Robust optical delay lines via topological protection

Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we show how exploiting topological properties of optical systems can be used to implement robust photonic devices. We demonstrate how quantum spin Hall Hamiltonians can be created with linear optical elements using a network of coupled resonator optical waveguides (CROW) in two dimensions. We find that key features of quantum Hall systems, including the characteristic Hofstadter butterfly and robust edge state transport, can be obtained in such systems. As a specific application, we show that the topological protection can be used to dramatically improve the performance of optical delay lines and to overcome limitations related to disorder in photonic technologies.Comment: 9 pages, 5 figures + 12 pages of supplementary informatio

Reflection and transmission of waves in surface-disordered waveguides

The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type disorder on the behavior of the ensemble average and fluctuations of the reflection and transmission coefficients, reflectance, transmittance, and conductance. Our results show anomalous effects stemming from the combination of mode dispersion and rough surface scattering: For a given waveguide length, the larger the mode transverse momentum is, the more strongly is the mode scattered. These effects manifest themselves in the mode selectivity of the transmission coefficients, anomalous backscattering enhancement, and speckle pattern both in reflection and transmission, reflectance and transmittance, and also in the conductance and its universal fluctuations. It is shown that, in contrast to volume impurities, surface scattering in quasi-one-dimensional structures (waveguides) gives rise to the coexistence of the ballistic, diffusive, and localized regimes within the same sample.Comment: LaTeX (REVTeX), 12 pages with 14 EPS figures (epsf macro), minor change

Pseudospin-1 Physics of Photonic Crystals.

We review some recent progress in the exploration of pseudospin-1 physics using dielectric photonic crystals (PCs). We show some physical implications of the PCs exhibiting an accidental degeneracy induced conical dispersion at the Γ point, such as the realization of zero refractive index medium and the zero Berry phase of a loop around the nodal point. The photonic states of such PCs near the Dirac-like point can be described by an effective spin-orbit Hamiltonian of pseudospin-1. The wave propagation in the positive, negative, and zero index media can be unified within a framework of pseudospin-1 description. A scale change in PCs results in a rigid band shift of the Dirac-like cone, allowing for the manipulation of waves in pseudospin-1 systems in much the same way as applying a gate voltage in pseudospin-1/2 graphene. The transport of waves in pseudospin-1 systems exhibits many interesting phenomena, including super Klein tunneling, robust supercollimation, and unconventional Anderson localization. The transport properties of pseudospin-1 systems are distinct from their counterparts in pseudospin-1/2 systems, which will also be presented for comparison

Coherent transport through graphene nanoribbons in the presence of edge disorder

We simulate electron transport through graphene nanoribbons of experimentally realizable size (length L up to 2 micrometer, width W approximately 40 nm) in the presence of scattering at rough edges. Our numerical approach is based on a modular recursive Green's function technique that features sub-linear scaling with L of the computational effort. We identify the influence of the broken A-B sublattice (or chiral) symmetry and of K-K' scattering by Fourier spectroscopy of individual scattering states. For long ribbons we find Anderson-localized scattering states with a well-defined exponential decay over 10 orders of magnitude in amplitude.Comment: 8 pages, 6 Figure

Quantifying the robustness of topological slow light

Low-dimensional nanostructured materials can guide light propagating with very low group velocity vg. However, this slow light is significantly sensitive to unwanted imperfections in the critical dimensions of the nanostructure. The backscattering mean free path, xi, the average ballistic propagation length along the waveguide, quantifies the robustness of slow light against this type of structural disorder. 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 xi exceeds the waveguide length L. 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 ng which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, xi and ng, should be taken into account when quantifying the robustness of topological and conventional (non-topological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over conventional one is not justified

Coupled paraxial wave equations in random media in the white-noise regime

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schr\"{o}dinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.Comment: Published in at http://dx.doi.org/10.1214/08-AAP543 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org