Polarization Mode Dispersion In Single-mode Fibers Research Articles

Stokes Space Representation of Modal Dispersion

Polarization-mode dispersion in single-mode fibers can be viewed as a special case of modal dispersion in multimode and multicore optical fibers. Exploiting the similarity between these two transmission effects, modal dispersion can be modeled in a way analogous to that of polarization-mode dispersion by modifying the conventional Jones–Stokes formalism. In this paper, we review the geometrical representation of modal dispersion in the generalized Stokes space by means of the modal dispersion vector. We summarize and unify the fundamental equations that encapsulate the properties of the modal dispersion vector. We prove that the modal dispersion vector can be expressed as a linear superposition of the Stokes vectors representing the principal modes. The coefficients of this expansion are the corresponding differential mode group delays. This concise and elegant expression can be considered as a simplified definition of the modal dispersion vector and can be used to facilitate analytical calculations.

Orbital-Angular-Momentum Polarization Mode Dispersion in Optical Fibers

The orbital-angular-momentum (OAM) modes in optical fibers have polarization mode dispersion (PMD) properties similar to those of single-mode fibers (SMFs). The + l and − l order OAM modes supported by the same fiber vector modes undergo random cross coupling and exhibit a frequency-dependent time delay. We name this effect “OAM-PMD” and extend the formalism developed for PMD in SMFs to describe OAM-PMD. The characteristics of the modal beat lengths, birefringence correlation lengths, and the mean value of OAM-PMD are investigated. A fixed-analyzer technique is proposed and demonstrated to characterize this phenomenon in OAM fibers. Two different types of OAM fiber are examined. The measured results are compared with the theoretical calculations.

Principal Modes in Graded-Index Multimode Fiber in Presence of Spatial- and Polarization-Mode Coupling

Power-coupling models are inherently unable to describe certain mode coupling effects in multimode fiber (MMF) when using coherent sources at high bit rates, such as polarization dependence of the impulse response. We develop a field-coupling model for propagation in graded-index MMF, analogous to the principal-states model for polarization-mode dispersion in single-mode fiber. Our model allows computation of the fiber impulse response, given a launched electric-field profile and polarization. In order to model both spatial- and polarization-mode coupling, we divide a MMF into numerous short sections, each having random curvature and random angular orientation. The model can be described using only a few parameters, including fiber length, number of sections, and curvature variance. For each random realization of a MMF, we compute a propagation matrix, the principal modes (PMs), and corresponding group delays (GDs). When the curvature variance and fiber length are small (low-coupling regime), the GDs are close to their uncoupled values, and scale linearly with fiber length, while the PMs remain highly polarized. In this regime, our model reproduces the polarization dependence of the impulse response that is observed in silica MMF. When the curvature variance and fiber length are sufficiently large (high-coupling regime), the GD spread is reduced, and the GDs scale with the square root of the fiber length, while the PMs become depolarized. In this regime, our model is consistent with the reduced GD spread observed in plastic MMF.

Statistical distribution of polarization-dependent loss in the presence of polarization-mode dispersion in single-mode fibers

The statistical distribution of polarization-dependent loss in single-mode fibers is studied via Monte-Carlo simulations. In the presence of polarization-mode dispersion, it is found that the probability density function of polarization-dependent loss is a combination of Rayleigh and Maxwell distributions.

Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers

The random coupling-length basis was used in the numerical simulation of single-mode fibers (SMF's) with the coarse step method. We show that a single set of coupling lengths, angles and phases accounts for both, the Maxwellian statistics and the nonperiodical differential group delay spectral dependence in agreement with experimental observations. An SMF and a polarization mode dispersion (PR ID) emulator were both measured and simulated. The comparison between the experimental results and numerical simulations shows that the random coupling-lengths mathematical model and the emulator device provide good descriptions either for the first-order PMD statistics or second-order PMD, being powerful tools for the simulation of signal distortion.

Analytical treatment of polarization-mode dispersion in single-mode fibers by means of the backscattered signal

We present analytical results on the polarization-mode dispersion characteristics of single-mode birefringent fibers based on statistical properties of the backscattered signal. In particular, we calculate exactly the relationship between polarization-mode dispersion characteristics in forward propagation with respect to round-trip propagation in terms of dynamical equations, differential group delays, correlation lengths, and second-order effects. The theory applies to fibers affected by superposition of linear and circular birefringence in both the short-length and the long-length regimes.

Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling: errata

A simple frequency-domain technique for measuring polarization-mode dispersion in single-mode fibers with random mode coupling is used to give what is to my knowledge the first direct experimental demonstration of the transition of the dispersion from a linear length dependence to a square-root-of-length dependence. Sensitivity to external perturbations is demonstrated by an order-of-magnitude increase in dispersion when the fiber is removed from a conventional spool and placed on a large-diameter drum. An expression for the length-dependent probability density function that describes the dispersion for highly coherent sources is also presented and confirmed experimentally.

Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling

A simple frequency-domain technique for measuring polarization-mode dispersion in single-mode fibers with random mode coupling is used to give what is to my knowledge the first direct experimental demonstration of the transition of the dispersion from a linear length dependence to a square-root-of-length dependence. Sensitivity to external perturbations is demonstrated by an order-of-magnitude increase in dispersion when the fiber is removed from a conventional spool and placed on a large-diameter drum. An expression for the length-dependent probability density function that describes the dispersion for highly coherent sources is also presented and confirmed experimentally.