Birefringence Parameters Research Articles

Simultaneous Measurement of Phase Retardation and Fast-Axis Angle of Phase Retardation Plate

A phase retardation plate, such as a quarter-wave plate, is able to control the state of polarization. Thus, a precise simultaneous determination of phase delay between two eigen-polarization states and its fast-axis angle is essential to the performance of the phase retardation plate to control the state of polarization. Consequently, the measurement of the two-dimensional spatiotemporal distribution of phase retardation and the fast-axis angle become crucial when a large-area of phase retardation plate, such as that for a liquid crystal display, is characterized, due to the inhomogeneity of the retardation plate. In order to measure the linear birefringence parameters, phase retardation and fast-axis angle at the same time, a novel polarized optical heterodyne interferometer is developed, with which the parameters of a quarter-wave plate are successfully measured and verified. The features of this device are (1) a common-path configuration, (2) measurement independent of laser intensity, and (3) the capability of simultaneously determining the spatiotemporal distributions of phase retardation and fast-axis angle of a retardation plate.

Strehl ratio for focusing into biaxially birefringent media

The Strehl ratio for focusing into biaxially birefringent media with small birefringence is investigated. An analytical expression for the Strehl ratio as a function of the polarization and birefringence parameters is derived in the paraxial limit from a generalization of the scalar aberration theory. The expression agrees well with results of a numerical calculation.

Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers

We study the elliptically polarized states in the spin-flip model for vertical-cavity-surface-emitting lasers. The stability analysis reveals some unexpected features. In correspondence with particular values of the birefringence parameter, which are shown to scale very simply with the ratio of the spin-flip rate to the linewidth enhancement factor, the stability domain can be quite large. Moreover, in some cases two different dynamical regimes can arise from the destabilization of the elliptically polarized states, and they can coexist in a finite interval of the pump parameter. Finally, we show that the bifurcation from the lower frequency linearly polarized state to the elliptically polarized states can be subcritical when the linewidth enhancement factor is roughly smaller than 1.

Image assessment of a birefringent lens based on the factor of encircled energy

The factor of encircled energy (FEE) in the diffraction pattern formed by an optical system consisting of an aberration-free birefringent lens sandwiched between two linear polarizers is computed directly from the optical transfer function (OTF) of the system. FEE curves are given showing the variation of image quality of the proposed system at the Gaussian image plane and other observation planes with the birefringent lens parameters and the azimuthal settings of the transmission axes of the polarizers. The performance is compared to that of an ideal conven- tional glass lens. © 2003 Society of Photo-Optical Instrumentation Engineers.

Transient evolution of the polarization-dispersion vector's probability distribution

We determine the transient evolution of the probability distribution of the polarization dispersion vector both analytically and numerically, using a physically reasonable model of the fiber birefringence. We show that, for all practical birefringence parameters, the distribution of the differential group delay (DGD), which is the magnitude of the polarization dispersion vector, becomes Maxwellian in just a few kilometers, except in the tail region, where the DGD is large. In this limit, the approach to a Maxwellian distribution takes much longer, of the order of tens of kilometers. In addition, we show that in the transient regime the DGD distribution is very different from Maxwellian. We also find that the probability-distribution function for the polarization-dispersion vector at the output of the fiber depends upon the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

Frequency response characteristics of a birefringent lens

The diffraction-based optical frequency response characteristic of a birefringent crystal lens sandwiched between two linear polarizers has been studied analytically using the autocorrelation of the pupil function over the lens aperture. The optical transfer function (oTf) of this proposed system depends on the material as well as design parameters of the crystal lens, along with the orientations of the transmission axes of the two polarizers relative to each other and to the optic axis of the birefringent lens. Naturally, the OTF of such a system can be varied at the lens fabrication stage like other lenses. An online variation of the OTF is also possible just by rotating any of the two polarizers included in the system. It has been shown that the proposed system can be adapted either for apodization or for super-resolution simply by rotating any of the two polarizers. This system may be designed for obtaining high depth of focus without significant image degradation, as well as for image processing operations like high frequency enhancement. The response of the system is studied at the Gaussian image plane as a function of the line frequencies in the object for different values of the birefringent lens parameters, and also for two different settings of the analyzer. The results are compared with the response of an ideal lens.

