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Comptes Rendus Physique

Slow light pulse propagation in dispersive media

Torben Roland Nielsen, Jesper Mørk, Andrei V. Lavrinenko

Published Dec 1, 2009• 2 citations
Publisher

Abstract

We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse.

DOI
10.1016/j.crhy.2009.11.006

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We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse.
We study slow light pulse propagation in a photonic crystal structure consisting of a dispersive and absorptive dielectric material and compare it with the constant wave case. The group index and the transmission are investigated for the example of an ensemble of semiconductor quantum dots embedded in a photonic crystal waveguide by FDTD Maxwell‐Bloch simulations. The total group index scales linearly with the material based group index while the transmission has a power dependency on the material based absorption coefficient.
On the basis of a general analysis of waveguides containing a dispersive material, we identify conditions under which slow-light propagation may enhance the gain, absorption, or phase change. The enhancement is shown to depend on the slow-light mechanism and the translational symmetry of the waveguide. A combination of material and waveguide dispersion may strongly enhance the control of light speed, e.g., using electromagnetically induced transparency in quantum dots embedded in a photonic crystal waveguide.
We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher order dispersion. As the group velocity was reduced to 0.116(9) .c, we found group velocity dispersion of -1.1(3) .10(6) ps(2)/km and third order dispersion of up to 1.1(4) .10(5) ps(3)/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.
Slow and fast light processes, based on both structural and material dispersions, are realized in a wide tuning range in this article. Coherent population oscillations (CPO) in electrically tunable quantum dot semiconductor optical amplifiers lead to a variable group index ranging from the background index ( n bgd ) to ∼ 30. A photonic crystal waveguide is then dispersion engineered and a group index of 260 with the normalized delay-bandwidth product (NDBP) of 0.65 is achieved in the proposed waveguide. Using comprehensive numerical simulations, we show that a considerable enhancement of slow light effect can be achieved by combining both the material and the structural dispersions in the proposed active QDPCW structure. We compare our developed FDTD results with analytical results and show that there is good agreement between the results, which demonstrates that the proposed electrically-tunable slow light idea is obtainable in the QDPCW structure. We achieve a total group index in a wide tuning range from n bgd to ∼ 1500 at the operation bandwidth, which shows a significant enhancement compared with the schemes based only on material or structural dispersions. The tuning range and also NDBP of the slow light scheme are much larger than those of the electrically tunable CPO process.