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Physical Review A

Transition from slow and frozen to superluminal and backward light through loss or gain in dispersion-engineered waveguides

Thomas P. White, Andrey A. Sukhorukov

Published Apr 11, 2012• 9 citations
Publisher

Abstract

We describe the generic effects of loss or gain on pulse propagation in photonic-crystal and plasmonic waveguides that support ``frozen'' or ``in-band'' slow light at dispersion inflection points in the absence of loss (or gain). Using an analytical perturbation theory, we find that propagating and evanescent modes hybridize when loss exceeds a certain threshold, resulting in a reduced attenuation rate and switching from slow to superluminal velocity. Numerical simulations for photonic-crystal waveguides reveal the dynamic nature of this transition with forward-backward pulse velocity oscillations for loss above the threshold. Importantly, we show that the light intensity is enhanced close to the input end of the waveguide even under strong material losses, indicating the potential for slow-light enhancement of optical effects, even in such lossy waveguides.

DOI
10.1103/physreva.85.043819

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We describe the generic effects of loss or gain on pulse propagation in photonic-crystal and plasmonic waveguides that support frozen'' or in-band'' slow light at dispersion inflection points in the absence of loss (or gain). Using an analytical perturbation theory, we find that propagating and evanescent modes hybridize when loss exceeds a certain threshold, resulting in a reduced attenuation rate and switching from slow to superluminal velocity. Numerical simulations for photonic-crystal waveguides reveal the dynamic nature of this transition with forward-backward pulse velocity oscillations for loss above the threshold. Importantly, we show that the light intensity is enhanced close to the input end of the waveguide even under strong material losses, indicating the potential for slow-light enhancement of optical effects, even in such lossy waveguides.
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.
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.
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Slow light is a regime of reduced group velocity, resulting in increased photon density in optical pulses and enhanced nonlinear effects. Here, we propose the realization of slow light in the regime of strong light-matter interaction between waveguide photons and semiconductor excitons. We design a dielectric superlattice structure with a nearly-flat band characterized by low group velocity and group velocity dispersion, both required for enhancing nonlinear effects with ultrashort pulses. Furthermore, by applying this general framework to a perovskite-based structure, we demonstrate an enhancement of the single-particle phase shift by a factor of more than 20, representing a significant step toward the few-photon quantum regime. Our results provide a blueprint for accessible strong interactions in solid-state integrated optics.
The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.