Principal States Of Polarization Research Articles

Fast tracking of polarization impairments using DSP algorithms in fiber for a coherent optical communication system

AbstractIn a 100G coherent optical fiber communication system, the equalization algorithm of polarization effects in fibers is generally integrated in digital signal processing (DSP) using a multiple input/multiple output (MIMO) equalizer to overcome the impairment due to the polarization effects in fiber. However, it was found in some extreme scenarios, such as the lightning strikes near the fiber cables, the Kerr effect and Faraday effect would induce very fast time‐varying state‐of‐polarization (SOP) and transient variation of principal‐state‐of‐polarization (PSP) of polarization mode dispersion (PMD) which would result in the coherent receivers unlocking. Faced with the difficulty, we propose a 3‐parameter RSOP model and design a window‐split structured Kalman filter equalization scheme instead of conventional MIMO equalizer to cope with this extreme scenario of large PMD combined with ultra‐fast rotation of SOP in presence of residual chromatic dispersion (RCD). The proposed equalization method has an excellent performance and can cope with RCD in the range of ±820 ps/nm under RSOP from 100 krad/s to 3 Mrad/s and DGD = 200 ps.

Retrieve and preserve arbitrary polarization states endlessly at uniform high speed

We put forward a novel scheme based on open-loop polarization control (OLPC) to retrieve and preserve arbitrary polarization states endlessly at uniform high speed, with average error of ~0.035 rad and time cost less than 300 μs, which breaks through the limitation of those depend on close-loop polarization control (CLPC). Utilizing perfect modules we build an experimental OLPC system and establish its matrix model with control programme. Results show that the two-unit PC always has blind zone which can not be suppressed to zero, and the blind area centres exactly on the principal state of polarization (PSP) of the second unit. Then we start the third unit to retrieve the SOP from the blind area thus we achieve arbitrary SOPs on the Poincaré sphere endlessly. Subsequently, we demonstrate the great capacity of the OLPC scheme by successfully carrying on retrieving and preserving arbitrary SOPs disturbed by a polarization scrambler, while for sudden and huge disturbance it still shows quite robust and extremely strong. As a result, we fulfill the scheme in practical case of polarization encoded communication system with various environmental disturbance, and further reveal its prominent performance on improvement of signal quality and preservation of reliable communications, which manifests that it is suitable for field applications where exists much disturbance.

Impact of Wind Gust on High-Speed Characteristics of Polarization Mode Dispersion in Optical Power Ground Wire Cables.

Polarization mode dispersion is recognized as a key factor limiting optical transmission systems, particularly those fiber links that run at bit rates beyond 10 Gbps. In-line test and characterization of polarization mode dispersion are thus of critical importance to evaluate the quality of installed optical fibers that are in use for high-speed signal traffics. However, polarization-based effects in optical fibers are stochastic and quite sensitive to a range of environmental changes, including optical cable movements. This, in turn, gives rise to undesired variations in light polarization that adversely impair the quality of the signal transmission in the link. In this work, we elaborate on experimental testing and theoretical analysis to asses changes of polarization mode dispersion in optical fibers that are caused by environmental variations, here wind gusts in particular. The study was performed on commercially harnessed optical fibers installed within optical power ground wire cables, taking into account different weather conditions. More specifically, we showed that changes caused by wind gusts significantly influence the differential group delay and the principal state of polarization in those optical fibers. For this, we experimentally measured a number of parameters to characterize light polarization properties. Measurements were carried out on C-band operated fiber-optic link formed by 111-km-long power ground wire cables and 88 spectral channels, with a test time step of 1 min during 12 consecutive days. Variations in differential group delay allowed for sensitive testing of environmental changes with measured maxims up to 10 ps under the worst wind conditions. Moreover, measured parameters were used in a numerical model to assess the quality of transmitted high-bit-rate optical signals as a function of wind conditions. The analysis revealed a negligible impact of wind on a 10 Gbps transmission, while substantial influence was noticed for higher bit rates up to 100 Gbps. These results show promises for efficient sensing of environmental changes and subsequent monitoring of the quality of recently used fiber-optic link infrastructures.

