Random Birefringence Research Articles

Influences of polarization-mode dispersion on soliton transmission systems

In soliton transmission systems with polarization-mode dispersion (PMD), random birefringence causes solitons to generate dispersive waves, which degrade soliton transmission systems in two aspects. First, the dispersive waves cause solitons to continuously lose energy, thus induce pulse broadening. Second, the dispersive waves interact with other soliton pulses and cause distortion of a sequence of soliton pulses. Both of these effects induce performance degradation of soliton transmission systems. We study these effects of PMD on both conventional and dispersion-managed (DM) soliton transmission systems. We show that, for conventional soliton systems, although single pulse has robustness to PMD, the interplay between the dispersive waves and solitons would seriously distort a sequence of pulses and make soliton systems worse than linear systems if all other transmission impairments are neglected. We also show that DM solitons are more robust to PMD than both conventional solitons and linear systems due to the enhanced nonlinearity and less sensitivity of DM solitons to perturbations. We further point out that soliton collision-induced polarization scattering causes additional timing jitter and system performance penalty in WDM soliton systems.

Determination of molecular weight and its distribution of flexible chain polymer by phase-modulated flow birefringence technique

The objective of this study is to develop a systematic method to determine molecular weight and its distribution of flexible chain polymer by birefringence experiments. Using the random walk model, birefringence δn and orientation angle ξ have been optically obtained as functions of molecular weights. To confirm the theory, polystyrene solutions with different molecular weights dissolved in polychlorinated biphenyl were experimented by the phase-modulated flow birefringence (PMFB) method. Birefringence of polystyrene solutions is proportional to (Σc i M i 1.6 )γ2, and cot(2χ) to (Σc i M i 1.6 /B1Σc i M i −0.2 )γ. The experimental results agreed well with the theoretical predictions proposed in this study.

Influence of the symmetry rules for Raman susceptibility on the accuracy of nonlinear index measurements in optical fibers

A general expression for a nonlinear polarization in fibers, in which the different symmetry rules for the electronic and Raman contributions to the susceptibility are taken into account, is derived. The contribution of the Raman effect to the total nonlinearity is calculated for different polarizations of a pump and the Stokes wave in polarization-maintaining fibers as well as in fibers with randomly varying birefringence. The error in the measurements of the n2 coefficient caused by the different symmetry rules for the Raman and electronic contributions is shown to depend on germanium concentration and a frequency shift varying from 3.3% in polarization-maintaining fibers to 10% in fibers with random birefringence. The ratio between cross-phase modulation and self-modulation strengths strongly depends on a frequency shift and the polarization state of the interacting waves and varies from 1.2 to 2 in fibers with germanium concentration from 0 to 18 mol.%.

Statistical characterization of fiber random birefringence

The statistical properties of the random birefringence that affects long single-mode fibers are experimentally evaluated by means of a polarization-sensitive optical time-domain reflectometry. The measurements are in good agreement with theoretical predictions and show, for what we believe is the first time, that the components of the local birefringence vector are Gaussian random variables.

Dispersion-managed solitons in a periodically and randomly inhomogeneous birefringent optical fiber

The propagation of dispersion-managed vector solitons in optical fibers with periodic and random birefringence is studied. With the help of a variational approach, the equations that describe the evolution of pulse parameters are derived. Numerical modeling is performed for variational equations and for fully coupled periodic and stochastic nonlinear Schrodinger equations. It is shown that variational equations can be effectively used to describe the averaged dynamics of dispersion-managed vector solitons with stochastic perturbations. It is shown, analytically and numerically, that dispersion-managed (DM) solitons have the same resistance to random birefringence as do ordinary solitons. The dependence of the mean decay length of a DM vector soliton on the strength of random birefringence and on the energy of the initial pulse is found.

Measurements of beat length and perturbation length in long single-mode fibers

Experimental results of measurement of the beat length and the differential group delay of several types of long single-mode fiber are presented. The proposed measurement technique is based on a polarization-sensitive analysis of the backscattered signal and allows one to calculate the correlation length of the random birefringence affecting the fiber.

A phenomenological model of random birefringence in single-mode optical fibers

A phenomenological model of random birefringence in single-mode optical fibers

Nonlinear-optical loop mirror demultiplexer using a random birefringence fiber: comparisons between simulations and experiments

A numerical simulation of the switching characteristics of a polarization multiplexed nonlinear-optical loop mirror demultiplexer is presented and compared with experiment. The model assumes that the optical fiber that composes the loop has a randomly varying birefringence, that the signal and the control pulses have the same frequency, and that these pulses are nearly solitons. Factors that affect the shape and the width of the switching window curve are discussed. A phase-dependent modulation of the switching window curve, which is due to incomplete averaging of the light polarization state, is observed both experimentally and numerically. Models in which the randomness is neglected are not able to describe this modulation adequately.

PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems

Effects of polarization mode dispersion (PMD) on 2.48 Gb/s IM-DD lightwave systems are experimentally observed by using PMD emulators made with segments of highly birefringent fiber with random-mode coupling splices. Random birefringence between mode couplings was also included in the emulator. The measurements indicate that the eye diagram is corrupted by PMD values above 10 ps.

Polarization dependent gain in erbium-doped fiber amplifiers: computer model and approximate formulas

A computer model for polarization dependent gain (PDG) in Er-doped fiber amplifiers (EDFA) is presented. The model assumes that each erbium ion possesses an ellipsoidal gain surface and that all ion orientations are equally likely. By dividing the ions into subsets based upon orientation and computing the inversion of each subset in the presence of polarized pump and signal waves, the model predicts the dependence of the PDG induced by this polarization hole-burning (PHB) on the design of the EDFA, the signal degree and state of polarization (SOP), and the pump SOP. For moderate gain amplifiers (made from the same fiber) with the same gain peak wavelength and the same compression level, the magnitude of the PDG is nearly independent of the EDFA gain. Internal and random fiber birefringence are included to model real fibers. In fibers which cause the signal SOP to walk rapidly around the Poincare sphere, the PDG is reduced by a factor of 2/3 when compared with a linear polarization-maintained signal. Scrambled signals and partially-polarized saturating tones are also considered. Simple rules are derived for predicting the PDG of a given EDFA.

Stochastic simulation of pulses in nonlinear-optical fibers with random birefringence

Numerical simulations of nonlinear pulse propagation in optical fibers with randomly varying birefringence are presented. For short-length-scale randomness the dominant effect is due to phase-velocity birefringence and produces a probabilistic uncertainty that increases with propagation distance for the expected value of the pulse’s polarization state. An approximate evolution equation for the probability distribution of the polarization state was derived previously [ Physica D55, 166 ( 1992)]. Comparisons between this distribution and Monte Carlo simulations are presented that demonstrate the validity of the analytical results. The simulations also show that the polarization state of a pulse is completely randomized on the longer soliton-period length scale. This provides justification for the assumption of a uniformly distributed polarization state used in previous analyses of this problem [ Opt. Lett.16, 1231 ( 1991); J. Lightwave Technol.10, 28 ( 1992)]. Furthermore, the higher-order effects of group birefringence are assessed. In particular, the polarization-state fluctuations induced by the randomness are shown to reduce significantly the effects of pulse splitting and dispersive radiation loss caused by group-velocity birefringence.

Dynamics of optical pulses in randomly birefringent fibers

A nonlinear optical fiber with random birefringence is modeled by a system of nonlinear Schrödinger (NLS) equations with stochastic coupling. An average variational principle is used to obtain the approximate evolution of the parameters describing pulses with NLS-soliton-like shapes. Then, in the diffusion limit, the stochastic problem is reduced to a partial differential equation of the Poincaré sphere. Solutions to this equation give probability densities for the polarization state of a propagating pulse.

Vector solitons in fiber waveguides with a random birefringence

A study is made of the propagation of soliton pulses in single-mode fiber waveguides with a birefringence that gives rise to a nonlinear interaction between the polarizations and to a difference between their group velocities. It is shown that a vector soliton decays if a parameter representing the birefringence intensity exceeds a certain critical value. The case when the birefringence can be described by a random function is of special interest. It is demonstrated that fluctuations of the birefringence then split the vector solitons into separate polarizations and the characteristic distance governing such splitting is calculated analytically.

Random coupling theory of single-mode optical fibers

A random coupling theory is developed for analyzing the propagation characteristics of the polarization state of light in single-mode optical fibers (including conventional and polarization maintaining fibers) under random disturbances. The basic idea is that the disturbances that a fiber suffers in practice continuously change with time and space, so time-varying coupling will occur along the fiber between two linearly polarized modes HE/sub 11/ that may propagate in the fiber. A coupled-mode equation of single-mode fibers under random disturbances is derived and solved rigorously with few assumptions. A random coupled-mode equation is derived considering time and space variation. Analytic solutions are obtained and used for analyzing the effect of random birefringence, polarization dispersion, polarization fluctuation, and evolution of the degree of polarization in single-mode fibers and for characterizing fiber properties. >

Growth of coprus chloride single crystals for optical modulators

Single crystals of CuCl have been grown by the vertical Bridgman technique in a flux solvent of KCl. The lower melting point of the CuCl/KCl mixture avoids the solid state wurtzite-zincblende phase transition at 408°C. Flux-grown Bridgman crystals show far less residual strain than crystals grown by other methods. The electro-optic properties of the flux-grown Bridgman crystals are equivalent to those of crystals grown of pure melts of coprous chloride, but have the advantage that they do not exhibit the random birefringence of crystals grown from pure melt.