Principal States Of Polarization Research Articles

Effect of first-order PMD compensation on the statistics of pulse broadening in a fiber with randomly varying birefringence

Polarization mode dispersion in standard telecommunication fibers can be compensated to first order by using the concept of principal states of polarization. At the receiver the pulse is decomposed into the two waveforms polarized along the two principal states for the optical link and their delay is removed. We show by Monte Carlo simulation that compensation sharpens the probability distribution function of the pulse durations by a factor that decreases with increasing polarization dispersion.

First-order PMD compensation in nonlinearly dispersive optical communication systems via transmission over the principal states of polarization

Soliton propagation in the presence of polarization mode dispersion (PMD) is studied with an analytical approach. It is shown that there exist two peculiar initial states of polarization that may prevent the soliton to undergo shape distortions. These states coincide with the states that, in the absence of chromatic dispersion and nonlinearity, are usually referred to as principal states of polarization. This fact is used to show that it is possible to improve the performance of an optical transmission system operating in the presence of chromatic dispersion, PMD and Kerr nonlinearity by coupling the input pulses to one of the principal states of polarization.

The statistics of PMD-induced chromatic fiber dispersion

This paper presents a statistical description of polarization dependent chromatic dispersion (PCD) in optical fibers due to second-order polarization mode dispersion (PMD). This chromatic dispersion is the cause of pulse broadening and compression of the signal components propagating in the principal states of polarization. We show here that, remarkably, the probability density function of PCD has the form of the energy density of a first-order optical soliton. We report measurements that are in agreement with the prediction of this soliton density. Moreover, since a large number of independent experimental samples are difficult to obtain, we also report simulations of the experimental process and these serve to underscore the agreement between theory and measurement. The probability density functions of first and second-order PMD vectors are spherically symmetric. However, these vectors are not statistically independent. The mean square depolarization with respect to wavelength of a launched pulse is revealed to be 33% stronger than expected for spherical symmetry in the absence of dependence, while the mean square PCD is weaker by 67%.

PMD second-order effects on pulse propagation in single-mode optical fibers

The time-space varying birefringence in single-mode optical fibers causes the polarization mode dispersion (PMD) to be a serious problem in high bit-rate transmissions. The PMD first- and second-order statistics are well known in the literature, but second-order PMD-induced pulse distortions have still to be clarified for sequences of pulses of arbitrary shape. We give, for the first time, the exact PMD time impulse response, up to second order. We show, both numerically and experimentally, that the effect of the rotation of the principal states of polarization (PSP) is to generate power overshoots on the "1" and "0" bit sequences.

Measurement of a parameter limiting the analysis of the first-order polarization-mode dispersion effect

A necessary condition to guarantee the existence of the principal state of polarization is experimentally examined. The P parameter, which is defined as the product of the differential group delay and the bandwidth of the principal state of polarization, is measured. The P parameter of long single-mode fibers is assessed. Average P values of 0.26 for dispersion-shifted fiber and 0.45 for conventional single-mode fiber were obtained. Combining these results with published results, one finds that P is not determined solely from the state of the polarization-mode coupling.

Simple and accurate wavemeter implemented with a polarization interferometer

A simple and accurate wavemeter for measuring the wavelength of monochromatic light is described. The device uses the wavelength-dependent phase lag between principal polarization states of a length of birefringent material (retarder) as the basis for the measurement of the optical wavelength. The retarder is sandwiched between a polarizer and a polarizing beam splitter and is oriented such that its principal axes are 45 deg to the axis of the polarizer and the principal axes of the beam splitter. As a result of the disparity in propagation velocities between the principal polarization states of the retarder, the ratio of the optical power exiting the two ports of the polarizing beam splitter is wavelength dependent. If the input wavelength is known to be within a specified range, the measurement of the power ratio uniquely determines the input wavelength. The device offers the advantage of trading wavelength coverage for increased resolution simply through the choice of the retarder length. Implementations of the device employing both bulk-optic components and fiber-optic components are described, and the results of a laboratory test of a fiber-optic prototype are presented. The prototype had a wavelength accuracy of +/-0.03 nm.

Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers

A general description of the effects of combined polarization mode dispersion (PMD) and polarization dependent losses (PDL) in single-mode optical fiber networks is presented. It generalizes the concept of principal polarization states and its associated dynamical equation to the case where PDL is significant. The dynamical equation for the PDL vector Λ , defined as the least attenuated polarization state, is also derived. In the presence of both PMD and PDL, the two principal polarization states are not orthogonal, leading to interferences producing anomalously large pulse spreading. This may affect the transmission capacity of the optical network. Our description also shows that the global attenuation and PDL of the fiber becomes a statistical quantity, varying with the w1avelength.

Measurement of polarization mode dispersion in systems having polarization dependent loss or gain

The principal states of polarization and their propagation characteristics are analyzed for both unitary and nonunitary optical systems in terms of the complex plane representation of polarization. A new method for the estimation of the polarization mode dispersion of the system is proposed together with experimental and simulation results.

Unitarity-conserving construction of the Jones matrix and its application to polarization-mode dispersion analysis

We propose a method to measure the Jones matrix of the transmission medium without violating the unitarity of the matrix. Our method consists of defining the normalized Jones matrix each time the unitarity is lost by experimental error. Numerical simulation is performed to show the feasibility of the proposed method. The method is applied to polarization-mode dispersion analysis. We derive an explicit expression that allows us to evaluate the polarization-mode dispersion vector directly from the elements of the Jones matrix. We also introduce a parameter ∑ to determine a suitable wavelength step size for the measurement of the differential group delay of the principal states of polarization.