Evaluation of the Form Birefringence and Other Structural Parameters Due to Thermal Annealing for Nylon 6 Fibers

In the present work nylon 6 fibers were annealed at 155±1 ○C at different times and allowed to cool down in the oven to room temperature (27±1 ○C). A Pluta polarizing interference microscope was used for measuring the changes in the optical parameters. From the optical and density parameters the optical orientation values of F2(Θ), F4(Θ), F6(Θ) and Fav were calculated. Also, the dielectric constant, dielectric susceptibility, molar refractivity, segment anisotropy, optical stress coefficient, optical configuration and the form birefringence were evaluated. The segment anisotropy and deformational thermal stress was evaluated. Relationships between the measured and calculated parameters are given for illustration. The mechanism of structural variations for nylon 6 fiber due to the annealing process is discussed, and structural details for opto thermal parameters are explained. The present study throws light on the changes due to thermal annealing conditions for nylon 6 fibers. Microinterferograms and curves are given for illustration.

Polarization eigenvectors for reflective twisted nematic liquid crystal displays

We compare the reflective and transmissive properties (inten- sity transmission and phase shift) for a twisted nematic liquid crystal display (LCD). Our goal is phase-mostly modulation with a phase shift that exceeds 2p rad and the reflective geometry is of interest because the phase modulation depth increases with the double pass. We exam- ine the polarization eigenvectors for two reflective geometries, by includ- ing or not including a wave plate between the LCD and the mirror. The LCD behavior is modeled with a simplified physical model that uses two birefringence parameters that depend on the addressed gray level. Ex- perimental results show excellent agreement with theoretical predictions including a large phase modulation depth with an almost flat transmis- sion response. © 2001 Society of Photo-Optical Instrumentation Engineers.

Propagation of polarized light in birefringent turbid media: time-resolved simulations

A Monte Carlo model was used to analyze the propagation of polarized light in linearly birefringent turbid media, such as fibrous tissues. Linearly and circularly polarized light sources were used to demonstrate the change of polarizations in turbid media with different birefringent parameters. Videos of spatially distributed polarization states of light backscattered from or propagating in birefringent media are presented.

Synthesis, phase transitions and optical properties of novel tetrathiafulvalene derivatives with extremely high molecular polarizabilities

The synthesis of novel unsymmetrically-substituted tetrathiafulvalene derivatives based on lithiation procedures is described. The disubstituted derivatives were synthesized as 1:1 cis/trans-isomeric mixtures, the compositions of which were established by 1H NMR and 13C NMR spectroscopy. The transition temperatures, refractive indices, birefringence, polarizability and order parameter of each of the mixtures were determined and the values are discussed in comparison with analogous compounds with the tetrathiafulvalene unit replaced by a 1,4-phenylene group. In addition, we describe the synthesis of a number of monosubstituted tetrathiafulvalene derivatives and their associated thermal properties. The isomeric compounds presented in this paper have exceptionally large values of polarizability anisotropy, as compared with their phenyl-containing counterparts.

Role of polarization mode dispersion on modulational instability in optical fibers.

We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we give the explicit form of the effective matrix and numerically compute the maximal eigenvalue. In the anomalous dispersion regime, polarization dispersion widens the unstable bandwidth. Depending on the type of variations of the birefringence parameters, polarization dispersion reduces or enhances the MI gain peak. In the normal dispersion regime, random effects may extend the instability domain to the whole spectrum of modulations. The linear stability analysis is confirmed by numerical simulation of the full stochastic coupled nonlinear Schrödinger equations.

Propagation of partially polarized light in dichroic and birefringent media

We report on an exact analytical solution for the Jones and Mueller matrices for the most general uniform, linear non-depolarizing media with an arbitrary dichroism and birefringence. We show that this Mueller matrix is a Mueller-Jones matrix. An analytical expression for the degree of polarization (DoP) has been derived as a function of the parameters of birefringence and dichroism. In our formalism six cases for the DoP are analysed. An oscillatory behaviour for the DoP has been reported in the case when the net birefringence is greater than the net dichroism. A method to determine all the physical parameters of a transmission medium, such as a total birefringence and a total dichroism, from the measurements of the DoP has been proposed.

Elliptical-hole photonic crystal fibers

We study the dispersive properties of photonic crystal fibers (PCF's) with elliptical air holes. The unusual guidance of PCF leads to novel behavior of the birefringence, group-velocity walk-off, and dispersion parameters, including the possibility of zero walk-off with high birefringence in the single-mode regime. A number of these effects are closely tied to the underlying radiation states of the air-hole lattice.

The Mechanism of the Polarizational Mode Instability in Birefringent Fiber Optics

We show that the soliton solutions of the integrable Manakov equation exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability arises from eigenvalues embedded in the essential spectrum of the associated linearized operators; these eigenvalues are dislodged by smooth perturbations. Specifically we consider perturbations which arise in fiber optics as a result of birefringence, including the so-called four-wave mixing term. Employing the Evans function and a Dirichlet expansion on the stable manifold of the linearized system, we obtain rigorous perturbation results and compute the stability diagram of the fast wave for all physical values of the birefringent parameters, using a novel numerical scheme derived from the Dirichlet expansion.

