Principal States Of Polarization Research Articles

Interaction between polarization mode dispersion and polarization-dependent losses in optical communication links

The interplay between polarization mode dispersion (PMD) and polarization-dependent losses (PDLs) is systematically analyzed by a model that assumes the concatenation of independent birefringent and PDL elements in a distributed way. It is shown that PDL enhances the differential group delay for the optical link and also induces a faster frequency decorrelation that increases the magnitude of higher-order PMD. In addition, PDL converts the real-valued PMD vector into a complex vector, giving rise to a loss of orthogonality between the principal states of polarization that scales with the link PDL. The dynamic equation for the global PDL vector that characterizes the polarization states with maximum and minimum attenuation is also solved. The frequency dependence of this vector is found to be a function of the total link PMD. Finally, the probability density functions for both the PMD and the PDL vectors will be discussed.

Is there life beyond the principal states of polarization?

In this paper we show that it is possible to describe exactly the field intensity distorted by polarization mode dispersion (PMD) at the output of a single-mode fiber, without resorting to the principal states of polarization (PSPs). Such description is based on the eigenmodes of what we call the extracted matrices, for which we establish relationships with the PSPs, e.g., by showing their alignment with the PSPs when these are not depolarized over the signal bandwidth. We also show that the eigenmodes of the extracted matrices are less depolarized than the PSPs, and are thus the most convenient frame of reference to express the output field and intensity for high bit rate transmitted signals. We thoroughly investigate the properties of a recently introduced fiber model, which we refer to as the rotation model, based on the rotation of the extracted eigenmodes, which extends the intuition of Bruyère's PSPs rotation model (1996) to the most stable frame of reference, and hence is expected to give the most accurate description of the PMD fiber for large bandwidth signals. We finally provide a novel eye closure penalty (ECP) formula based on the extracted eigenmodes, and show its relation with the currently available ECP formulas. The accuracy of the novel ECP formula is tested against simulation results of transmission through a fiber synthesized by the rotation model.

π-shifted Sagnac interferometer for characterization of femtosecond first- and second-order polarization mode dispersion

A novel configuration for measuring femtosecond polarization mode dispersion (PMD) with a pi-shifted Sagnac interferometer is studied. The advantages of this configuration include a response that is independent of the orientation of the device under test. This independence allows characterization of the first-and second-order PMD by measurement of the wavelength dependence of the differential group delay and of the orientation of the device's principal states of polarization. The method provides an extension of the dynamic range of the Sagnac interferometer technique to few-femtosecond PMD measurement.

PMD—Induced Pulse Broadening in Optical Fibers

In this paper, by means of analytical expressions we compare the expected pulse broadening in a fiber-optic transmission system suffering from both first- and higher order Polarization Mode Dispersion (PMD). The results are compared for compensated fiber with uncompensated fiber. Compensation could be achieved both before the transmission or after the transmission, accordingly it is classified as Pre-Transmission Compensation or Post-Compensation techniques. We discuss the influence of both the PMD Compensation schemes. Firstly, we analyze the First-Order PMD Compensation and subsequently the Principal State of Polarization (PSP) Transmission Compensation scheme.

광 위상지연기를 이용한 온도측정

광 위상지연기에서 두 편광축 사이의 위상차가 온도의 함수라는 현상을 이용하여 새로운 온도측정기를 제안하였다. 특정한 파장의 입력광이 일정한 길이의 광 위상지연기를 통과하면 온도에 따라 그 편광상태가 바뀌게 된다. 이때의 편광성분을 진행방향에 수직한 두 축 성분으로 분리하여 그 출력을 비교하면 광 위상지연기의 온도를 결정할 수 있다. 본 연구에서는 광 위상지연기로 길이 100mm의 편광유지 광섬유를 이용하여 온도측정기를 구현하였다. 온도에 대한 위상차 변화율은 0.236<TEX>$^{\circ}C$</TEX><TEX>$_{-1}$</TEX>이었고, -2.6<TEX>$^{\circ}C$</TEX>~3.4<TEX>$^{\circ}C$</TEX>에서 <TEX>$\pm$</TEX>0.038<TEX>$^{\circ}C$</TEX>의 측정오차를 보였다. We proposed a novel temperature sensor based on the phenomena that the phase difference between principal polarization states in an optical retarder is a function of temperature. The polarization state of an optical beam is changed as it passes through the optical retarder, with the change dependent on the temperature. The temperature of the optical retarder is determined by comparison of the power difference between principal polarization states. A temperature sensor was successfully implemented using a polarization maintaining fiber of length 100 mm as the optical retarder. The change rate of phase difference on temperature was 0.236<TEX>$^{\circ}C$</TEX><TEX>$_{-1}$</TEX> and the measurement error was <TEX>$\pm$</TEX>0.038<TEX>$^{\circ}C$</TEX> over the temperature region of -2.6<TEX>$^{\circ}C$</TEX>~3.4<TEX>$^{\circ}C$</TEX>.

