Berreman Matrix Research Articles

Lasing chirality control of thin-film defect-mode lasers based on cholesteric liquid crystal polymer mirrors

This work investigates the emission chirality of a chiral distributed Bragg reflector (DBR) laser, which is composed by incorporating an isotropic medium containing laser dye between two cholesteric liquid crystal polymer films. The emitted laser showed different ratios of circularly polarized states corresponding to different pitch numbers of the chiral mirror. Through Berreman matrix numerical calculations and experimental results, we validated the variations of the emission chirality coupling in the defect resonance mode as a function of pitch numbers, as well as the effect of the defect layer thickness on the wavelength and mode number of the emitted laser. We also observed the cone-shape emission and examined the threshold of the lasing. The results successfully demonstrated the realization of DBR laser with controllable orthogonal circular polarization ratios in the emitted laser light. These results offer considerable potential for the development of micro-laser sources with different emission chirality and wavelengths for various applications.

Photonic properties of polymer-stabilized photosensitive cholesteric liquid crystal studied by combination of optical activity, transmission and fluorescence

ABSTRACT We report complex optical investigations of polymer-stabilised cholesteric photonic liquid crystal doped by a dichroic fluorescent dye. For the first time, we employed a combination of various experimental methods, including measurements of spectra of transmission, reflection, rotation of the plane of polarisation of light, fluorescence, to characterise the properties of the photonic crystal. The peculiarity of the reported investigations is employing a photosensitive cholesteric mixture forming the photonic crystal. The position of the photonic band could be changed by illumination with ultraviolet light and stabilised by thermopolymerisation. In this way, the position of the cholesteric band was matched with the emission band of the fluorescent dye, which enabled to perform diversified studies on the same photonic crystal. We determined the parameters, which defined the optical properties of the photonic crystal, spectral dependence of the transformation of linearly polarised light to elliptically polarised as the light passes the photonic crystal, the photonic density of states. The interpretation of the experimental data was performed using analytical expressions obtained from the solution of Maxwell’s equations, numerical calculations by the Berreman matrix method.

2 × 2 anisotropic transfer matrix approach for optical propagation in uniaxial transmission filter structures.

Multi-layered metamaterial structures show promise in a wide variety of optical applications such as superlenses, electromagnetic cloaking, tunable filters, sensors, and spatial light modulators. Optical transmission analysis of multilayer metallo-dielectric stacks with overall thickness less than the wavelength of light can be modeled using effective medium theory and the Berreman matrix method. For multilayer anisotropic stacks of arbitrary thickness, a rigorous 4 × 4 transfer matrix embodiment is typically used. In this work, a 2 × 2 anisotropic transfer matrix method is developed to analyze optical propagation through multilayer uniaxial stacks of arbitrary thicknesses. Optical transmission of a multilayer silver-zinc oxide stack deposited on a quartz substrate is modeled with this 2 × 2 anisotropic transfer matrix method and reconciled with experimental observations. Results indicate that this numerical approach is applicable to in situ assessment of the complex refractive indices of constituent metal and dielectric layers. Additionally, the anisotropic 2 × 2 transfer matrix method enables the possibility of modeling the transmission of the same metallo-dielectric structure deposited on an electro-optic, uniaxial substrate. Simulation results predict that adjusting the bias field across the substrate results in an electrically tunable transmission filter.

Spectral and Polarization Characteristics of the Light Passing through a Cholesteric Photonic Crystal

Combined optical studies of a cholesteric photonic crystal are performed: the transmission spectra and the rotation of the plane of polarization of light (RPPL) spectra of the crystal are recorded, and the polarization characteristics of the light having passed through the photonic crystal are measured. The RPPL spectra have specific features related to the presence of a photonic quasi-band gap. The photonic density of states and its transformation with the photonic crystal temperature and thickness are determined. The ellipticity (ratio of the minor to the major axis of ellipse) of the light having passed through the sample is maximal at the center of the band gap and decreases when the distance from the band gap increases. At the center of the photonic quasi-band gap, the ellipticity increases with increasing photonic crystal thickness L and decreasing temperature, and it is close to a circular one in samples with L > 5 μm. The results obtained are compared with the existing theories, the analytical expressions derived from the Maxwell equations, and the results of numerical calculations performed by the 4 × 4 Berreman matrix method

A simplified transfer function approach to beam propagation in anisotropic metamaterials