Arc-Induced Long Period Gratings in Polarization-Maintaining Panda Fiber

In this letter, we report about the fabrication of long period gratings (LPGs) in a polarization-maintaining Panda optical fiber, by means of the electric arc discharge technique. This is the first time that LPGs are arc-induced in a polarization maintaining fiber. The dependence of the LPG’s spectral features on the input light polarization alignment is illustrated, by considering the two principal polarization states, i.e., along the fast and slow axes of the Panda fiber. Moreover, an investigation about the surrounding refractive index sensitivity, as a function of the two principal polarization states, is also reported with interesting results.

Polarization-resolved sensing with tilted fiber Bragg gratings: theory and limits of detection

Polarization based sensing with tilted fiber Bragg grating (TFBG) sensors is analysed theoretically by two alternative approaches. The first method is based on tracking the grating transmission for two orthogonal states of linear polarized light that are extracted from the measured Jones matrix or Stokes vectors of the TFBG transmission spectra. The second method is based on the measurements along the system principle axes and polarization dependent loss (PDL) parameter, also calculated from measured data. It is shown that the frequent crossing of the Jones matrix eigenvalues as a function of wavelength leads to a non-physical interchange of the calculated principal axes; a method to remove this unwanted mathematical artefact and to restore the order of the system eigenvalues and the corresponding principal axes is provided. A comparison of the two approaches reveals that the PDL method provides a smaller standard deviation and therefore lower limit of detection in refractometric sensing. Furthermore, the polarization analysis of the measured spectra allows for the identification of the principal states of polarization of the sensor system and consequentially for the calculation of the transmission spectrum for any incident polarization state. The stability of the orientation of the system principal axes is also investigated as a function of wavelength.

Determining principal modes in a multimode optical fiber using the mode dependent signal delay method

Mode dispersion can negatively impact optical fiber communication over multimode optical fibers (MMFs). Principal modes are a basis of spatial modes that do not experience mode dispersion up to the first order in frequency. In this work, a method to determine the principle modes of a MMF is proposed. This method is referred to as the mode dependent signal delay method, being the extension to a MMF of the analogous method to determine the principal states of polarization of a single-mode optical fiber. Using this method, principal modes can be determined by measuring N2−1 mean signal time delays at a MMF input for N2−1 launch conditions generated at a MMF output. The differences of the mode dependent signal delay method from the polarization signal delay method and its experimental implementation are discussed.

Performance characterization of multicanonical Monte Carlo method applied to polarization mode dispersion

The numerical accuracy of the results obtained using the multicanonical Monte Carlo (MMC) algorithm is strongly dependent on the choice of the step size, which is the range of the MMC perturbation from one sample to the next. The proper choice of the MMC step size leads to much faster statistical convergence of the algorithm for the calculation of rare events. One relevant application of this method is the calculation of the probability of the bins in the tail of the discretized probability density function of the differential group delay between the principal states of polarization due to polarization mode dispersion. We observed that the optimum MMC performance is strongly correlated with the inflection point of the actual transition rate from one bin to the next. We also observed that the optimum step size does not correspond to any specific value of the acceptance rate of the transitions in MMC. The results of this study can be applied to the improvement of the performance of MMC applied to the calculation of other rare events of interest in optical communications, such as the bit error ratio and pattern dependence in optical fiber systems with coherent receivers.

Method for determination of the principal modes in a few-mode optical fiber using a multibranch doe

We propose a method intended for reconstructing a fiber propagation matrix in few-mode regime and determination of the corresponding principal modes. The method is based on the idea of extending the Jones Matrix Eigenanalysis (JME) technique, which provides.the determination of both the propagation matrix and the principal states of polarization in a single-mode fiber, to the basis of spatial modes in a few-mode fiber. We propose that a multibranch diffractive optical element should be used as a correlation filter, which can be implemented by means of a spatial light modulator (SLM). The efficiency of the proposed method is numerically verified for a stepped-index few-mode fiber in the strong coupling regime.

