Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach

Thomas, Nicolas Le; Houdré, R.

doi:10.1364/josab.27.002095

Cited by 6 publications

(6 citation statements)

References 39 publications

(56 reference statements)

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“…In the dispersive regime that corresponds to a well-defined dispersion curve x(k), a group index n g or equivalently a group velocity v g can be defined. 10 No function x(k) can be defined anymore in the diffusive regime. The group index at the transition reaches a maximum value that depends on the amount of residual disorder with a high precision, as will be presented in the following.…”

Section: Design and Fabricationmentioning

confidence: 99%

“…In particular, recent theoretical predictions of the impact of residual disorder on the slow light regime are based on an averaging of different configurations of the disordered dielectric map for a given structure with the assumption of Gaussian distributions. [8][9][10] Although such theoretical approaches constitute guidelines for the understanding of the impact of residual disorder, they always start with an a priori choice of the statistical distribution of the disorder. There is currently no direct link between theoretical modeling and disorder distribution in real structures.…”

Section: Introductionmentioning

confidence: 99%

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Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties

Thomas

Diao

Zhang

et al. 2011

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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The authors present a statistical study of residual disorder in nominally identical planar photonic crystal waveguides operating in the slow light regime. The focus is on the role played by the subnanometer scaled residual disorder inherent to state-of-the-art electron-beam (EB) lithography systems, in particular, on the impact of the nature of the residual disorder on the maximum value of the guided mode group index. The authors analyze the statistical properties of the surface area, the position, and the shape of the air holes that define the photonic crystal with optimized scanning electron microscope micrographs. The authors identify the hole-area fluctuation as the main source of degradation of the dispersive slow light regime by correlating such a microscopic analysis of the structural disorder with large field-of-view optical characterizations based on a Fourier space imaging technique. The structure with the largest group index (ng = 40) exhibits a standard deviation σ of the radius of the hole as low as 0.4 nm. Such a low value of σ, which already significantly limits the maximum achievable group index of the guided mode, stresses the drastic impact of the residual disorder on the performances of the slow light regime. A mean square analysis of the electronic micrographs reveals that the standard deviation of the hole position is lower than an upper limit of 0.6 nm. This upper bound comes from the intrinsic imperfections of the scanning electronic microscope itself, which hinders to quantify the position disorder induced by the EB lithography system. The authors have identified no correlation between the shape of the holes and the group index as for the hole position. As a result, the hole-area fluctuation is currently the main parameter to control in order to improve the performance of the slow light regime.

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Section: Design and Fabricationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties

Thomas

Diao

Zhang

et al. 2011

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

Self Cite

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“…This indicates that in those structures where this theorem is no longer valid, such as disordered and finite photonic crystals, the properties of ⃗v g may be substantially different from those of ⃗v E , including conceptual and quantitative differences. The latter is clearly illustrated in [9], where the effects of residual disorder in periodic photonic structures on the properties of ⃗v g and ⃗v E were investigated. It was shown that, whereas ⃗v g diverges near the band edges of a given band for any amount of disorder, ⃗v E remains finite and follows essentially the group velocity in absence of disorder.…”

Section: Introductionmentioning

confidence: 96%

“…The properties of ⃗v g and its connections to both pulse propagation and ⃗v E have been widely discussed in the literature in the presence [5][6][7] and absence [8][9][10][11][12][13] of looses. In this paper, we will focus our attention on transparent media.…”

Section: Introductionmentioning

confidence: 99%

Group velocity and nonlocal energy transport velocity in finite photonic structures

Dios-Leyva

Drake-Pérez

2012

J. Opt. Soc. Am. B

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We have derived an explicit relation between the group delay velocity v gd ω, determined by the slope of the dispersion curves, and the nonlocal energy transport velocity v E ω in a lossless, finite, one-dimensional photonic crystal. Using this relation, we find a simple link between v gd ω and the group velocity v ω g ω defined in terms of the electromagnetic dwell time. It is shown that v E ω ≤ v gd ω for any frequency and v E ω v gd ω v ω g ω at the resonance frequencies of the transmission coefficient. It was established that the band structure of a finite periodic crystal is of great importance to describe and understand the properties of these velocities. In particular, it was shown that the occurrence of superluminal group delay velocities in these structures is closely related to the existence of null gaps in their dispersion relation. Calculations performed for a half-wave-quarter-wave stack show that the energy velocity remains always subluminal.

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“…Variations of the W1 design can help improve these numbers somewhat in terms of reducing the loss per group index [29,30]. However, in all of these conventional designs, operation near the mode edge (slow light regime) becomes impractical because of significant disorder-induced backscattering [2,26,[31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

Sauer

Vasco

Hughes

2020

Phys. Rev. Research

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Using a semianalytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic bandgap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line (at least in the absence of disorder).

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Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach

Cited by 6 publications

References 39 publications

Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties

Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties

Group velocity and nonlocal energy transport velocity in finite photonic structures

Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

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