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A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions, accounting for random polarization drifts, emulating a random walk on the Poincaré sphere, which has been successfully verified using experimental data. The model is described in the Jones, Stokes and real four-dimensional formalisms, and the mapping between them is derived. Such a model will be increasingly important in simulating and optimizing future systems, where polarization-multiplexed transmission and sophisticated digital signal processing will be natural parts. The proposed polarization drift model is the first of its kind as prior work either models polarization drift as a deterministic process or focuses on polarization-mode dispersion in systems where the state of polarization does not affect the receiver performance. We expect the model to be useful in a wide-range of photonics applications where stochastic polarization fluctuation is an issue.

We investigate and experimentally demonstrate a fast and robust chromatic dispersion (CD) estimation method based on temporal auto-correlation after digital spectrum superposition. The estimation process is fast, because neither tentative CD scanning based on CD compensation nor specific cost function calculations are used. Meanwhile, the proposed CD estimation method is robust against polarization mode dispersion (PMD), amplified spontaneous emission (ASE) noise and fiber nonlinearity. Furthermore, the proposed CD estimation method can be used for various modulation formats and digital pulse shaping technique. Only 4096 samples are necessary for CD estimation of single carrier either 112 Gbps DP-QPSK or 224 Gbps DP-16QAM signal with various pulse shapes. 8192 samples are sufficient for the root-raised-cosine pulse with roll-off factor of 0.1. As low as 50 ps/nm standard deviation together with a worst estimation error of about 160 ps/nm is experimentally obtained for 7×112 Gbps DP-QPSK WDM signal after the transmission through 480 km to 9120 km single mode fiber (SMF) loop using different launch powers.

We investigate a time-domain implementation of generalized phase-conjugated twin waves which we call conjugate data repetition. A theory based on time-domain perturbation analysis explaining the mitigation of nonlinear effects is provided, and the concept is evaluated using numerical simulations. Compared to PM-QPSK at the same channel bit rate, the single-channel transmission reach in a conventional system with standard single-mode fiber of conjugate data repetition-QPSK is increased by approximately a factor of 2.

In this paper, we investigate the performance limits of electronic chromatic dispersion compensation (EDC) and digital backpropagation (DBP) for a single-channel non-dispersion-managed fiber-optical link. A known analytical method to derive the performance of the system with EDC is extended to derive a first-order approximation for the performance of the system with DBP. In contrast to the cubic growth of the variance of the nonlinear noise-like interference, often called nonlinear noise, with input power for EDC, a quadratic growth is observed with DBP using this approximation. Finally, we provide numerical results to verify the accuracy of the proposed approach and compare it with existing analytical models.

We investigate 128-level set-partitioning quadrature amplitude modulation (128-SP-QAM) experimentally and compare the performance to polarization-multiplexed 16QAM both at the same bit rate and at the same symbol rate. Using a recirculating loop we study both single channel and wavelength-division multiplexing (WDM) transmission and demonstrate a reach of up to 2680 km at a bit-error rate of 10(-3) for 128-SP-QAM. We confirm that 128-SP-QAM has an increased sensitivity compared to PM-16QAM and show that the maximum transmission distance can be increased by more than 50 % at the same bit rate for both single channel and WDM transmission. We also investigate the performance at the same symbol rate as a possible fall back solution in a degrading link.

In this paper we investigate an interesting modulation format for fiber optic communications, set-partitioning 128 polarization-multiplexed 16-QAM (128-SP-QAM), which consists of the symbols with even parity from the symbol alphabet of polarization-multiplexed 16-QAM (PM-16-QAM). We compare 128-SP-QAM and PM-16-QAM using numerical simulations in long-haul transmission scenarios at bit rates of 112 Gbit/s and 224 Gbit/s, and at the same symbol rates (14 and 28 Gbaud). The transmission link is made up of standard single-mode fiber with 60, 80 or 100 km amplifier spacing and both single channel and WDM transmission (25- and 50 GHz-spaced) is investigated. The results show that 128-SP-QAM achieves more than 40% increase in transmission reach compared to PM-16-QAM at the same data rate for all cases studied for a bit error rate of 10⁻³. In addition, we find that in single channel transmission there is, as expected, an advantage in terms of transmission distance when using a data rate of 112 Gbit/s as compared to 224 Gbit/s. However, when comparing the two different WDM systems with the same aggregate data rates, the reach is similar due to the smaller impact of nonlinear crosstalk between the WDM channels in the systems with 50 GHz spacing. We also discuss decoding and phase estimation of 128-SP-QAM and implement differential coding, which avoids error bursts due to cycle slips in the phase estimation. Simulations including laser phase noise show that the phase noise tolerance is similar for the two formats, with 0.5 dB OSNR penalty compared to the case with zero phase noise for a laser linewidth to symbol rate ratio of 10⁻⁴.

