Jones Matrix Representation Research Articles

Vectorial eigenvector method for simulating the polarization dependent resonator.

Derived from the eigenvector method (EM), a vectorial eigenvector method (VEM) for the mode calculation of polarization dependent resonator is presented. New transfer matrices of laser resonant cavities with polarization-selective devices are built by using Jones matrix representation. The eigenvectors computed by solving the matrix eigenequation manifest the mode characteristics of resonators, including cylindrical vector (CV) modes. Comparing with EM, the VEM inherits EM's superiorities and extends scalar models to vector models. Then, an example utilizing VEM to simulate axicon mirror resonator was given, which proved the VEM feasible and efficacious. Finally, upon a fast axial flow (FAT) CO2 laser with an axicon mirror as rear mirror, we experimentally corroborated the validity of the VEM and a working-stable 1.5 kW radially polarized beam was obtained.

Analysis and Design of Intrinsically Dual Circular Polarized Microstrip Antennas Using an Equivalent Circuit Model and Jones Matrix Formulation

Planar dual circular polarization (CP) antennas can be realized with a linearly polarized antenna and a quadrature hybrid, but the hybrid is lossy and undesirable for satellite communications applications where efficiency is paramount. There are surprisingly few hybrid-free, intrinsically dual CP microstrip antenna (MSA) designs in the literature. One reason for this is that it is challenging to obtain high isolation between ports while maintaining low return loss and good polarization quality. To resolve this problem, a method for multicriterion design optimization of dual-CP MSAs is proposed. The method is based on an accurate equivalent circuit model combined with a Jones matrix representation of the antenna response. The model explains the counter-intuitive tradeoff between cross-polarization isolation and impedance mismatch factor. The model also provides an analytical relationship between axial ratio bandwidth and impedance bandwidth, and allows the Wheeler cap method to be generalized to multiport, dual polarization antennas. Based on insights provided by the analysis, an effective matching and decoupling scheme is proposed, leading to an intrinsically dual CP MSA design that is competitive in performance with a dual linear antenna combined with a hybrid. Results are validated by comparison to full wave simulations for practical dual CP antenna examples.

Accurate Evaluation of Polarization Characteristics in the Integrated Optic Chip for Interferometric Fiber Optic Gyroscope Based on Path-matched Interferometry

Accurate evaluation of polarization characteristics in the integrated optic chip (IOC) for interferometric fiber optic gyroscope was performed. Spatial distribution of optical wavetrains caused by the polarization parameters such as local polarization cross-coupling and polarization rejection coefficient of the IOC were measured utilizing the path-matched optical coherence domain polarimetry (PM-OCDP). With the analytic model deduced from Jones matrix representation, we could accurately identify the polarization characteristics of the IOC. Both degree of measurement error due to the imperfect equipment conditions in PM-OCDP and birefringence of IOC chip were also characterized.

Jones precoder for polarization mode dispersion compensation

A new electrical-domain precoder is proposed to mitigate polarization mode dispersion (PMD) in optical communications by modeling a PMD-dominant fiber optical channel using a single input multiple output (SIMO) channel. Employing a bank of finite impulse response filters and a polarization modulator, and using parameters derived from the Jones matrix representation of PMD, the proposed precoder efficiently adapts to the time-varying nature of PMD and simultaneously pre-equalizes both polarization modes at the transmitter. The transmitter-only structure avoids losing phase and polarization information due to the nonlinearity of the commonly used square law direct-detection receiver. Analysis is performed to evaluate the impact of channel mismatch due to feedback delay, channel estimation errors, and the impact of the finite length of the precoder filters. The analytical results are used to guide selection of the appropriate feedback rate for the adaptive system. Extensive simulation results confirm the efficiency of the proposed Jones precoder, and present it as an effective, low-cost replacement to the complicated, expensive optical-domain counter-parts.

