Polarization Mode Dispersion Emulator Research Articles

Frequency-Correlation Analysis of PMD Emulators With Symmetric Polarization Scrambling

The authors investigate the artificial frequency correlation induced by polarization scrambled statistical polarization-mode-dispersion emulators. A simple model is derived that accurately predicts the average frequency correlation when the scrambling is symmetric. It is shown that the nature of the symmetry affects the emulator performance, and that increasingly, isotropic scrambling gives lower correlation. The derived model shows a good agreement with Monte Carlo simulation and experiment

Autocorrelation function of the single PC polarization-mode dispersion emulator

The discrete structure of multisection polarization-mode dispersion (PMD) emulators is known to artificially correlate the PMD affecting different channels in a wavelength-division multiplexing system, thus limiting their usefulness in accurately emulating broad-band PMD. We report on the correlation properties of a novel single polarization controller (PC) PMD emulator, which offers scalability with the number of emulator sections through component reuse. We report a background level of the PMD frequency autocorrelation function of 0.66%, for a 50-section emulator, the lowest experimentally demonstrated for a PMD emulator, which makes the single PC PMD emulator an instrument of choice for research and development of broad-band PMD mitigation strategies.

Geometrical interpretation of second-order PMD

A geometrical interpretation of second-order polarization mode dispersion (SOPMD) as the curved three-dimensional (3-D) area swept by the PMD vector as it increases with propagation in a birefringent system is introduced. The depolarization and polarization-dependent chromatic dispersion parts of the SOPMD can be viewed as projections of this area in orthogonal directions. This interpretation enables us to translate the problem of maximizing the SOPMD in, e.g., PMD emulators and programmable PMD sources to an isoperimetric problem, i.e., a problem of maximizing the area enclosed by a given perimeter, which has well-known solutions. Both the discrete problems corresponding to a set of birefringent wave plates are discussed, and the continuous problem in which an arbitrary birefringent medium is considered. Analytic formulas are derived for the first time for the maximum SOPMD, depolarization, and polarization-dependent chromatic dispersion that can be realized in PMD emulators.

Scalable polarization-mode dispersion emulator with proper first- and second-order statistics

We present a novel polarization-mode dispersion emulator design that overcomes the scalability issue limiting conventional concatenated-section emulators by replacing the multiple mode coupling stages with a single modified Lefe/spl grave/vre polarization controller (PC). We demonstrate that undesirable correlation in the sections PC transfer functions can be mitigated through proper optimization of the free design parameters. Monte Carlo simulations and experimental results confirm that first- and second-order statistics for rare events are accurately emulated in a compact low-cost device.

Efficient DOP monitoring of WDM channels for simultaneous PMD compensation

We demonstrate averaged-DOP monitoring of WDM channels for simultaneous PMD compensation. Using a single PMD compensator for four 10Gbit/s WDM channels, we achieve a significant power penalty reduction of more than 10 and 3dB for NRZ and RZ, respectively, in the worst-case of first-order PMD emulation. The 2% worst-case performance of the averaged-BER is improved by two orders of magnitude and averaged-DOP is enhanced by 20%.

Broad-band concatenated-section PMD emulator design for low interchannel correlation

The coarsely discrete structure of polarization-mode dispersion (PMD) emulators can artificially correlate the PMD affecting different wavelength-division-multiplexed channels. We present a model that predicts the background autocorrelation of concatenated-section emulators with independently rotatable elements, and show how emulators with low interchannel correlation can be designed.

Independently tunable first- and second-order polarization-mode dispersion emulator

By solving the equation set for the first- and second-order polarization-mode dispersion (PMD) in retro-verse manner, we show that the independent control of first- and second-order PMD is possible, with only two control parameters. The analysis on the emulation algorithm as well as the operation range/resolution shows excellent agreement with the experimental demonstration operated with a sample emulator constructed of a fixed differential group delay (DGD), a polarization rotator, and a variable-DGD element.

Combinatorial polarization scramblers for many-segment PMD emulator

In this letter, we present a combinatorial approach to build polarization scramblers in a many-segment polarization-mode dispersion (PMD) emulator. This approach significantly reduces the required number of phase plates and their corresponding controls. It exploits the fact that rotation matrices are noncommutative which gives many different ways of building polarization scramblers out of just a few phase plates. Although these polarization scramblers are correlated, we show, numerically and experimentally, that there is sufficient polarization scrambling between segments to achieve the important key properties of a PMD emulator.

Theoretical study of polarization mode dispersion emulators

The performances of the three polarization mode dispersion (PMD) emulators commonly used today are analyzed and compared among them through numerical simulation of their differential group delay (DGD) statistical characteristics and PMD vector autocorrelation function. The results demonstrate that to produce DGD that can match theoretical distribution, one DGD generator is adequate, while at least 15 sections are necessary in the emulator built by polarization maintaining fibers and rotatable connectors. And the autocorrelation function of the emulator based on polarization maintaining fibers depends on DGD of every section, while that of the emulator based on DGD generators is smooth and can be regarded as constant outside the central frequency range.

PMD compensation using a fuzzy automatic polarization controller

A new first-order polarization mode dispersion (PMD) compensation technique is experimentally demonstrated in a 2.5 Gbit/s optical transmission system. It achieves adaptive compensation over a wide range of differential group delay (DGD) values, since it does not try to compensate it, but to eliminate one of the principal states of polarization by means of a liquid crystal polarization controller and a polarizer. The PMD parameters of the received signal are measured in real time through its spectrum analysis, and used as the feedback signal in a fuzzy logic algorithm controlling the liquid crystal device. The algorithm achieves a response time faster than the PMD variations in real links, also featuring endless operation. Moreover, a deterministic compact PMD emulator has been implemented in order to test the PMD compensator system.

