s$ exciton through the Bragg-periodic $\mathrm{MQW}$ structure for increasing intensities. (a) Normalized corss-correlation traces and (b) transmitted spectra. (c),(d) Numerical simulations based on the semiconductor Maxwell-Bloch equations for increasing pulse area $\Theta \propto \sqrt{I.}$ (c) Normalized transmitted intensities ${\mid E\left(t\right)\mid }^2$ and (d) ${\mid E\left(\Delta \lambda \right)\mid }^2$. In experiment and theory, the lowest curves represent the input pulses.

Figure 9

Carrier densities in the $60$th $\mathrm{QW}$ (thick solid lines) and normalized field envelopes of the resonant $650\mathrm{fs}$ input(thin dashed lines) and transmitted pulses (thin solid lines) calculated for the Bragg-periodic $\mathrm{MQW}$ structure. (a) $\Theta =2.0\pi$ and (b) $\Theta =10\pi$.

Figure 10

High-intensity propagation of $560\mathrm{fs}$ input pulses (short-dashed lines) resonant to the $\mathrm{hh}1s$ exciton through the Bragg-periodic $\mathrm{MQW}$ structure (solid lines). (a) Normalized cross-correlation traces and (b) transmitted spectra. (c) Normalized calculated intensities ${\mid E\left(t\right)\mid }^2$ and (d) ${\mid E\left(\Delta \lambda \right)\mid }^2.$