Omnidirectional narrow optical filters for circularly polarized light in a nanocomposite structurally chiral medium.

We consider the propagation of electromagnetic waves throughout a nanocomposite structurally chiral medium consisting of metallic nanoballs randomly dispersed in a structurally chiral material whose dielectric properties can be represented by a resonant effective uniaxial tensor. It is found that an omnidirectional narrow pass band and two omnidirectional narrow band gaps are created in the blue optical spectrum for right and left circularly polarized light, as well as narrow reflection bands for right circularly polarized light that can be controlled by varying the light incidence angle and the filling fraction of metallic inclusions.

Dispersion relation for electromagnetic propagation in stochastic dielectric and magnetic helical photonic crystals.

We theoretically study the dispersion relation for axially propagating electromagnetic waves throughout a one-dimensional helical structure whose pitch and dielectric and magnetic properties are spatial random functions with specific statistical characteristics. In the system of coordinates rotating with the helix, by using a matrix formalism, we write the set of differential equations that governs the expected value of the electromagnetic field amplitudes and we obtain the corresponding dispersion relation. We show that the dispersion relation depends strongly on the noise intensity introduced in the system and the autocorrelation length. When the autocorrelation length increases at fixed fluctuation and when the fluctuation augments at fixed autocorrelation length, the band gap widens and the attenuation coefficient of electromagnetic waves propagating in the random medium gets larger. By virtue of the degeneracy in the imaginary part of the eigenvalues associated with the propagating modes, the random medium acts as a filter for circularly polarized electromagnetic waves, in which only the propagating backward circularly polarized wave can propagate with no attenuation. Our results are valid for any kind of dielectric and magnetic structures which possess a helical-like symmetry such as cholesteric and chiral smectic-C liquid crystals, structurally chiral materials, and stressed cholesteric elastomers.

Saturation and stability of nonlinear photonic crystals.

We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions.

Tunable omni-directional mirror based on one-dimensional photonic structure using twisted nematic liquid crystal: the anchoring effects.

We present the tunability of the omnidirectional band gap (OBG) in a one-dimensional photonic structure consisting of N nematic liquid-crystal slabs in a twisted configuration. It is alternated by N isotropic dielectric layers by a dc electric field aligned along the periodicity axis. We consider the general case for which arbitrary anchoring of the nematic at the boundaries is taken into account. The threshold electric field for which the OBG is created decreases as the anchoring strength diminishes. The width of this band gets larger as the electric field increases and its center frequency is modified slightly.

Mechanically tuned defect-mode multiplet for cholesteric photonic elastomers.

The multiplet structure of the optical defect modes generated within the bandgap are analyzed by a finite number of identical equispaced twist defects in axially elongated cholesteric elastomers. It is shown that n(0) defect modes induced by n(0) twist defects can be mechanically tuned. The transfer matrix is obtained and the defect frequencies when n(0)=1,2 are expressed in terms of twist angle, fractional shape anisotropy, and longitudinal deformation. For n(0)=2, the coupling between modes is analytically studied and it is shown that when the separation between defects is much larger than the line width, the defect modes do not interact and become degenerated.

Spatial solitons in chiral media.

We study theoretically the nonlinear propagation of a narrow optical wave packet through a cholesteric liquid crystal. We derive the equations governing the weakly nonlinear dynamics of an optical field by taking into account the coupling with the liquid crystal. We constructed the solution as the superposition of four narrow wave packets centered around the linear eigenmodes of the helical structure whose corresponding envelopes A are slowly varying functions of their arguments. We found a system of four coupled equations to describe the resulting vector wave packet which has some integration constants and that under special conditions reduces to the nonlinear Schrödinger equation with space-dependent coefficients. We solved this equation both, using a variational approach and performing numerical calculations. We calculated analytically the soliton spatial scales, the transported power, the nonlinear refraction index, and its wavelength dependence, showing that this has its maxima at the edges of the reflection band. We also exhibit the existence of some other exact but non-self-focused solutions.