First- and second-order polarization mode dispersion generated by a two-stage emulator

A two-stage polarization mode dispersion (PMD) emulator design consisting of two variable delay lines separated by a rotatable half-wave linear retarder is analyzed and shown to generate an adjustable amount of first- and second-order PMD without any higher orders. This two-stage PMD emulator configuration provides a simple easy-to-breadboard solution for second-order PMD emulators. When compared with PMD emulators based on birefringent crystals, this two-stage emulator is simpler to calibrate.

PMD emulation

PMD emulation

Statistics of the DGD in PMD Emulators

We give the statistics of the differential group delay at the output of a polarization-mode dispersion emulator made of a chain of fiber sections with constant birefringence, fixed and arbitrarily selected lengths, and randomly oriented polarization controllers in between.

An Experimental Approach to Multicanonical Sampling

We determine experimentally, to our knowledge for the first time, the probability distribution functions (pdfs) of a general stochastic system through multicanonical sampling. Our specific implementation relates to a fiber-based polarization-mode dispersion emulator and yields the pdf of the differential group delay for probabilities to 10/sup -6/ with only 8000 samples.

Versatile Integrated PMD Emulation and Compensation Elements

Highly versatile building blocks for polarization-mode dispersion (PMD) emulation and compensation are demonstrated using tunable all-pass filters fabricated in 4%-index-contrast planar waveguides. While the all-pass filters can approximate any phase response, the complexity in setting the individual filter parameters is minimized by restricting the all-pass filter responses to realize a range of differential delays, dispersion, and dispersion slope. A single section can approximate first-order or a higher-order PMD term or emulate chromatic or higher-order dispersion. A differential group delay (DGD) tuning range over 100 ps is demonstrated for 10 Gb/s and 25 ps for 40 Gb/s data. Second-order PMD with a tuning range of 255 ps/sup 2/ and third-order PMD with a range of 2430 ps/sup 3/ are also demonstrated. The larger index contrast required for the ring-resonator-based all-pass filters is advantageous in reducing the thermooptic response time to achieve polarization rotation speeds on the order of 0.1 /spl mu/s/degree. The device is interferometrically stable and compact in size. It can be fully integrated, scaled to many sections, and can implement a variety of PMD synthesis and statistical-emulation approaches.

Electrically Controllable All-Fiber PMD Emulator Using a Compact Array of Thin-Film Microheaters

An electrically controllable, all-fiber polarization-mode dispersion (PMD) emulator is constructed using thin-film microheaters to temperature tune the birefringence of 30 PM-fiber sections spliced at 45/spl deg/ angles. Compact packaging is achieved by mounting the fiber heaters onto an array of silicon V-grooves. The advantages of this electrically tunable emulator design are low loss, negligible PDL, simple construction, no internal reflections, and no moving parts.

Polarization-Mode Dispersion Emulation With Maxwellian Lengths and Importance Sampling

We describe an efficient polarization-mode dispersion (PMD) emulation method that combines a concatenation of birefringent sections having Maxwellian-distributed lengths with importance sampling. The method generates PMD statistics with accurate tail distributions using relatively few sections and reasonable numbers of samples, and allows the targeting of specific, arbitrarily large, first- and second-order PMD values.

PDL Effects in PMD Emulators Made Out With HiBi Fibers: Building PMD/PDL Emulators

Nonnegligible polarization-dependent loss (PDL) arises when HiBi fiber-based polarization-mode dispersion (PMD) emulators are spooled in small diameters. PMD/PDL emulators with random fluctuating PDL can be made with loops along the polarization-maintaining fiber sections. Theoretical predictions for PDL statistics agree with the experimental results.

Impact of SOIP on Optical Transmission System With First- and Second-Order PMD

A new approach is proposed that allows one to qualify the impact of state of input polarization (SOIP) on a 10-Gb/s optical transmission system using a polarization-mode dispersion (PMD) emulator with first- and second-order PMD for the first time. Through experimentations, we found that the system Q penalty as a function of SOIPs denoted by Stokes' vector is symmetrical by the S/sub 1/-O-S/sub 2/, S/sub 1/-O-S/sub 3/, and S/sub 2/-O-S/sub 3/ planes in Stokes' space when first-order PMD is only taken into account; but this kind of symmetry will be broken when second-order PMD is added. Also, an excellent linear fitting between maximum and average Q penalty is obtained in experiments with a PMD emulator for a group of SOIPs uniformly distributed on the Poincare/spl acute/ sphere.

A PMD emulator with tunable second-order PMD and constant mean first-order DGD

We present, for the first time, a second-order polarization mode dispersion (SOPMD) emulator with tunable SOPMD and constant mean first-order differential group delay (DGD). The emulator is based on a variable DGD line (variable from /spl tau//sub variable//sup min/ to /spl tau//sub variable//sup max/), a polarization controller, and a high birefringent (HiBi) fiber segment with a DGD value of /spl tau//sub fixed/. Theoretical calculations predict that after careful calibrations, by tuning the variable DGD line, the emulator can provide a variable SOPMD value from /spl Phi//sub 0/ to (1/2)/spl tau//sub fixed//sup 2/+/spl Phi//sub 0/ (/spl Phi//sub 0/ is a constant), while its mean first-order DGD is kept at a constant value of about /spl tau//sub fixed/. The implications of this SOPMD emulator on high-speed (/spl ges/10 Gb/s) optical communications are discussed.