Large Polarization Mode Dispersion Research Articles

Polarization‐directed nanophotonic routers based on two‐dimensional inorganic molecular crystals

AbstractPhotonic and plasmonic hybrid nanostructures are the key solution for integrated nanophotonic circuits with ultracompact size but relative low loss. However, the poor tunability and modulability of conventional waveguides makes them cumbersome for optical multiplexing. Here we make use of two‐dimensional molecular crystal, α‐Sb2O3 as a dielectric waveguide via total internal reflection, which shows polarization‐sensitive modulation of the propagating beams due to its large polarization mode dispersion. Both experiments and simulations are performed to verify such concept. These Sb2O3 nanoflakes can be coupled with plasmonic nanowires to form nanophotonic beam splitters and routers which can be easily modulated by changing the polarization of the incidence. It thus provides a robust, exploitable and tunable platform for on‐chip nanophotonics.image

Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

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.

Joint equalization scheme of ultra-fast RSOP and large PMD compensation in presence of residual chromatic dispersion.

Polarization demultiplexing is generally carried out by a multiple-input multiple-output (MIMO) based algorithm in polarization division multiplexing (PDM) coherent systems. However, in some extreme environments, the MIMO algorithm becomes inapplicable due to the ultra-fast rotation of the state of polarization (RSOP) and large polarization mode dispersion (PMD). In addition, the residual chromatic dispersion (RCD) is always present because of the mismatch of the compensated chromatic dispersion and real value induced in the optical fiber channel. According to the literature, the Kalman filter-based polarization demultiplexing algorithms possess very weak RCD tolerance. Faced with this dilemma, in this paper, a new Kalman filter structure is proposed, which can jointly compensate ultra-fast RSOP, large PMD and RCD. This Kalman filter structure enables the equalization of the RSOP in the time domain and compensation for RCD and PMD in the frequency domain. We verified the performance of the proposed Kalman scheme in the 28 Gbaud PDM-QPSK/16 QAM coherent system, with a comparison to constant modulus algorithm/multiple modulus algorithm (CMA/MMA). The simulation results confirm that, compared with CMA/MMA, the proposed Kalman scheme can provide a significant performance enhancement to cope with ultra-fast RSOP (up to 3 Mrad/s) and large PMD (more than 200 ps) with a large tolerance to RCD (over the range of ± 820 ps/nm in PDM-QPSK and ± 500 ps/nm in PDM-16 QAM).

An adaptive Kalman filter for extreme polarization effects equalization in coherent optical communication system

The specially designed Kalman filter was proved to be competent to complete the polarization equalization in some extreme environments with the large time-varying polarization mode dispersion (PMD) and the ultrafast rotation of state of polarization (RSOP). But the performance of this kind of Kalman filter is strongly restricted by the initial noise statistics represented by the process noise covariance Q and the measurement noise covariance R which will limit its effectiveness in an actual scene. To solve this problem, this paper proposes an adaptive Kalman filter structure by an adjustable way of estimating the process noise covariance Q and the measurement noise covariance R based on the measurement residual in order to be adaptive to the time-varying environments. The performance of the proposed adaptive Kalman scheme is checked both by the simulation and experiment on the 28 Gbaud PDM-QPSK/16QAM coherent optical communication system platforms. The simulation and experiment results demonstrate that the proposed adaptive Kalman filter scheme has a stable and better performance of the equalization for large PMD combined with ultrafast RSOP, with a greater tolerance the to time-varying extreme polarization environments than that using the extended Kalman filter scheme adopted in our previous work.

Window-split structured frequency domain Kalman equalization scheme for large PMD and ultra-fast RSOP in an optical coherent PDM-QPSK system.

A window-split frequency domain Kalman scheme is proposed in this paper for the equalization of large polarization mode dispersion (PMD) and ultra-fast rotation of state-of-polarization (RSOP) which is an extreme environment due to the Kerr effect and the Faraday effect under the lightning strike near the fiber cables. In order to carry out the proposed Kalman scheme, we give a simplified and equivalent fiber channel model as a replacement for the general model of the polarization effect of the co-existence of PMD and RSOP. With this fiber channel model, we can conduct compensation for PMD in the frequency domain and tracking RSOP in time domain. A half analytical and half empirical theory for the initialization of the process and measurement noise covariance is also presented in theory and verified by the numerical simulation. The performance of the proposed Kalman scheme is checked in the 28Gbaud PDM-QPSK coherent system built on both simulation and experiment platforms. The simulation and experiment results confirm that compared with the generally used constant modulus algorithm (CMA), the proposed scheme provides excellent performance and stability to cope with large range DGD from 20ps to 200ps and RSOP from 200krad/s to 2Mrad/s, with less computational complexity.

Single-Pump Parametric Amplification in Randomly Birefringent Unidirectionally Spun Fibers

A systematic study of the effects of polarization mode dispersion on broad-band and narrow-band, single pump, fiber parametric amplifiers is realized through numerical solutions of the equations governing the interaction. The nonlinear polarization rotation is shown to be a relevant effect that can increase gain randomness when it mixes with polarization mode dispersion. In unidirectionally spun fibers the signal-pump alignment can be highly increased and the gain enhanced. However, in spite of the enhanced alignment, large polarization mode dispersion phase-mismatches the interaction and the gain decreases to zero.