Second-Order PMD-Induced Crosstalk Between Polarization-Multiplexed Signals and Its Impact on Ultrashort Optical Pulse Transmission

We present an analytical description and experimental demonstration of inter-polarization crosstalk caused by second-order polarization-mode dispersion (PMD). Even if the first-order PMD is completely compensated for, second-order PMD leads to large transmission impairments in ultrashort optical pulse transmissions through signal depolarization, which is caused by the frequency dependence of the principal state of polarization. In particular, depolarization in a polarization-multiplexed transmission inevitably prevents the complete separation of the two channels at the polarization demultiplexing. The analytical results show that the crosstalk increases in proportion to the fourth power of the signal bandwidth and grows by the square of distance as also verified by the experiments.

In-band optical signal-to-noise ratio monitoring for suppression of effects of both polarization mode dispersion and the polarization extinction ratio of a polarization beam splitter based on enhanced tracking of the principal states of polarization

An improved in-band, optical signal-to-noise ratio (OSNR)-monitoring method suppressing the effects of both polarization mode dispersion (PMD) and the polarization extinction ratio of a polarization beam splitter (PBS) by using enhanced tracking of the principal states of polarization is proposed and theoretically and experimentally demonstrated. The experimental results show that the OSNR measured by using the proposed method agrees well, within an error of 1 dB, with the OSNR measured by using an optical spectrum analyzer (OSA). The proposed per-channel OSNR monitoring method was demonstrated to be applicable to future dynamically-reconfigurable wavelength-division-multiplexed (WDM) optical networks.

Principal State Analysis for a Compact in-Line Fiber Polarization Controller

A compact in-line fiber-based polarization controller (FPC) made of a rotatable fiber squeezer is investigated in detail with the Mueller matrix model established based on the generalized principal state of polarization (PSP). The PSP caused by the fiber squeezing is in the equator plane, which turns around S3 axis on the Poincaré sphere when rotating the squeezer. Subsequently, a programmable polarization control method is proposed to realize the polarization conversion between arbitrary polarization states, in which only two parameters of phase shift and rotation angle need to be controlled. This type of FPC, which has a highly compact structure, lower insertion loss, and can be directly embedded into any fiber devices without any extra delay, will be an ideal PC for high-speed optical communication and all-optical signal processing.

Pulse Propagation in Presence of Polarization Mode Dispersion and Chromatic Dispersion in Single Mode Fibers

The presence of (first and second orders) polarization mode dispersion (PMD), chromatic dispersion, and initial chirp makes effects on the propagated pulses in single mode fiber. Nowadays, there is not an accurate mathematical formula that describes the pulse shape in the presence of these effects. In this work, a theoretical study is introduced to derive a generalized formula. This formula is exactly approached to mathematical relations used in their special cases. The presence of second-order PMD (SOPMD) will not affect the orthogonality property between the principal states of polarization. The simulation results explain that the interaction of the SOPMD components with the conventional effects (chromatic dispersion and chirp) will cause a broadening/narrowing and shape distortion. This changes depend on the specified values of SOPMD components as well as the present conventional parameters.

Fast Algorithm to Find the Minimal Polarization Change Points on a Fiber-Optic Stretcher Using One Polarization Rotator and a Polarimeter

Fiber stretchers are used to stabilize the effective length of optical fiber links, but if they are not carefully calibrated, they can produce polarization changes and instabilities, which interact with the polarization mode dispersion (PMD) of the fiber link producing phase changes on the transmitted signals. Those can be minimized if the input polarization is aligned to one of the two orthogonal polarization states of the fiber stretcher, which show minimum polarization change across the dynamic range of the stretcher. This paper presents a noniterative method to find these eigenstates, dubbed “sweet spots,” based on the Jones matrix Eigen-analysis known for measuring PMD of optical fibers, and its application to the line length correction system of the Atacama Large Millimeter/submillimeter Array (ALMA). The paper reviews the theoretical relationship between the sweet spots and the principal states of polarization of the fiber in the stretcher. The proposed method was found to be more accurate and faster than the iterative optimization method originally used for this system.