Investigation of the effective space-time of the vacuum nonlinear electrodynamics in a magnetic dipole field

The metric tensor of the effective pseudo-Riemannian space–time for an electromagnetic wave propagating in the magnetic dipole field and the gravitational field of a neutron star is obtained within a parameterized post-Maxwellian vacuum electrodynamics. The angles of the nonlinear electrodynamic and gravitational ray bending for electromagnetic waves propagating in the magnetic equatorial plane of the star are calculated based on an analysis of isotropic geodesics of this space. We show that for all nonlinear theories whose post-Maxwellian parameters do not coincide, the velocity of the electromagnetic signal propagation in external fields and the rays along which these signals propagate depend on the polarization of the electromagnetic waves. The difference of the source-to-detector propagation time of these signals for two principal polarization states is calculated.

Statistical description of optical system performances due to random coupling on the principal states of polarization

Due to polarization-mode dispersion (PMD), the performances of an optical transmission system show a random behavior. We calculate the probability density function of the Q-factor due to PMD. We adopt the principal states of polarization model, and we also consider the clock recovery behavior at the receiver. Theoretical results are reported for a 40-Gb/s system, and are compared with those obtained considering the effect of pulse broadening due to PMD.

Calculation of signal outage due to polarization mode dispersion

A method to calculate signal outage due to polarization mode dispersion (PMD), i.e., PMD outage, when differential group delay, as well as principal state of polarization are varying is presented. The most common way to analyze this problem has been based on assuming worst case polarization, which will give too high a value for PMD outage.

Polarization mode dispersion and polarization dependent loss for a pulse in single-mode fibers

Polarization mode dispersion (PMD) and polarization dependent loss (PDL) for a pulse in optical fibers are calculated with a model of two concatenated fibers. Each of the two fibers has both elliptical birefringence and PDL. The results show that the PMD and PDL for a short pulse can be very different from those for a narrow-band pulse in optical fibers. Two anomalous results are reported: (1) the effective PDL for a pulse can be smaller than the PDL difference of the two fibers and (2) the effective PMD for a pulse can be either larger than the sum of the differential group delays (DGDs) of the two fibers or less than the DGD difference of the two fibers, depending on the input pulsewidth. The pulse distortions when the pulses are launched into the two principal states of polarization (PSPs) are discussed.

Real-time principal state characterization for use in PMD compensators

Most polarization-mode dispersion (PMD) compensation systems rely on many feedback parameters that contribute to complexity, instability, and speed limitations. We demonstrate a method that quickly and accurately determines the principal states of polarization of a fiber afflicted with PMD. This information can be used in a feedforward configuration, thereby reducing the number of feedback parameters in a complete compensation system.

Polarization mode dispersion in radio-frequency interferometric embedded fiber-optic sensors

The effect of fiber birefringence on the propagation delay in an embedded fiber-optic strain sensor is studied. The polarization characteristics of the sensor are described in terms of polarization mode dispersion through the principal states of polarization and their differential group delay. Using these descriptors, an analytical expression for the response of the sensor for an arbitrary input state of polarization is given and experimentally verified. It is found that the differential group delay, as well as the input and output principal states of polarization, vary when the embedded fiber is strained, leading to fluctuations in the sensor output. The use of high birefringence fibers and different embedding geometries is examined as a means for reducing the polarization dependency of the sensor.

Anomalous pulse-width narrowing with first-order compensation of polarization mode dispersion

We present analytical and experimental results to demonstrate the narrowing of pulses transmitted through optical fibers, with polarization mode dispersion compensated for to first order in frequency. The compensation technique splits the optical signal at the fiber output into polarization components that are aligned with the output principal states of polarization, and only one of the two components is subsequently detected. It is shown that it is possible with this compensation technique to have output pulses that are narrower than the input pulses. Pulse narrowing can also be found when the optical signal is split into orthogonal polarization components that are not principal states of polarization.