We perform experimental and numerical investigations of the transmission reach of polarization-switched QPSK (PS-QPSK) and polarization-multiplexed QPSK (PM-QPSK) for three different fiber span lengths: 83, 111 and 136 km. In the experimental comparison we investigate the performance of PS-QPSK at 20 Gbaud and PM-QPSK at the same bit rate (60 Gbit/s) and at the same symbol rate, both the single channel case and a WDM system with 9 channels on a 50 GHz grid. We show that PS-QPSK gives significant benefits in transmission reach for all span lengths. Compared to PM-QPSK, use of PS-QPSK increases the reach with more than 41% for the same symbol rate and 21% for the same bit rate. In the numerical simulations we use the same data rates as in the experiment. The simulation results agree well with the experimental findings, but the transmission reach is longer due to the absence of various non-ideal effects and higher back-to-back sensitivity. Apart from using data coded in the absolute phase in the simulations, we also investigate differentially coded PS-QPSK for the first time and compare with PM-QPSK with differential coding. The power efficiency advantage of PS-QPSK then increases with approximately 0.3 dB at a bit error rate of 10⁻³, resulting in a further relative transmission reach improvement over PM-QPSK. Both the experimental and the numerical results indicate that PS-QPSK has slightly higher tolerance to inter-channel nonlinear crosstalk than PM-QPSK.

We present the first experimental results for polarization-switched QPSK (PS-QPSK) and make a comparison with polarization-multiplexed QPSK. Our measurements confirm the predicted sensitivity advantage of PS-QPSK. We have also studied the single channel performance after transmission over 300 km and support the results with numerical simulations. It is shown that the two modulation formats have similar nonlinear tolerance and that optical dispersion compensation outperforms compensation with digital signal processing in the single channel case. Finally, we propose a novel transmitter for PS-QPSK based on an IQ modulator and two amplitude modulators driven in a push-pull configuration., (© 2011 Optical Society of America)

By using a generalized cost function, a modified constant modulus algorithm (CMA) that allows polarization demultiplexing and equalization of polarization-switched QPSK is found. An implementation that allows easy switching between the conventional and the modified CMA is described. Using numerical simulations, the suggested algorithm is shown to have similar performance for polarization-switched QPSK as CMA has for polarization-multiplexed QPSK., (© 2011 Optical Society of America)

We propose a novel 16-quadrature amplitude modulation (QAM) transmitter based on two cascaded IQ modulators driven by four separate binary electrical signals. The proposed 16-QAM transmitter features scalable configuration and stable performance with simple bias-control. Generation of 16-QAM signals at 40 Gbaud is experimentally demonstrated for the first time and visualized with a high speed constellation analyzer. The proposed modulator is also compared to two other schemes. We investigate the modulator bandwidth requirements and tolerance to accumulated chromatic dispersion through numerical simulations, and the minimum theoretical insertion attenuation is calculated analytically.

A regenerator for differential phase-shift keying data, consisting of two Mach-Zehnder interferometers and two amplitude regenerators, is examined theoretically. The result, which shows that the phase error is suppressed if phase-preserving amplitude regenerators are used, provides a theoretical description of an already experimentally implemented regenerator.

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high-energy charged-particle beams. The model includes the nonlinear self-consistent interaction between the beam and its surroundings in terms of a coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalized nonlinear Schrödinger equation including a nonlocal nonlinear term. The consequences of the resistive part on the propagation of particle bunches are examined using analytical as well as numerical methods.