Demonstration of Frequency-Domain Averaging Based Channel Estimation for 40-Gb/s CO-OFDM With High PMD

We experimentally demonstrate the intrasymbol frequency-domain averaging based channel estimation for a 40-Gb/s polarization-division-multiplexed coherent optical orthogonal frequency-division multiplexing signal with eight quadrature amplitude modulation under large polarization-mode dispersion, showing improved efficiency as compared to the time-domain averaging based scheme.

160-Gb/s 200-km Field Transmission Experiment With Large PMD Using a Time-Domain Optical Fourier Transformation Technique

A 160-Gb/s single-polarization differential phase-shift-keying transmission using time-domain optical Fourier transformation (OFT) was demonstrated over a 200-km installed fiber link with large polarization-mode dispersion (PMD). First, we suppressed differential group delay (DGD) by coupling to the principal state of polarization (PSP) launch, where the power penalty was 2.8 dB. Then, by further applying OFT, which enables us to reduce time-dependent DGD and second-order PMD that cannot be removed with the PSP launch alone, excellent error-free performance with a power penalty of 1.5 dB has been successfully achieved.

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.

Compensation of higher order polarization-mode dispersion using phase modulation and polarization control in the transmitter

We demonstrate a higher order polarization-mode dispersion (PMD) compensation scheme using a polarization controller and a phase modulator in the transmitter, as well as a traditional first-order compensator in the receiver. The effectiveness of this approach is experimentally demonstrated for a 10-Gb/s nonreturn-to-zero (NRZ) transmission over a link with an average PMD of 50 ps. Under this large PMD condition, the system power penalty can be reduced from /spl sim/4 dB that is achieved with a first-order compensator to 1 dB using the proposed technique. According to a reasonable outage criterion, simulation results show that the tolerance to average PMD for the 40-Gb/s NRZ system is improved to /spl sim/10 ps, as compared to the 7-ps value using only first-order PMD compensation. Such improvement may double the PMD-limited transmission distance.

Emulator of first- and second-order polarization-mode dispersion

Contrary to approaches which try to mimic a standard fiber as closely as possible, the emulator presented here gives constant (but user adjustable) values for differential group delay (DGD) and ratio of first- to second-order polarization-mode dispersion (PMD). Once it is set, the ratio is conserved while the DGD can be easily varied within a range of 0-300 ps. This allows to investigate the low-probability events of large DGD and second-order PMD important for system outage.

Polarization dependence of gain in discrete Raman amplifiers with dispersion compensating fibres

Polarization dependence of stimulated Raman scattering is a fundamental physical effect, which influences the design and application of Raman amplifiers for optical networks. We report experimental data of the study of polarization dependence of Raman gain in dispersion compensating fibres (DCF). The investigation displays a strong variation of the polarization dependence of Raman gain versus average polarization mode dispersion (PMD) values of DCF for both co-propagating and counter-propagating pump configurations. The reported data show, for the first time to our knowledge, that, for large PMD values, such a dependence may be as small as to be comparable with the accuracy of the measurements. The results of the study may be used to simplify the design of Raman amplifiers to avoid depolarization of pump sources that are currently used to decrease polarization dependence of Raman gain.

Probability density functions of the differential group delay in optical fiber communication systems

Fiber communication systems limited by polarization-mode dispersion (PMD) are usually analyzed using statistics. The probability density function (pdf) of the differential group delay (DGD) is then crucial to know. There are cases for which the commonly used Maxwellian pdf is only approximate, e.g., PMD emulators, or systems with components having single components with large deterministic PMD. Those cases are discussed in this paper, and their pdfs are derived. To do this, we present a very general theory that allows for the derivation of the pdf for almost any birefringent transmission line. As a side result, we are able to prove that the square-sum concatenation formula is valid in almost every case of interest, even if the pdf is far from Maxwellian.

Ultra-high speed soliton transmission in presence of polarisation mode dispersion using in-line synchronous modulation

It is shown numerically that in-line synchronous modulation is especially useful for extending the transmission distance in the presence of large polarization-mode dispersion in ultra-highspeed (40 and 80 Gbit/s) optical soliton transmission systems.

Influence of optical source characteristics on the measurement of polarization-mode dispersion of highly mode-coupled fibers

A new theoretical analysis of the interferometric polarization-mode dispersion (PMD) measurement predicts, in the limit of large PMD, a new relationship to the highly mode-coupled principal states model. This theory is confirmed by computer simulation of the ratio of the mean differential group delay (DGD) to the interferometric PMD. Jones matrix eigenanalysis and wavelength scanning with extrema counting are shown to measure the mean DGD independently of the optical source spectrum, whereas interferometrically measured PMD is shown to depend on the optical source spectrum as well as on the characteristics of the fiber to be measured.

Polarization mode dispersion minimization in fiber-wound piezoelectric cylinders

We describe a technique for minimizing polarization mode dispersion (PMD) in broadband interferometry for use with phase modulators of the type formed by coiling nominally circular-core single-mode optical fiber onto piezoelectric cylinders. The technique involves using two piezoelectric elements, arranged to be optically orthogonal. We show that in the general case the two cylinders give rise to four distinct interferograms, but by careful alignment of the elements we reduce these to two coincident interferograms. Hence the large PMD of a single-element modulator is reduced to a negligible level.