Sami Mumtaz

Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6

We report simultaneous transmission of six spatial and polarization modes, each carrying 40 Gb/s quadrature-phase-shift-keyed channels over 96 km of a low-differential group delay few-mode fiber. The channels are successfully recovered by offline DSP based on coherent detection and multiple-input multiple-output processing. A penalty of <;1.2 dB is achieved by using 6 × 6 feed-forward equalizers with 120 taps each. The 6 × 6 impulse-response matrix fully characterizing the few-mode fiber is presented, revealing the coupling characteristics between the modes. The results are obtained using mode multiplexers based on phase plates with a mode selectivity of >;28 dB.

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We investigate theoretically nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate the case where linear coupling among spatial modes of the fiber is weak and derive new Manakov equations after averaging over random birefringence fluctuations. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms vanish. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We verify the accuracy of new Manakov equations by simulating the transmission of multiple 114-Gb/s bit streams in the PDM-QPSK format over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equations. The agreement is excellent in all cases studied. A major benefit of the new Manakov equations is that they typically reduce the computation time by more than a factor of 10. Our results show that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. The extent of improvement depends on the fiber design and how many spatial modes are used for SDM transmission. We also consider the case where all spatial modes experience strong random linear coupling modeled using a random matrix. We derive new Manakov equations in this regime and show that the impact of some nonlinear effects can be reduced relatively to single-modes fibers. Finally, we extend our analysis to multicore fibers and show that the Manakov equations obtained in the strong- and weak-coupling regimes can still be used depending on the extent of coupling among fiber cores.

6 MIMO Processing

We study intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated by including all nonlinear contributions to the phase-matching condition and FWM bandwidth. We find that one of the FWM processes has a much larger bandwidth than the other. We include random linear mode coupling among fiber modes using three different models based on an analysis of the impact of random coupling on differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to its vale in the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes are linearly coupled but can become very large (> 40 dB) when all modes couple strongly. In the limit of a coupling length much shorter than the nonlinear length, intermodal FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.

Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations

We present a general model for studying nonlinear effects in multicore fibers. Our results show that a strong linear coupling among fiber cores can reduce nonlinear impairments and improve system performance when digital signal processing is used to compensate for all linear degradations.

Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers.

Polarization effects may induce severe performances degradation in polarization multiplexed optical fiber transmis- sions. Those systems can be seen as 2×2 multi-antennas systems as the emitted polarizations can be considered as 2 input signals and the received polarizations as 2 output signals. Therefore, Space-Time code can be used to take benefit of this configuration and enhance the transmission performances but they have to be combined with optical OFDM to suppress the fiber dispersion and allow their decoding. In wireless 2×2 multi-antennas systems, the Golden and the Silver code are respectively the two best Space- Time codes so, we propose to use those two codes on polarization multiplexed systems. The performances of the Space-Time codes on the optical fiber channel are different than on the wireless channel. Simulations show than the Silver code outperforms the Golden code. Nevertheless, we also show that Space-Time coding can dramatically mitigate the polarization dependent loss (PDL) impairments.

Reduction of Nonlinear Penalties Due to Linear Coupling in Multicore Optical Fibers

We discuss the nonlinear performance of space-division multiplexed systems under realistic conditions using a comprehensive numerical model. Newly derived Manakov equations allow us to include birefringence effects for both multimode and multicore fibers.

Space-Time Codes for Optical Fiber Communication with Polarization Multiplexing

For the first time, we demonstrate experimentally that PDL can be highly mitigated by the use of Polarization-Time coding in OFDM transmissions. We show that Silver code performs better than Golden and Alamouti codes.

Nonlinear performance of SDM systems designed with multimode or multicore fibers

We study numerically intermodal four-wave mixing (IM-FWM) in few-mode fibers including both birefringence fluctuations and random linear coupling. We find that linear mode coupling reduces idler power by 3.5 dB for non-degenerate IM-FWM.

Experimental Demonstration of PDL Mitigation using Polarization-Time Coding in PDM-OFDM Systems

We derive a generalized Manakov equation for multimode fiber to study the rapidly varying birefringence effects in space-division multiplexed fiber systems and show through numerical simulations that birefringence can reduce the impact of nonlinearities.

Effect of random linear mode coupling on intermodal four-wave mixing in few-mode fibers

Considering coherent optical transmissions with PDL disturbance, we evaluate how far from the fundamental limit (based on the outage probability) are conventional coding schemes using Polarization-Time codes and/or LDPC codes.