Rewritable Liquid Crystal Gratings Fabricated Using Photoalignment Effect in Dye-Doped Poly(vinyl alcohol) Film

In this paper, we present rewritable liquid crystal (LC) gratings based on azo dye-doped polyvinyl alcohol films. The mechanism of such rewritable characteristics is attributable to the irradiation of these films with a suitable linearly polarized light beam which reorients dyes and then aligns LCs. Two gratings, one with a 90° twist nematic (TN)/homogeneous periodical alignment and the other with a 45° TN/-45° TN reversely twisted periodical alignment, are fabricated. The polarizations of the beams diffracted from these two gratings are studied. A single model using the Jones matrix representation is formulated and used to analyze these two gratings. Experimental results are consistent with theoretical results and show that the gratings can be used as polarization beam splitters and are electrically switchable.

Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations

Various representations of polarization aberrations are described and compared for optical lithography. Polarization aberrations, which are potentially important with hyper-numerical-aperture tools, are a complicated phenomena that refer to induced polarization-dependent wavefront distortions as light propagates through an imaging system. Pupil representations based on the following concepts are discussed: the physical polarization properties, the Mueller matrix, the Jones matrix, and the Jones matrix decomposed into a Pauli spin matrix basis. Although each has its own advantages and disadvantages, it is concluded that the Jones matrix representation decomposed into a Pauli spin matrix basis offers the most useful format for the lithographer due to its compact notation, physically intuitive interpretation, ability to be implemented into standard imaging equations, and its usefulness as an input into a lithographic simulator. Depending on the assumptions that can be made, the pupil specification consists of three to eight independent functions, where a normalization constant is calculated to ensure a physically realizable pupil. An example is shown to illustrate the usefulness of this strategy. Additionally, a simple metric for lens polarization quality based on this representation is proposed.

Polarization elements: a group-theoretical study

The classification of polarization elements, the polarization affecting optical devices that have a Jones-matrix representation according to the type of eigenvectors they possess, is given a new visit through the group-theoretical connection of polarization elements. The diattenuators and retarders are recognized as the elements corresponding to boosts and rotations, respectively. The structure of homogeneous elements other than diattenuators and retarders are identified by giving the quaternion corresponding to these elements. The set of degenerate polarization elements is identified with the so-called null elements of the Lorentz group. Singular polarization elements are examined in their more illustrative Mueller-matrix representation, and, finally the eigenstructure of a special class of singular Mueller matrices is studied.

Measurements of Cell Parameters in Reflective Liquid Crystal Cells by using a Stokes Parameter Method

We propose an application of Stokes Parameter Method (SPM) for determining cell parameters of reflective twisted nematic (TN) liquid crystal (LC) cells by measuring Stokes parameters of the LC cells. The relationship between the Stokes parameters of the reflection light of the reflective TN LC cells and cell properties such as the thickness and twist angle are given on Jones matrix representation. The cell properties of the reflective LC cell are discussed and compared with those of the transmissive LC cell. The cell thickness of the reflective TN LC cell can be measured, but the twist angle cannot be determined by this method.

Permanent polarization gratings in photosensitive Langmuir–Blodgett films

An investigation was carried out on thin permanent phase polarization gratings recorded in Langmuir–Blodgett films using two orthogonal circularly polarized Ar-ion laser beams. The films are composed of amphiphilic azo-dye molecules and manifest an extremely large value of photoinduced optical anisotropy, Δn≈0.36. The experimental results are in excellent accord with the theoretical model based on the Jones matrix representation of the polarization pattern. The gratings are stable at least, for half a year.

Polarization properties of inversely twisted nematic liquid-crystal gratings

Based on the Jones matrix representation of twisted nematic liquid crystals (LC's), we have carried out a theoretical analysis of the polarization properties of inversely twisted nematic (ITN) LC gratings. Some interesting polarization behaviors are expected in the ITN LC grating. When a linearly polarized light parallel or perpendicular to the grating direction is incident on the ITN LC grating, the diffracted light in the 0th order is linearly polarized with the same polarization direction of incident light, while the diffracted light in high orders is linearly polarized perpendicular to that of incident light. Using a multirubbing alignment technique, we have practically prepared an ITN LC grating with ?45 degrees inversely twisted structures. The experimental investigations of the optical characteristics of the ITN LC grating demonstrate agreement with theoretical expectations.

