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Applied Physics Letters

Slow light in quantum dot photonic crystal waveguides

Torben Roland Nielsen, Andrei V. Lavrinenko, Jesper Mørk

Published Mar 16, 2009• 23 citations
Publisher

Abstract

A theoretical analysis of pulse propagation in a semiconductor quantum dot photonic crystal waveguide in the regime of electromagnetically induced transparency is presented. The slow light mechanism considered here is based on both material and waveguide dispersion. The group index ng for the combined system is significantly enhanced relative to slow light based on purely material or waveguide dispersion.

DOI
10.1063/1.3103286

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A theoretical analysis of pulse propagation in a semiconductor quantum dot photonic crystal waveguide in the regime of electromagnetically induced transparency is presented. The slow light mechanism considered here is based on both material and waveguide dispersion. The group index ng for the combined system is significantly enhanced relative to slow light based on purely material or waveguide dispersion.
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.
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 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.
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.
A variable semiconductor optical buffer based on the electromagnetically induced transparency in a quantum dot waveguide is theoretically investigated with feasible parameters for applications to a 40 Gbps optical network. We show the refractive index and absorption spectra of the quantum dot waveguide at various pump levels, which exhibit an optimal pump power for maximum slow-down factor, in agreement with the previous experimental observation using a Pr-doped solid. The group velocity slow-down factor is theoretically analysed as a function of the pump intensity at different broadened linewidths. Inhomogeneous broadening in self-assembled quantum dots degrades the slow-down factor. In order to reduce the inhomogeneous broadening effects, we propose to use a resonant microcavity structure with quantum dots embedded in the active layer to enhance the slow-down factor.