Abstract
The backscattering mean free path ξ, the average ballistic propagation length along a waveguide, quantifies the resistance of slow light against unwanted imperfections in the critical dimensions of the nanostructure. This figure of merit determines the crossover between acceptable slow-light transmission affected by minimal scattering losses and a strong backscattering-induced destructive interference when the waveguide length L exceeds ξ. Here, we calculate the backscattering mean free path for a topological photonic waveguide for a specific and determined amount of disorder and, equally relevant, for a fixed value of the group index n_{g} which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, ξ and n_{g}, should be taken into account when quantifying the robustness of topological and conventional (nontopological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over a conventional one is not justified.
Highlights
Slowing the speed of a light pulse down to human pace requires complex interference effects [1] which manifest as a flat dispersion relation ν 1⁄4 νðkÞ, where k is the conserved wave vector and νðkÞ the frequency
The group velocity vg of this slow light is determined by the derivative of the flat band and the slowdown factor is given by the group index as ng 1⁄4 c=vg, where c is the speed of light in vacuum. ng is the figure of merit for slow light and it determines the enhancement factor for diverse applications such as optical nonlinearities [2], optical switching [3], pulse delay [4], quantum optics [5], optical storage [6], and optical gain [7]
Flat bands arise naturally in these systems based on the periodic modulation of the refractive index at optical or near infrared wavelengths [8,9] for which the group index diverges as ng ∝ ð∂ν=∂kÞ−1 in the ideal situation
Summary
Slowing the speed of a light pulse down to human pace (meters per second) requires complex interference effects [1] which manifest as a flat dispersion relation ν 1⁄4 νðkÞ, where k is the conserved wave vector and νðkÞ the frequency. We engineer slow light in a valley-Hall waveguide [15] to calculate its backscattering length ξ versus disorder and ng and we compare the results to those of a conventional photonic waveguide.
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