Birefringence Vector Research Articles

Vector distribution measurement of PMD in optical fiber links employing a wavelength-tunable SOP-OTDR.

A measurement of polarization mode dispersion (PMD) vector distribution is implemented with a wavelength-tunable state-of-polarization-detection-based optical time domain reflectometry (SOP-OTDR). Derived from the dynamic equation between the PMD vector and the birefringence vector with a piecewise approximation method, we present an equation for piecewise expression of the relation between the two vectors based on the approximation that the second-order partial derivative of the PMD vector with respect to the length is negligible in each short-enough segment of optical fiber. Utilizing the birefringence vector distributions at three adjacent wavelengths, both the magnitude and the direction distributions of the PMD vector have been calculated through the numerical solution algorithm. The calculation results indicate that the measured magnitudes of PMD vectors are consistent with the statistical experience, which is the Maxwell probability distribution, and the second-order partial derivative magnitudes of the PMD vectors conform to the lognormal distribution. This method could provide a distributed approach for optical performance monitoring by PMD-related characteristics in optical fiber links.

Coupling effects between dichroism and birefringence of anisotropic media

The basic polarization properties of media are their dichroism and birefringence. In this work we report the possible consequences of the coupling effects between dichroism and birefringence of anisotropic media. Our analysis is based on a solution of the differential equation of the Stokes four-dimensional vector. It is shown that there exist three types of coupling effects between the components of the dichroism vector and birefringence vector of the medium. The conditions under which the polarization properties of a continuous medium can be calculated are identified. These results are helpful for any study involved an interpretation of the measured Mueller matrix of continuous anisotropic medium.

Analysis of the Transmission Characteristic and Stress-Induced Birefringence of Hollow-Core Circular Photonic Crystal Fiber

Orbital angular momentum modes in optical fibers have polarization mode dispersion. The relationship between polarization mode dispersion and the birefringence vector can be deduced using an optical fiber dynamic equation. First, a mathematical model was established to formulate mode dispersion caused by stress-induced birefringence. Second, in the stress-induced birefringence simulation model, the finite element method was used to analyze the transmission characteristics of the hollow-core circular photonic crystal fiber. Finally, mode dispersion caused by stress-induced birefringence was obtained using theoretical derivation and simulation analyses. The results showed that the new fiber type has good transmission characteristics and strong stress sensitivity, which provide key theoretical support for optimizing the structural parameters of optical fiber and designing stress sensors.

An optical channel modeling of a single mode fiber

The evaluation of the optical channel model that accurately describes the single mode fibre as a coherent transmission medium is reviewed through analytical, numerical and experimental analysis. We used the numerical modelling of the optical transmission medium and experimental measurements to determine the polarization drift as a function of time for a fixed length of fibre. The probability distribution of the birefringence vector was derived, which is associated to the ‘Poole’ equation. The theory and experimental evidence that has been disclosed in the literature in the context of polarization mode dispersion – Stokes & Jones formulations and solutions for key statistics by integration of stochastic differential equations has been investigated. Besides in-depth definition of the single-mode fibre-optic channel, the modelling which concerns an ensemble of fibres each with a different instance of environmental perturbation has been analysed.

Polarization averaged short-time Fourier transform technique for distributed fiber birefringence characterization using Brillouin gain

A polarization averaged short-time Fourier transform (PASTFT) technique is developed for distributed fiber birefringence characterization based on counterpropagating stimulated Brillouin scattering (SBS) gain signal. This technique can be used for the birefringence characterization of the general elliptical birefringent fiber. A theoretical model on polarization matching of counterpropagating SBS process is established. The performance of the short-time Fourier transform (STFT) method and the PASTFT technique is analyzed by using the simulation of the theoretical model. Simulation results show that the process of polarization average could effectively reduce the birefringence characterization error caused by the polarization dependence of the local period of SBS gain. A less than 8% normalized root mean square error is achieved for the characterization of the length of the birefringence vector on elliptical birefringent fibers. The PASTFT technique is experimentally verified by the distributed measurement of beat length and differential group delay of a standard single-mode fiber via the Brillouin optical time domain analysis system.