The Berreman analysis for plane wave propagation through an anisotropic metamaterial is modified to derive the transfer function matrix for propagation in such a structure. The eigenvalues of the Berreman matrix, which determine the transfer function, depend on the anisotropy. Using the transfer function, propagation of TM and TE polarized beams in hyperbolic metamaterials is analyzed theoretically, and numerically based on the developed theory. For TM polarization, self-focusing of Gaussian beams in a hyperbolic metamaterial can be analytically explained using the q-parameter approach. Furthermore, the transmission coefficient for plane wave propagation through an anisotropic metamaterial slab is extended to a transmission transfer function, which is then used to analyze the propagation of beams through hyperbolic metamaterials and the ensuing spatial shifts. For TM polarized beams, negative refraction is verified. The main objective of this paper is to provide simple analytical tools for understanding self-focusing and negative refraction in anisotropic hyperbolic metamaterials as an alternative to, and check the validity of, rigorous numerical computations. Propagation of the longitudinally (z-) polarized optical field profile is derived. The transfer function approach should be useful for the analysis of arbitrary beam profiles through composite metamaterials.

Electric field-controlled transformation of the eigenmodes in a twisted-nematic Fabry\u2013P\xe9rot cavity

The polarized optical states in the transmission spectrum of a twisted-nematic Fabry–Pérot cavity with the distinctly broken Mauguin’s waveguide regime have been theoretically and experimentally investigated. Specific features of the electric field-induced transformation of the polarization and spectral characteristics of eigenmodes of the neighboring series at the overlap resonant frequencies have been examined. It is demonstrated that the linear polarizations of eigenmodes at the cavity boundaries remain nearly orthogonal and their frequency trajectories reproduce the avoided crossing phenomenon. The experimental data are confirmed analytically and by the numerical simulation of light transmission through the investigated anisotropic multilayer with the use of a Berreman matrix method. The results obtained can be generalized to any materials with the helix response.

Optical propagation through anisotropic metamaterials: Application to metallo-dielectric stacks

We perform numerical simulations to compare the Berreman matrix method using effective medium results for an anisotropic material with exact calculations of a multi-layer metallo-dielectric stack using the transfer matrix method and finite element techniques. Results are given for a wide band of wavelengths and incident angles. For fixed sample thickness the number of layers is increased to study convergence of the optical characteristics (transmittance and reflectance). It is shown that the Berreman matrix method with effective medium results for an anisotropic material provides a fast and reliable estimate of the optical characteristics of the composite material. The Berreman technique readily leads to the transfer function matrix for propagation in anisotropic materials.

Resonances in Bianisotropic Layers

This paper rigorously studies the resonant transmission of electromagnetic waves around embedded trapped modes in bianisotropic films and derives the dispersion relations, the embedded mode condition, and the coupling and tunneling of the evanescent wave within the reciprocal lossless bianisotropic layer. The Berreman's matrix model has been developed to obtain the transmission characteristics through the bianisotropic film. When the layer structure was perturbed, a resonance phenomenon was perceived around the distinct trapped modes; these resonances lead to anomalous transmission and field amplifications around the trapped mode frequencies. The parameters of the magnetoelectric tensors can be used to control the number of the trapped modes and accordingly the resonances in the bianisotropic layer material.

Optically Controllable Linear-Polarization Rotator Using Chiral-Azobenzene-Doped Liquid Crystals.

A linear-polarization rotator based on the optically tunable pitch of chiral-azobenzene-doped liquid crystals (CAdLCs) has been investigated. It is shown that the orientation of linearly polarized (LP) light can be optically tuned using CAdLCs and that the transmitted light possesses a good degree of linear polarization (DoLP). Experimental and simulation (4 × 4 Berreman matrix) results show that the rotation angle is dependent on the pitch as well as the number of turns of the cholesteric LC helix. Some causes to affect the DoLP of the output LP lights during photoisomerization are also discussed. Moreover, a calibration term, β(t), is also introduced to elucidate the behavior of the discontinuous change of the CAdLC pitch in a fixed cell thickness.

FFS모드 LCD의 투과율 향상을 위한 전극 구조 개선

In this study, we proposed a novel electrode structure for the fringe field switching (FFS) mode LCD and performed a three-dimensional computer simulation to calculate the optical transmittance for the new structure. In the simulation Erickson-leslie equation and Berreman matrix were used for obtaining the director distribution profiles of liquid crystal molecules and the electro-optical characteristics, respectively. Considering the complexity of the motional equation of the liquid crystal molecules, FDM (finite difference method) was used as a numerical method. From the results, We revealed that the light transmission of the newly designed pixel structure is expended to the edge of the pixel electrode. We also confirmed that the light transmittance increased more than 13% compared to that of the conventional electrode structure.

