Bound states in the continuum in waveguide arrays within a symmetry classification scheme.

We study a photonic implementation of a modified Fano-Anderson model - a waveguide array with two additional waveguides and by using the coupled mode theory we calculate its spectral and scattering properties. We classify eigenmodes according to vertical symmetry of the structure given by self-coupling coefficients of the additional waveguides and establish the conditions for bound states in the continuum (BIC) existence. The main predictions drawn from the theoretical model are verified by rigorous full-wave simulations of realistic structures. We use the Weierstrass factorization theorem and interpret the scattering spectra of the systems with broken symmetry in terms of the eigenmodes. The Fano resonance related with excitation of quasi-BIC is explained as arising from the interference between this mode and another leaky mode.

Surface plasmon polariton Wannier-Stark ladder.

The propagation of a surface plasmon polariton on a planar metal surface perturbed by N equally spaced rectangular grooves, each with the same width but with varying depths, is investigated by the finite-difference time-domain method. For a linear dependence of the depth of the nth groove on n, the transmissivity of the surface plasmon polariton and of the power radiated into the vacuum above the surface, as functions of its frequency, consist of N equally spaced dips and peaks, respectively. These are the signatures of the surface plasmon polariton analog of a Wannier-Stark ladder.

Polarization-dependent tunneling of light in gradient optics.

Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S - and P -polarized electromagnetic waves are examined by means of exactly solvable models. We present generalized Fresnel formulas, describing the influence of the nonlocal dispersion on the reflectance and transmittance of single- and double-layer gradient photonic barriers for S and P waves and arbitrary angles of incidence. The nonlocal dispersion of such layers, arising due to a concave spatial profile of dielectric susceptibility across the plane film, is shown to result in a peculiar heterogeneity-induced optical anisotropy, providing the propagation of S (P) waves in tunneling (traveling) regimes. The results obtained indicate the possibility of narrow-band nonattenuated tunneling (complete transmittance) of oblique S waves through such heterogeneous barriers, and the existence of spectral areas characterized by the strong reflection of P waves and profound contrast between transmitted S and P waves. The scalability of obtained exact analytical solutions of Maxwell equations into the different spectral ranges is discussed and the application potential of these phenomena for miniaturized polarizers and filters is demonstrated.

Nature of the intrinsic relation between Bloch-band tunneling and modulational instability.

In an example of Bose-Einstein condensates embedded in two-dimensional optical lattices, we show that in nonlinear periodic systems modulational instability and interband tunneling are intrinsically related phenomena. By direct numerical simulations we find that tunneling results in attenuation or enhancement of instability. On the other hand, instability results in asymmetric nonlinear tunneling. The effect strongly depends on the band gap structure and it is especially significant in the case of the resonant tunneling. The symmetry of the coherent structures emerging from the instability reflects the symmetry of both the stable and the unstable states between which the tunneling occurs. Our results provide evidence of the profound effect of the band structure on the superfluid-insulator transition.