Method to measure the second-order birefringence vector distribution along optical fibers based on high-speed polarization optical time domain reflectometry

Based on a high-speed polarization optical domain reflectometry, an innovative method to measure the second-order birefringence vector distribution along optical fibers was proposed and implemented in this paper. Some interesting data were obtained along a 1 km long single mode fiber by only one detection. The second-order birefringence magnitude distribution curve can reflect both magnitude and direction change information of the first-order birefringence, and it was more stable (except the catastrophe points) than that of the first-order. The larger variable range of the second-order birefringence magnitude may provide a higher sensitivity than the first-order for birefringence-based distributed sensors.

A New Distributed Measurement of Birefringence Vectors by P-OTDR Assisted by a High Speed Polarization Analyzer

A new polarimetric optical time domain reflectometry (P-OTDR) measurement device assisted by a high speed polarization analyzer is designed and a new algorithm, which can be used to accurately measure the birefringence vector, is proposed. In this method, only one measurement is required and the result is insensitive to the input state of polarization. An 1-km single mode fiber (SMF) is measured and the distribution of the local birefringence vector along the SMF is obtained with a resolution of 2 cm.

Propagation of light polarization in a birefringent medium: Exact analytic models

Driving the analogy between the coherent excitation of a two-state quantum system and the torque equation of motion, we present exact analytic solutions to different models for manipulation of polarization in birefringent medium. These models include the one-dimensional model, the Landau–Zener model, and the Demkov–Kunike model. We also give an example for robust, broadband manipulation of polarization by suitably tailoring the birefringence vector.

Mueller-Matrix-Based Differential Rotation Method for Precise Measurement of Fiber Birefringence Vector

The method of complete polar decomposition for arbitrary Mueller matrixes is introduced to analyze the birefringence vector induced in a fiber, and then based on the Mueller matrix (MM) method, three kinds of computation methods including the absolute, the relative, and the differential rotation methods are proposed and investigated in detail. A computer-controlled measure system is employed to measure the Mueller matrix and birefringence vector for a 2.5-km fiber system with length 5 mm under lateral press in complicated environment with much perturbation. Experimental results show that the differential rotation (DR) method is the optimal approach to achieve fiber birefringence vectors in a large dynamic range of lateral press on fibers in perturbed situations, which reaches the highest linearity of 0.9998 and average deviation below 2.5%. Further analyses demonstrate that the DR method is also available for accurate orientation of lateral press direction and the average deviation is about 1.1°.

Analysis of the Polarization-Mode-Dispersion Vector Distribution for the Foschini and Poole's Birefringence Vector Model

This paper analyzes transient behaviors of the polariza-tion-mode-dispersion (PMD) vector for the Foschini and Poole's birefringence vector model. We find an asymptotic solution of the corresponding Fokker-Planck equation representing the solution as a superposition of angular components characterized by the Legendre polynomials. The distribution tail for the PMD vector magnitude evolves slowly to the Maxwellian owing to the residual couplings between adjacent angular components. Of particular interest, the distribution tail for the PMD vector magnitude lies well below the Maxwellian fit during the transient.

Reflectometric measurement of birefringence rotation in single-mode optical fibers

We present a novel reflectometric technique for the measurement of orientation and modulus of the linear birefringence vector in single-mode optical fibers. The technique provides information also on circular birefringence, although this component, if present, appears as a rotation of the linear birefringence. A detailed theoretical analysis is reported and validated by experimental results.

Stress distribution and induced birefringence analysis for pressure vector sensing based on single mode fibers

We propose a theoretical approach to analyze the pressure stress distribution in single mode fibers (SMFs) and achieve the analytical expression of stress function, from which we obtain the stress components with their patterns in the core and compute their induced birefringence. Then we perform a pressure vector sensing based on approximately 2 km SMF. Using Mueller matrix method we measure the birefringence vectors which are employed to compute the pressure magnitudes and their orientation. When rotating the pressure around the fiber, the corresponding birefringence vector rotates around a circle with double speed. Statistics show the average deviation of calculated pressure-magnitude to practical value is approximately 0.17 N and it is approximately 0.85 degrees for orientation.