Unusual Odd-Even Effects in Vinyl Ether and Acrylated Direactive Liquid Crystals

Four series of direactive liquid crystals are presented and their physical properties characterised. The core groups are based on either a lateral chloro or methyl terphenyl and the reactive groups are either acrylates or vinyl ethers. It is shown that reactive liquid crystals with vinyl ether reactive groups have higher transition temperatures, birefringence, and order parameter than the corresponding acrylates. Both the vinyl ether and acrylate series show an odd-even effect in transition temperatures, birefringence and order parameters. The odd-even effect in the vinyl ether series is particularly marked.

Opto-mechanical properties of fibres. Part 2. Effect of stretching on some optical and structure parameters of PET fibres (woollen type)

The influence of cold drawing on the birefringence, orientation, crystallinity and other structural parameters is examined for polyester (Egyptian PET woollen type). A two-beam Pluta polarizing interference microscope connected to a device for dynamically studying the effect of the draw ratio on the refractive indices has been used. The optical data obtained the densities and crystallinities of the samples. The mean square density fluctuation 〈η2〉, crystalline orientation function, amorphous orientation function, the number of chains per unit volume Nc and the number of random links between the network junction points N1 are then calculated. Calculations are also carried out to determine the strain optical coefficient, the orientation factor, the orientations angle, the number of molecules per unit volume N, and the isotropic refractive index. In addition, Poisson's ratio over all strain ranges, the distribution of segment at an angle θ with respect to the draw ratio, the electric polarizability constant (Δα/3α0) and other structural parameters and constants are calculated. An empirical formula is suggested to correlate the change in Δ n, Fc , Fa , ω(cos θ), A and Nc , and its constants are determined. The refractive index profile is studied. Interferograms and curves are given for illustration. © 1999 Society of Chemical Industry

Evaluation of hydroxyl content in commercial <inline-formula>X</inline-formula>-cut <inline-formula><roman>LiNbO</roman><sub><roman>3</roman></sub></inline-formula> wafers for optical waveguide devices

Usually the quality of commercial LiNbO3 (LN) wafers is checked by their crystalline homogeneity. In X cut wafers, which are labeled for optical waveguide applications, however, the existence of a significant change in the hydroxyl content along the polarizedZ axis is found by Fourier transform IR (FTIR) spectrometry, although a corre- sponding inhomogeneity was not observed about the lattice parameters, the Li and Nb contents, and the optical birefringence parameters. Such a difference in hydroxyl content might influence quality and stability of the obtained waveguides, and one should consider this before designing waveguide devices and fabrication processes. © 1998 Society of Photo- Optical Instrumentation Engineers. (S0091-3286(98)01905-9)

Physical and Molecular Properties of Three Mesogenic Phenyl Cyclohexyl Compounds

Experimentally determined values of density, optical birefringence (Δn) and moleculer parameters obtained from X-ray diffraction analysis of three mesomorphic compounds, two having non-polar phenyl cyclohexane and one alkyl phenyl cyclohexane with a polar terminal group are reported here.Orientational order parameters at different temperatures were calculated both from birefringence and X-ray diffraction of aligned compounds.

Birefringence parameters: Indicators of anisotropic symmetry systems

The difference in travel times between split shear waves (travel-time splitting) in anisotropic media depends on nine combinations of the density normalized elastic parameters (the birefringence parameters). These combinations are all zero in isotropic media, where there is no shear-wave splitting. The number of nonzero birefringence parameters increases with decreasing symmetry elements in the medium: from one in cubic media to nine in triclinic media. The birefringence parameters may be recovered from travel-time splitting observations. Their azimuthal behavior may then be interpreted in terms of crack orientation (strike and dip directions).

Interactions in bright N-soliton trains propagating in birefringent optical fibres

The role of birefringence in bright soliton interactions in an optical fibre is investigated numerically. Groups containing up to five solitons have been used as the input condition, with an angle ψ being used to determine the amplitudes of the resulting partial pulses in the slow (u) and fast (v) polarisation states. The concept of displacement length, ξ1, is used to characterise the interactions and general plots of the variation of this quantity with group velocity birefringence parameter, δ, and interpulse separation, are presented. Both a minimum and a maximum are found. Unequal amplitudes and interpulse phase differences are also investigated. Amplitude variations are shown to be effective in improving ξ1 but phasing has a negative effect. Finally, shadow amplitudes for pairs of solitons in the u and v states are given as a general function of offset and interpulse parameters.