Craig D. Poole

Statistical theory of polarization dispersion in single mode fibers

An analytical characterization of polarization dispersion measurements is presented. The authors report the solution of Pooles stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. The authors extend this to a more complete description by considering small, second-order dispersion effects through the frequency derivative of the dispersion vector. The complete analytical solution is seen to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivatives. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, and the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector. >

Polarization-mode dispersion measurements based on transmission spectra through a polarizer

Routine characterization of polarization-mode dispersion (PMD) in single-mode fiber, both at the manufacturing stage and in installed systems, requires an easy-to-implement measurement technique. One method that is particularly simple to implement involves counting the number of extrema (i.e., maxima and minima) per unit wavelength interval in the transmission spectrum measured through a polarizer (analyzer) placed at the output of a test fiber. In this paper, we establish accurate equations relating both the extrema density and mean-level crossing densities in such spectra to the expected value of PMD. These equations are used to measure several fiber samples, and are compared to measured values obtained with a commercially available test set. It is shown that measuring both mean-level crossings and extrema densities provides a simple means for establishing whether a fiber is scaling as /spl radic/L (long-length regime) or L (short-length regime). Using Monte Carlo simulations, the accuracy of the fixed-analyzer measurements is examined as a function of the width of the wavelength interval over which measurements are made. In addition, the simulations indicate that fixed-analyzer measurements are quite robust with respect to the presence of polarization-dependent loss (PDL) in the span, an important consideration for measurements in amplified systems. >

Optical fiber-based dispersion compensation using higher order modes near cutoff

Higher order spatial modes in optical fibers exhibit large, negative chromatic dispersion when operated near their cutoff wavelength. By using a spatial mode-converter to selectively excite a higher order mode in specially designed multimode fiber, this dispersion can be used to compensate the positive dispersion in conventional single-mode fiber spans. In this paper, issues related to compensating fiber and mode-converter design are explored. Experimental measurements in specially designed two-mode fibers operated in LP/sub 11/ mode show negative dispersion as large as -70 ps/nm/spl middot/km at 1555 nm. Pulse propagation and system experiments employing spatial mode-converters to excite LP/sub 11/ mode in a two-mode fiber demonstrate the feasibility of this technique for dispersion compensation in lightwave systems. >

Polarization dispersion and principal states in a 147-km undersea lightwave cable

The authors describe measurements of polarization dispersion in a 147-km undersea lightwave cable at 1.56 mu m. The wavelength dependence of the transmitted state of polarization was measured and interpreted in terms of the principal states description of polarization dispersion to determine the difference in the propagation delay time between the two principal states of polarization. Measured differential propagation delay times ranged between 2.5 and 10 ps among the four fibers tested. Significant wavelength dependence in both the principal states and the propagation delay times was observed over a 12-AA interval. >

Broadband dispersion compensation by using the higher-order spatial mode in a two-mode fiber

A fiber-optic technique for compensating both first- and second-order group-velocity dispersion in single-mode fiber spans is demonstrated by using the large waveguide dispersion that occurs for the higher-order (LP11) spatial mode in a two-mode fiber near cutoff. Complete restoration of 7-ps pulses that had been dispersed by a factor of 10 in 5 km of single-mode fiber is demonstrated over a 20-nm-wavelength window. First-order dispersion as large as −228 ps/(nm km) is observed for the LP11 mode at 1560 nm in the two-mode fiber.

Helical-grating two-mode fiber spatial-mode coupler

The authors investigate a helical-grating geometry for coupling the spatial modes in a two-mode fiber. The feasibility of making fiber grating filters based on this geometry is investigated. By adding mode strippers at the input and output of a helical-grating spatial-mode coupler, an optical notch filter is demonstrated with 0.3-dB waveguide loss, 24-dB extinction, and 24-nm spectral width. The effect of small ellipticity in the fiber core is also investigated, and it is shown that polarization-insensitive coupling can be achieved in a fiber with a sufficiently circular core. >

Elliptical-core dual-mode fiber dispersion compensator

Chromatic dispersion compensation is demonstrated in a 2.5-Gb/s system experiment using an elliptical-core dual-mode fiber operated in the LP/sub 11/ mode near cutoff. With a measured dispersion of -548 ps/nm-km for the LP/sub 11/ mode and a novel double-pass configuration, complete compensation of the dispersion in 50 km of conventional single-mode fiber at 1530 nm is achieved with 0.72 km of dual-mode fiber. System degradation due to remnant LP/sub 01/ mode power in the dual-mode fiber is investigated and found to be small for relative LP/sub 01/ power levels less than -20 dB.<<ETX>>

Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers

We have used multilongitudinal mode lasers to investigate the polarization properties of long lengths of single-mode fiber cable. We find that the individual longitudinal modes are >99-percent polarized after propagation through 54.6 km of cabled fiber; however, the different longitudinal modes have different states of polarization at the output. This difference is caused by polarization dispersion, and we estimate a propagation delay difference for the two principal states of polarization to be 0.42 ps in the 54.6 km of cabled fiber.

Distortion related to polarization-mode dispersion in analog lightwave systems

Analog transmission in single-mode fiber using chirped sources gives rise to nonlinear distortion when polarization-mode dispersion (PMD) is present. We investigate experimentally and theoretically two mechanisms for this distortion: for chirped sources, PMD in the presence of polarization-mode coupling results in second-order distortion that is proportional to the square of the modulation frequency; when polarization-dependent loss is present, an additional second-order distortion term occurs that is independent of modulation frequency. Both mechanisms give rise to distortion that is time varying due to the sensitivity of PMD to ambient temperature changes. Numerical examples indicate that these effects can limit the capacity of analog systems that use directly modulated semiconductor lasers. >

Bend-induced loss for the higher-order spatial mode in a dual-mode fiber

Measured loss for the LP(11) mode in a dual-mode fiber subjected to a uniform bend shows a strong dependence on the orientation of the mode-field pattern relative to the plane of the fiber bend. Wavelength and bend-radius dependence of the loss indicates that operation within ~40 nm of cutoff is feasible in dispersion compensators based on dual-mode fibers operated in the LP(11) spatial mode near cutoff.