Wave amplitude gain within wedge waveguides through scattering by simple obstacles.

Wave confinement, e.g., in waveguides, gives rise to a huge number of distinct phenomena. Among them, amplitude gain is a recurrent and relevant effect in undulatory processes. Using a general purpose protocol to solve wave equations, the boundary wall method, we demonstrate that for relatively simple geometries, namely, a few leaky or opaque obstacles inside a θ wedge waveguide (described by the Helmholtz equation), one can obtain a considerable wave amplification in certain spatially localized regions of the system. The approach relies on an expression for the wedge waveguide exact Green's function in the case of θ=π/M (M=1,2,...), derived through the method of images allied to group theory concepts. The formula is particularly amenable to numerical calculations, greatly facilitating simulations. As an interesting by-product of the present framework, we are able to obtain the eigenstates of certain closed shapes (billiards) placed within the waveguide, as demonstrated for triangular structures. Finally, we briefly discuss possible concrete realizations for our setups in the context of matter and electromagnetic (for some particular modes and conditions) waves.

Soliton-like structures in the spectrum and the corresponding eigenstates morphology for the quantum desymmetrized Sinai billiard.

By continuously varying certain geometric parameters γ of the totally desymmetrized quantum Sinai billiard, we study the formation of the so-called soliton-like structures in the spectra of the resulting family of systems. We present a detailed characterization of the eigenstate ψn morphologies along such structures. Usually, scarring and bouncing ball mode states are expected to fully explain the solitons. However, we show that they do not exhaust all the possibilities. States with strong resemblance to very particular solutions of the associated integrable case ( 45°- 45° right triangle) also account for the ψn's. We argue that for the emergence of the solitons, in fact, there must be an interplay between the spatial localization properties of the soliton-related ψn's and the rescaling properties of the billiards with γ. This is illustrated, e.g., by comparing the behavior of the eigenwavelengths along the solitons and the billiard size dependence on γ. Considerations on how these findings could extend to other type of billiards are also briefly addressed.

Nematic reorientation effects on resonant modes, wavelength mismatch, and slow-light phenomena in one-dimensional magnetophotonic crystals with a dual anisotropic defect.

The present study is devoted to the investigation of spectral properties of an alternated sequence of magnetic and dielectric layers containing a dual defect based on magnetic and nematic layers. Combining the Hydrodynamic Continuum Theory for nematic liquid crystals and Berreman's formalism, we determine how the nematic ordering affects the light localization, polarization rotation, and slow-light phenomena observed in the magnetophotonic system. In particular, we analyze the effects associated with a field-induced reorientation of the director in a nematic defect with strong planar boundary conditions. Our results reveal that field-induced reorientation of the nematic ordering can be used as an efficient mechanism to tune and control the spectral properties of magnetophotonic structure, anomalies in group velocity, and the wavelength mismatch between resonant mode and maximum polarization. The effects of nematic layer thickness are also analyzed.

Birefringence-induced wavelength mismatch between the polarization rotation and resonant modes in magnetophotonic structures containing nematic layers.

The present work is devoted to the study of spectral characteristics of normal incident light transmitted by a multilayered structure composed of an alternated sequence of nematic and magnetic layers presenting a central magneto-optical defect. Using the Berreman 4 × 4 matrix formalism, we numerically obtain the transmission spectrum and the polarization rotation angle of the system as a function of the nematic optical axis direction. Our results reveal the emergence of a shift between the wavelengths of the resonant mode and polarization rotation angle, which strongly depends on the birefringence of the nematic layers. In particular, we show the existence of distinct regimes for the wavelength mismatch between the transmission of resonant modes and the maximum polarization rotation angle, which are governed by the ordinary and extraordinary refractive indices of nematic layers. The mechanism behind such shift is discussed under the light of propagation eigenmodes for a medium presenting circular and linear birefringence. The effects associated with the defect thickness are also analyzed.

Tunable reflectance spectra of multilayered cholesteric photonic structures with anisotropic defect layers.

In this paper, we investigate the spectral characteristics of normal incident light reflected by a multilayered structure composed of an alternated sequence of single-pitch cholesteric liquid-crystal (ChLC) and anisotropic layers. Using the Berreman 4x4 matrix formalism, we numerically obtain the reflection spectrum and the chromaticity diagram as a function of the anisotropic layers thickness d. For d-->0 , the structure behaves like a single ChLC layer, showing a single reflection band. As the anisotropic layer thickness increases, the reflection band shifts toward high-wavelength spectral regions, while new reflection bands appear. As a consequence, the reflection chromaticity continuously changes with d . It is observed that a suitable choice of the anisotropic layer thickness can produce a threefold reflection band with a red-green-blue associated color for both polarized and unpolarized incident lights.

Resonant modes in cholesteric liquid crystals with a gaussian pitch profile.

In this paper, we investigate the spectral properties of a cholesteric film presenting a pitch profile with a gaussian deformation. Using the Berreman 4 × 4 matrix formalism, we numerically obtain the transmission spectrum at normal and oblique light incidence as a function of width and the position of the deformation. Our results reveal that a pair of resonant modes emerges inside the main stop band of the transmission spectrum as the width of the deformation becomes comparable to the helical pitch length. The mechanism behind the emergence of the resonant modes is discussed. The case of a pitch profile with multiple gaussian deformations is also analyzed. At this configuration, a crossover from single to multiple band-gap pattern can be observed in the transmission spectrum, depending on the deformation parameters.