A Novel Method for Determining the Cell Thickness and Twist Angle of a Twisted Nematic Cell by Stokes Parameter Measurement

A novel method of determining the cell thickness and the twist angle of twisted nematic liquid crystal (TNLC) cells by measurement of the Stokes parameters of light transmitted through the cell is presented. The relationships of the Stokes parameters of transmission light to the cell thickness and the twist angle are reduced by use of Jones matrix representation. The cell thicknesses and twist angles of some TNLC cells are determined practically by this simple method. The experimental results indicate that this method is valid. Furthermore, some properties of this method are discussed and an accuracy analysis by theoretical calculation is undertaken.

A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays

A detailed derivation of the extended Jones matrix representation for twisted nematic liquid crystal displays at oblique incidence (which was previously published by the author) is given. It is shown that this representation reduces to the well-known ordinary Jones matrix representation at normal incidence.

Systematic method for the analysis of optical fibre circuits

The authors have developed a systematic and simple method of analysis for deriving steady-state transfer characteristics between input and output optical wave vectors, or powers, of linear optical fibre circuits formed from a variety of linear optical components. The analysis method is based on the Jones matrix representation and a functional block diagram description of fibre circuits. Using this method, the analysis of the optical fibre circuits becomes a series of well defined systematic procedures. This method provides a convenient route to determining the transfer function of relatively complex fibre circuits and can be viewed as a further development of the well-known Jones calculus. It has been applied to analyse a number of optical fibre circuit structures, such as Sagnac fibre optic interferometers, fibre Fabry-Perot resonators, fibre optic ring resonators and a novel enhanced sensitivity optical fibre gyroscope.

Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence

A simple and accurate extended Jones matrix representation for the twisted nematic liquid-crystal display at the oblique incidence was obtained for the first time. The results obtained by this extended Jones matrix representation are quite close to those obtained by the faster 4×4 matrix method with spectrum averaging to account for the nonzero bandwidth of the incident light. However, the computation time for the extended Jones matrix method is less than half that of the faster 4×4 matrix method without spectrum averaging. Furthermore, at normal incidence, this extended Jones matrix representation reduces to the ordinary Jones matrix representation.

The general and simplified Jones matrix representations for the high pretilt twisted nematic cell

A general Jones matrix representation for an arbitrary pretilt twisted nematic (TN) cell at any given applied voltage is obtained. A simplified Jones matrix representation for the high pretilt TN cell at the field-off state is derived from this general Jones matrix representation. The validity of this simplified representation is examined by comparing the optical transmission of a high pretilt angle TN cell, at the field-off state, as a function of the cell gap thickness obtained from this simplified representation with that obtained by the general representation. The result shows that the simplified Jones matrix representation for a TN cell at the field-off state works very well even for the pretilt angle as high as 30°. In addition, a property of the average tilt angle of a TN cell is reported.

Optimization of the off-states for single-layer and double-layer general twisted nematic liquid-crystal displays

The Jones matrix representation is used to obtain an analytic closed-form expression for the optical transmission of a general double-layer twisted nematic (TN) liquid-crystal display with arbitrary twist angles and uniform pretilt angles. Based on this result, the optimum off-state design criteria for both single-layer and double-layer TN displays are formulated. >

Effect of axial misalignment and multiple reflection on jones matrix of a four‐crystal light modulator

AbstractThe latest off‐the‐shelf 45 X‐cut (ADP or KDP) four‐crystal light modulators with low driving voltage consist of four crystal units to accomplish temperature compensation and to make possible a low driving voltage. Therefore, axial misalignment is not uncommon. Also, because there are many interfaces between the crystals and the matching dielectric fluid, multiple reflection may cause problems. the effects of these phenomena on the Jones matrix describing the fundamental characteristics of optical phase modulation are examined. First, the dielectric tensor of the crystals with axial misalignment and the characteristic plarizations in the crystal are derived. Then, using Berreman's 4 × 4 matrix formulation, the Jones matrix representation of a four‐crystal light modulator with axial misalignment is derived. It is pointed out that the off‐diagonal terms arise from axial misalignment, which is one cause of temperature variation of the light modulator characteristics. A numerical estimate is made of the effect of multiple reflection. It is pointed out that the effect of multiple reflection on the off‐diagonal elements of the Jones matrix is negligible while the effect of the diagonal elements is substantial. an experimental example with an actual modulator is given to determine the location of the axial misalignment.