An adaptive first-order polarization-mode dispersion compensation system aided by polarization scrambling: theory and demonstration

An adaptive polarization-mode dispersion (PMD) compensation system has been developed to cancel the effects of first-order PMD by producing a complementary PMD vector in the receiver. Control parameters for the PMD compensation system comprised of a polarization controller and a PMD emulator are derived from the nonreturn-to-zero (NRZ) signal in the channel to be compensated. Estimates of the link's differential group delay (DGD) and principal states of polarization (PSPs) based on this signal are reliable when the signal power is equally split between the link's two PSP's; however this condition cannot be assumed. To meet this requirement, we scramble the state of polarization (SOP) of the input signal at a rate much greater than the response time of the PMD monitor signal so that each sample represents many different SOP alignments. This approach allows the effective cancellation of the first-order PMD effects within an optical fiber channel.

On the second-order approximation of PMD

A second-order polarization mode dispersion (PMD) approximation based upon the pulse-width distortion has been studied. It shows that a complete second-order approximation should include the second derivative of the PR-ID vector as well as the first derivative of the PMD vector. Second-order pulse distortions are explicitly expressed including a 'first-order' term involving principal states of polarization (PSP) of the pulse and a second-order term involving the beating between fiber chromatic dispersion and effective PMD chromatic dispersion. An analytical result is derived for the probability of second-order PR-ID power penalty. It shows that the mean PMD of the fiber should be restricted to 26 ps and 18 ps, respectively for an optical link with zero and 850 ps/nm chromatic dispersion, in order to maintain a one dB second-order PMD power penalty with a probability below 10/sup -6/ at a data rate of 10 Gb/s. The analysis also indicates that a second-order PMD compensator can be used as a dynamic chromatic dispersion compensator.

Nonlinear principal states of polarization in optical fibers with randomly varying birefringence

The polarization properties of an electromagnetic field that propagates in a fiber with polarization-mode dispersion (PMD) and randomly varying birefringence are studied by resorting to the coupled nonlinear Schrodinger equations. It is shown that the concept of principal states of polarization (PSP’s), meant to be the states that allow undistorted pulse propagation to be achieved in the presence of PMD, may be defined even in the presence of dispersion and nonlinearity. Furthermore, nonlinear PSP’s are proved to coincide with linear PSP’s, as they are customarily defined through the frequency dependence of the fiber input/output relation. Finally, it is also shown that the propagation equations may be exactly reduced to the Manakov equations for any fixed realization of the random process accounting for the fiber PMD. As a result, a whole class of simulton pulses that preserve their shape in the presence of PMD is analytically found.

Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states

Using the retarded plate model, we derive the correlations and the mean-square values of all orders of polarization mode dispersion (PMD) as well as the autocorrelation function of the PMD vector. Our results provide the signal bandwidth below which the first-order approximation of the principal states of polarization is valid. We show that this bandwidth depends only on the mean value of the differential group delay. Our theoretical results are supported by simulations and experiments.

Limitations of first-order PMD compensation techniques in the presence of chromatic dispersion

The limitations of different techniques for first-order compensation of polarization mode dispersion (PMD) are examined. In the absence of chromatic dispersion the techniques can increase the allowable PMD value by factors ranging from 2.21 to 2.69. For the compensation technique in which the input state of polarization is aligned with the principal state of polarization that gives the least pulse distortion, the allowable PMD value is increased in the presence of chromatic dispersion. The effectiveness of the other compensation techniques is decreased in the presence of chromatic dispersion.

Autocorrelation function of the polarization-mode dispersion vector

We derive, for what is believed to be the first time, the autocorrelation function (ACF) of the polarization-mode dispersion (PMD) vector, which gives information on the bandwidths of the principal states of polarization. We compare the ACF with measured data and find good agreement. Finally, we apply the derived ACF to calculate the average pulse broadening that is due to PMD.

Jones matrix of polarization mode dispersion

We describe how to calculate the Jones matrix transfer function of a fiber if its principal states of polarization and its differential group delay as functions of frequency are known. Using two counterexamples related to second-order polarization mode dispersion (PMD), we also show that a previous method used for the same purpose induces overestimation of second-order PMD effects by a factor of 2. Our new method is used to solve the problem for both counterexamples.

Principal states of polarization for an optical pulse

We propose a generalized definition of principal states of polarization for an optical pulse with arbitrary spectral components. Similar to the principal states defined by Poole et al. (see Electron. Lett. vol. 22, p. 1029, 1986) we show that regardless of the spectral components of the pulse, there exist two orthogonal input states of polarization which minimize/maximize the delay of the pulse. At the output of the fiber, these two principal states of the pulse, although depolarized, are also always orthogonal to each other.