Juan Adrian Reyes

Guiding of optical fields in a liquid crystal cylindrical fiber

Abstract The propagation of optical fields in a cylindrical waveguide is studied. We consider that a quiescent nematic core is surrounded by an infinite homogeneous isotropic cladding. We propose an analytic although approximate description of the reorientation induced by the optical field. Then by making systematic approximations in powers of two well defined parameters of the system, we calculate the dielectric tensor of the core, the ray trajectories, the field distributions and the spatial electromagnetic energy distribution within the guide. These quantities are calculated for field frequencies such that the dielectric anisotropy of the nematic is always negative. We show that in this case there exists a wave guide effect that concentrates the ray trajectories and the electromagnetic energy around the central axis of the cylinder. We discuss the limitations of our model as well as its advantages over pure numerical descriptions.

Multiplet structure of the defect modes in 1D helical photonic crystals with twist defects

We theoretically analyse the defect modes generated by equispaced twist defects in 1D helical (cholesteric-like) structures within their frequency gap which is such that only the first two of the four eigenwaves 1±, 2± are exponentially attenuated. n0 identical defects generate n0 different defect modes, each one represented by a linear combination of the four eigenwaves. The components 1+ and 1− are by far the dominant ones and they are localized near the defect planes. We give exact analytic expressions for the elements of the transfer and scattering matrices of the defect planes, for the functions defining the defect mode when n0 = 1, and for the defect frequencies when n0 = 1, 2, 3. In the particular case n0 = 2 and twist angle θ = π/2, the difference between the two defect wavelengths λd2, λd1 depends exponentially on the distance z1 between the defect planes, going to zero for z1 → ∞ and becoming as large as the entire frequency gap for z1 → 0.

1D Schrödinger equations with Coulomb-type potentials

We employ Laplace and Fourier transforms in momentum space to find the bound states of the 1D Schr?dinger equations with two different potentials; and . By performing inverse transforms we show that for the potential the solutions in real space reduce to those of the 1D hydrogen atom with eigenenergies proportional to with n integer. Analogously, we find that for the potential the eigenenergies are proportional to and the eigenfunctions can be expressed in terms of fractional derivatives. Taking into account that both potentials are singular (the potential is analytical and the potential is not), we analyse the nature of their bound states.

Ray tracing and reflectivity measurements in nematic hybrid cells

Abstract We propose an experimental procedure to show that an optical beam may propagate in a planar-homeotropic hybrid nematic crystal cell for incidence angles i larger than the critical one. Its effect on the reflectance coefficient R as a function of i is accounted for by using total internal reflection techniques. We model the propagation of a linearly polarized Gaussian beam of finite diameter through the cell and the reflectance curves R vs. i are calculated theoretically in the total internal reflection regime by using an analytical description. The experimental procedure, cell assembling and methodology are designed so that there is reasonable consistency with the model assumptions. In the optical limit approximation this model allows us to calculate analytically the phase shift, the trajectory and the reflectivity curves of a beam traveling with an extraordinary polarization (P-polarization) inside the cell. Since only some parts of the reflected beams will interfere, Berreman’s method is not suitable for the physical situation considered. The possibility of leakage through the tunneling effect across the cell is also considered and estimated quantitatively. The comparison between the theoretical results and the experimental data shows good agreement between our experimental results and the theoretical curves R vs. i . We compare our results with other measurements reported in the literature and find that the behavior of the reflectance curve is highly affected by the cell thickness-beam waist ratio. The values of this parameter can produce different behaviors of the reflectivity measurements. The analysis of the model predictions and experimental results suggest a possible interpretation of the physical origin of the reflectivity curves and give a qualitative insight into the phenomena behind the total internal reflection regime. Finally, we emphasize the limitations and advantages of the model and of the experimental results presented.

Mechanically controlled defect mode in cholesteric elastomers

We consider an axially elongated cholesteric elastomer having a twist defect. We show that its localized mode can be mechanically tuned, and the scaling of the inverse relative line width can be largely enhanced when the values of the deformation and shape anisotropy are near the pseudoisotropic curve. This choice causes a tremendous variation in the behavior of the photon dwell time in the defect mode, which then grows linearly versus the sample thickness. The shift of the defect wavelength, the reflection band width, and the angle between the electric and magnetic fields are also calculated.

Lossy effects in a nonlinear nematic optical fiber

We use the multiple scales method to derive a generalized nonlinear Schrodinger equation that takes into account the dissipative effects in the reorientation of a nematic confined in a cylindrical waveguide. This equation has soliton-like solutions and predicts a decrease in the penetration length of the optical solitons for each propagating mode with respect to the dissipationless case.

The role of the anchoring conditions in the electrorheological behaviour of a nematic constrained by two coaxial cylinders and submitted by a pressure drop

ABSTRACT We study a nematic liquid crystal (NLC) filling the region between two coaxial cylinders subjected to the simultaneous action of both, a pressure gradient applied parallel to the axis of the cylinders and a radial low-frequency electric field. For the LC 4′-n-pentyl-4-cyanobiphenyl (5CB), we consider strong and weak anchoring conditions (WAC) to obtain the configuration of the director and the velocity profile for non-slip boundary conditions. Finally, we calculate the apparent viscosity for the nematic. GRAPHICAL ABSTRACT

Anchoring effects on the electrically controlled optical band gap in twisted photonic liquid crystals

We study a one-dimensional twisted photonic liquid crystal (TPLC), consisting of various nematic liquid crystal cells adopting a twisted configuration intercalated by isotropic dielectric layers, submitted to a dc electric field (Edc ) aligned along the periodicity axis. We write the corresponding Euler–Lagrange equations describing the nematic layer configuration. By assuming arbitrary anchoring quasi-planar boundary conditions, we calculate the equilibrium textures for the nematic, parametrized by the two types of strength of its interaction (polar and azimuthal) with the plane walls. We write the electromagnetic equations in a 4 × 4 matrix representation and using the transfer matrix formalism, we obtain the transmittance and reflectance coefficients for normal incidence as functions of the external electric field and anchoring strengths. We have observed a remarkable dependence of the electric field on the transmission and reflection spectra in opening and closing band gaps.

Ray propagation in antisotropic inhomogeneous media

We derive the eikonal and transport equations, in the transverse magnetic (TM) and electric (TE) representation, for an electric anisotropic and inhomegeneous media by using the limit of geometrical optics. We also calculate the Poynting vector and analyse the consequences of the Poynting theorem for our system. We study the Lagrangian representation for interpreting the trajectories and show that the TM ray trajectory in a uniaxial liquid crystal is that of the 2D projection of a 3D propagating ray in an isotropic medium, constrained by a surface. As an application of the formalism, we explicitly exhibit these surfaces for the radial and bipolar configuration in nematic droplets.

Band structure and reflectance for a nonlinear one-dimensional photonic crystal

Abstract We consider a model for a one-dimensional photonic crystal formed by a succession of nonlinear Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate analytically the band structure of this system as a function of the incident wave intensity, and find two main tendencies: the appearance of prohibited bands, and the separation and narrowing of these bands. We consider as well a finite version of this photonic crystal for a limited number of alternating linear and non linear set of stacks for which we calculate reflectance as a function of the electromagnetic wave intensity, band index and number of periods. A system with these features can be constructed by alternating very thin slabs of a nonlinear soft matter material with thicker solid films, which can be used to design a device to control light propagation for specific wavelength intervals and light intensities of the same propagating signal.