Total internal reflection in anisotropic crystals

Examples of total internal reflection manifestation have been considered on the basis of a solution to boundary problems of crystal optics using the Berreman matrix method and applying the Mathematica-5 system. It is shown how optical activity manifests itself in the total internal reflection and how this effect can be used to monitor the quality and homogeneity of film coatings.

Computational rheooptics of liquid crystal polymers

A computational rheooptical model based on the integration of liquid crystal polymer flow equations and two well-known polarized light transmission methods is formulated and applied to the ubiquitous periodic banded textures observed in sheared lyotropic nematic polymers. The selected optical methods are the matrix-type Berreman method and the finite-difference time-domain (FDTD) direct numerical simulation method. The optical response of a single unit cell of the periodic banded texture of sheared lyotropic nematic polymers to polarized light propagation under cross-polars is analyzed and correlated to the shear-induced orientation field previously reported in Han and Rey [W.H. Han, A.D. Rey, Theory and simulation of optical banded textures of nematics polymer during shear flow, Macromolecules 28 (1995) 8401–8405]. The role of orientation gradients on the optical response is elucidated and shown to be source of lack of accuracy of the Berreman matrix method. The findings provide robust guidelines on the applicability and accuracy of matrix and direct numerical simulation optical methods. Computational rheooptics of liquid crystal polymers based on the FDTD method is an additional tool to understand flow-induced texture formation when used in the direct forward mode, and in quantitative assessments of rheological material properties when used in backward mode.

Highly birefringent nematic and chiral nematic liquid crystals

We report a simple interference method to determine the dispersion of the extraordinary refractive index and birefringence of highly conjugated and coloured nematic liquid crystals used as light‐emitting materials in organic electroluminescent devices. The measurements are made in the nematic glass phase at room temperature. The birefringence is highly dispersive and values up to 1.1 are obtained. Chiral groups are incorporated into the end chains giving a chiral nematic liquid crystal with a very wide stopband in the visible region. The Berreman matrix method is used to simulate transmission through the chiral nematic liquid crystal cell using the refractive index parameters obtained experimentally. Excellent agreement between theory and experiment is found.

Comparison of extended Jones matrices for twisted nematic liquid-crystal displays at oblique angles of incidence

Detailed formulas were derived by using Yeh’s formulation of the extended 2×2 Jones matrix and applied to twisted nematic liquid-crystal displays at oblique angles of incidence. Numerical comparisons of this extended Jones matrix method with the exact 4×4 Berreman matrix and with the extended Jones matrix of Lien are presented. The various extended Jones matrix formulations differ in their approach to boundary-condition matching between the model birefringent layers. We show that Yeh’s version is a more accurate approximation to the full 4×4 matrix. This extended Jones matrix method is fast, direct, and simple. It is also physically more intuitive.

Jones matrix treatment of electromagnetic wave propagation in anisotropic stratified media

Light propagation in anisotropic stratified media may be conveniently described, in the quasi-adiabatic limit, by the so-called Jones matrix formalism. In systems like liquid crystals, the quasi adiabatic limit occurs when the director rotates very slightly over distances of the order of the light wavelength. This limit is of relevant interest in many optical devices. As known, the general solution of the Maxwell's equations in anisotropic stratified media may be obtained by using the 4 × 4 Berreman's matrix method. However, as long as the polarization properties of the light transmitted through the medium are concerned, a much simpler approach is possible, which consists in completely neglecting the solutions of the Berreman's equations corresponding to the waves propagating in the backward direction. In this case, the number of differential equations describing light propagation is reduced from 4 to 2. The 2 × 2 matrix introduced in this approximated fromalism is termed the Jones matrix of the problem. In this paper, we show that in general case of oblique incidence of light is possible to properly transform the original Berreman's matrix into a form suitable for reduction to a 2 × 2 Jones matrix.

Light Propagation in Antsotropic Stratified Media in the Quast Adiabatic Limit

Abstract We propose a new perturbative treatment of the equations for electromagnetic wave propagation in the adjabatic limit in liquid crystals where the director is continuosly rotatin through the sample with an arbitrary law. In this approach a simple, 2×2 Jones matrix is obtained by proper transformation of the conventional 4×4 Berreman matrix. An approximate propagation equation is deduced for the jones Vector giving the polarization state of the wave propagating in the forward direction. The results obtained by using this equation are compared with the exact ones and the limits of validity of the present approach are discussed.