Theoretical modeling and simulation for analysis of trapping of degree of polarization during polarization mode dispersion compensation

Theoretical modeling and simulation for investigating degree-of-polarization trapping in a local area during compensation for polarization mode dispersion are presented and performed. The simulation results show that the occurrence and the characteristics of unwanted local convergent peaks and ridges depend on both the differential group delay and the launch angle of the optical signal relative to the input principal state of polarization of the fiber transmission link and that the angle required to escape from those local trapping areas can be determined.

Iterative experimental method for generating eigenstates and principal states of polarization

Eigenstates of a given elliptical birefringent are determined at 1.530 and 1.580 μm by generating sequences of polarization states that converge to the eigenstates. The principal states of polarization of the device for the two considered wavelengths are shown to be eigenstates of the succession of two birefringents at 1.530 and 1.580 μm; they are produced by applying the previous iterative process. Experimental results are compared to theoretical estimates.

First-order polarization mode dispersion compensator using two independent feedback signals enabling separation of principal states of polarization and differential group delay controls

We propose and demonstrate a novel first-order polarization mode dispersion (PMD) compensator separating principal-states-of-polarization (PSP) control from differential-group-delay (DGD) control by using two independent feedback monitoring signals. To verify the proposed operating principle, we fabricated an automatically adaptive module-type 40-Gb/s PMD compensator on printed circuit boards. The results show that unlike previous typical compensation method of controlling alternately PSP and DGD, the proposed scheme provides independent continuous PSP tracking regardless of DGD control by delay line under rapidly varying PSP condition, thus resulting in stable compensated signal with reduction in compensation time.

PMD-Induced Crosstalk in Ultrahigh-Speed Polarization-Multiplexed Optical Transmission in the Presence of PDL

We present a new type of crosstalk in a polarization-multiplexed ultrahigh-speed transmission caused by polarization-mode dispersion (PMD) in the presence of polarization-dependent loss (PDL). When PMD and PDL are both present, the orthogonality between two principal states of polarization (PSP) is reduced. As a result, crosstalk inevitably occurs between two polarizations and prevents the two channels from being separated completely during polarization demultiplexing. The system impact of these effects in a polarization-multiplexed terabit/s transmission is also demonstrated experimentally.

High-speed polarization mode dispersion compensation in a 43-Gb/s RZ-DQPSK transmission system over 1200 km of standard single-mode fibre

This paper reports that the designed optical polarization mode dispersion compensator shows a good performance under the real-time variation of differential group delay, state of polarization and principal state of polarization in a (40×43)-Gb/s dense-wavelength-multiplexing, 1200-km enhanced return-to-zero differential-quadrature-phase-shift-keying (RZ-DQPSK) system. The polarization mode dispersion tolerance of the system is improved by 26 ps using the optical polarization mode dispersion compensator. The short and long time stabilities are tested with the bit error ratio recorded.

Principal modes in fiber amplifiers

The dynamics of the state of polarization in multimode fiber amplifiers is presented. The experimental results reveal that although the state of polarizations at the output can vary over a large range when changing the temperatures of the fiber amplifiers, the variations are significantly reduced when resorting to the principal states of polarization in single-mode fiber amplifiers and principal modes in multimode fiber amplifiers.

Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver

We propose a novel and unified algorithm that estimates linear impairments in optical transmission systems from tap coefficients of an adaptive finite-impulse response (FIR) filter in a coherent optical receiver. Measurable impairments include chromatic dispersion (CD), differential group delay (DGD) between two principal states of polarization, second-order polarization-mode dispersion (second-order PMD), and polarization-dependent loss (PDL). We validate our multi-impairment monitoring algorithm by dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.