Analysis of the Polarization-Mode-Dispersion Vector Distribution for Linearly Birefringent Optical Fibers

We analyze the polarization-mode-dispersion (PMD) vector distribution for linearly birefringent optical fibers. We assume the linear birefringence vector components as white Gaussian processes. From the corresponding Fokker-Planck equation, we find an asymptotic solution for the probability density function of the PMD vector. Our analysis shows that the PMD vector distribution is dependent on the polar angle during its transient and the distribution tail for the magnitude of the PMD vector is higher than the Maxwellian.

Spectral density matrix description of polarization mode dispersion

We introduce a power spectral density matrix formalism that incorporates both the pulse shape and the field polarization and can therefore easily describe averages over random fluctuations of the local birefringence vector. We demonstrate that quantities such as the differential time delay, power diffusion, and decoherence effects can be obtained directly from the equations of motion for the power density matrix. This approach can be applied to pulses with arbitrary frequency-dependent polarization and intensity distributions and in particular makes possible the minimization of the eye-opening penalty through the proper choice of the initial pulse profile.

Two-Dimensional Linear Birefringence Vector Measurement by Polarization-Stepping Interferometer

A simple polarization-stepping technique in combination with a common-path homodyne interferometer is proposed in order to measure the phase retardation and the fast-axis angle, which are defined as the linear birefringence vector (LBV), of a wave plate (WP). At three different orientation angles of the linear polarization of incident laser beam, two-dimensional (2-D) interference patterns with respect to different orientation angle are recorded by using a CCD camera. Thus, 2-D phase retardation and fast-axis angle distributions of WP are determined simultaneously. In addition, the elliptical polarization and misalignment of the orientation angle of the incident laser beam induced errors on LBV measurement are discussed.

Polarization-shifting interferometry on two-dimensional linear birefringent parameters measurement

A novel polarization-shifting interferometer in conjunction with a differential phase to amplitude conversion technique is proposed. It is able to determine the linear birefringence vector (LBV) of a quarter wave plate in two-dimension. The LBV consists of the phase retardation and the azimuth angle of fast axis of quarter wave plate. This vector is calculated by the ratio of the amplitudes of the heterodyne signals at different steps of linear polarization shifting. The effect which is due to the error of the polarization-shifting angle on LBV determination is discussed.

Two-dimensional optical measurement techniques based on optical birefringence effects

Some dielectric materials become birefringent when subjected to an external force, such as an electric field or a mechanical force. For more than a decade, our research group has been engaged in developing two-dimensionaloptical measurement techniques for the dynamic measurement of charge distributions on a dielectric surface using the electro-optic Pockels effect, the dynamic measurement of electrical field distributions in a liquid using the electro-optic Kerr effect, and the measurement of birefringence vector distributions in plastic plates using the photoelastic effect. The system nonuniformity and the system reliability are the inevitable problems in two-dimensional measurement systems, and make two-dimensional measurements quite different from point measurements. The common image-processing techniques that have been specially developed to overcome these problems are analyzed and summarized; detailed mathematical analysis is avoided.

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.

Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking

We demonstrate a new method to measure weak birefringence of dielectric mirrors with excellent spatial resolution and sensitivity (<10-7 radians). We exploit a well-known optical feedback scheme for line-width narrowing and frequency locking of a diode laser to a high-finesse cavity. Feedback comes from the intracavity field which builds up at resonance, selected by its change in polarization with respect to the incident field. This change, due to the residual birefringence of the cavity mirror coatings, was already exploited for birefringence measurements using an active laser-locking scheme. Here we measure the optical feedback rate as a function of rotation angle of one of the cavity mirrors (around the cavity axis). A stable feedback signal is obtained since the laser, as soon as it locks to a cavity resonance, effectively behaves as a monochromatic source. By fitting the data with a theoretical expression, we determine quantitatively the local birefringence vectors of both mirrors, which are around 10-6 radians. Our scheme is simple, works with cavities of very high finesse (F∼105), and is promising for measuring birefringence in gases induced by external fields.

Polarization mode dispersion probability distribution for arbitrary distances

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on 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.