The use of the principal states of polarization to describe tunability in a fiber laser

A novel approach for the description of the tunability of a fiber laser using principal states of polarization is introduced. Upon comparing the theoretical predictions with experimental measurements, it has been found that for a 4-m fiber laser, the proposed description is valid for a wavelength range of 2 nm.

Component for second-order compensation of polarisation-mode dispersion

The compensating polarisation-mode dispersion of long fibres using principal states of polarisation is limited in bandwidth when these states vary with frequency. A compensator, containing high birefringent fibres and polarisation controllers is described, which is adapted to these variations and promises an enlarged bandwidth.

Polarization mode dispersion compensation by phase diversity detection

A phase diversity detection method is described for compensating for polarization mode dispersion (PMD) in optical fiber at 10 Gb/s. The PMD distorted received signal is separated into its two constituent principal states of polarization (PSP) by maximizing the measured phase difference between the two pseudorandom data streams. The PMD is inferred from the measured phase and the two data streams are resynchronized by introducing appropriate delay/advance in their respective paths prior to merging in a combiner. The PMD source is a specially constructed three-sectioned polarization maintaining fiber that provides a controlled amount of PMD in the range of 1.6-42 ps.

Principal states of polarisation: time domain measurements with coherent optical pulse

The phenomenon of pulse splitting owing to fibre birefringence with polarisation mode coupling is studied experimentally. It is found that a sufficiently coherent optical pulse is split into two in spite of the effect of polarisation mode coupling. It is also confirmed experimentally that the pulse splitting is described by the principal states of polarisation.

Definition of polarization mode dispersion and first results of the COST 241 round-robin measurements

Two definitions and three measurement schemes for polarization mode dispersion are presented. Their relations, advantages and drawbacks are discussed. A connection with the dynamical equation for the principal polarization states is made. First results from the COST 241 interlaboratory measurement campaign are also presented.

Design and performance of magneto-optic enhanced Co/Pt-based trilayers having zero Kerr ellipticity

The design philosophy and objectives for producing phase-optimized trilayer structures for magneto-optic enhancement of the polar Kerr effect is outlined. A number of alternative designs is presented based on glass/Co-Pt/SiO2/Al. The performance of an actual device, as a function of the wavelength of the incident radiation, and of angle of incidence, for both of the principal polarization states, has been evaluated experimentally and theoretically. Results indicate excellent agreement and demonstrate the ease with which devices can be designed and fabricated.

Attosecond-resolution measurement of polarization mode dispersion in short sections of optical fiber

A new technique is presented for the measurement of the differential group delay (DGD) between principal states of polarization of an optical device, with a demonstrated accuracy and resolution of roughly 50 attoseconds (50 × 10−18 s). Accuracy was directly assessed by measurement of a crystal-quartz DGD Standard. This permits what is to the author's knowledge the first complete measurement of the polarization mode dispersion (PMD) of straight, submeter lengths of optical fiber. PMD can be reliably measured only when the fiber is straight, since spooling of the fiber changes its PMD by introducing additional mode coupling. Measurement of four fiber samples revealed correlation between DGD and fiber core ovality.

Measurement of fiber nonlinear Kerr coefficient by four-wave mixing

We demonstrate a Kerr coefficient measurement of dispersion-shifted fibers based on the nonlinear mixing process between two continuous pump waves and on the power measurements of the created frequencies. A numerical model simulates the experimental conditions and is exploited to determine the Kerr coefficient. Unavoidable polarization effects are precisely taken into account both experimentally and numerically by launching the pump waves on the principal polarization states. This allows us to obtain reproducible measured values and a better than 5% resolution. >

Accurate, automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis

Polarization mode dispersion can be described to first order by principal states of polarization (PSPs) and a differential group delay (DGD), and to second order by wavelength variation of the PSPs and by DGD dispersion (DGDD), the wavelength derivative of DGD. The high accuracy and wavelength resolution of Jones matrix eigenanalysis allows precise measurement of DGDD and PSP variation. A fast, automated system based on a tunable laser and an accurate, real-time polarimeter is used to measure DGD, DGDD, and PSP variation by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, and the system accuracy is demonstrated. Measurements at 2-nm intervals of a device whose DGDD is a known function of wavelength yield values of DGDD which differ from theory by less than 13 fs/nm. >

Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis

Polarization mode dispersion (PMD), which can limit the bandwidth of optical transmission links, has been difficult to measure in a manner independent of human judgment, leading to difficulties in automating the measurement. It is shown that PMD in any linear, time-invariant network can be completely characterized by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, even for networks exhibiting polarization-dependent loss. A fast, automated system using a tunable laser and an accurate, real-time polarimeter affords the temporal accuracy of approximately 2% down to a limit of several femtoseconds, as demonstrated by comparison with other techniques and comparison with known samples. Both the principal states of polarization and the group delay difference were measured as a function of optical frequency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time evolution of polarization mode dispersion in long terrestrial links

Although polarization mode dispersion is well characterized in terms of principal states of polarization (PSP) and of their differential group delay (DGD), both analytically and experimentally, very few data have been published on their time evolution in terrestrial links, where temperature fluctuations are larger than in undersea links. The authors demonstrate strong correlation between temperature fluctuations and evolution of DGD and PSP. Correlation is even stronger in links which include connectors. Also, they report that DGD, as a random function of time, has a Maxwellian distribution and thus shows that it is an ergodic process. >