Enhancing the Kramers-Kronig receiver via dispersion-based spatial diversity.

We report a scheme for reconstructing the complex envelope of an optical signal from two decorrelated measurements of its intensity. The decorrelation is achieved by splitting the received optical signal into two copies, and by dispersing one of the copies prior to photo detection. The reconstructed complex-valued signal is obtained by means of an iterative algorithm that requires only a few tens of iterations. The starting point of the search procedure is produced by Kramers-Kronig (KK) reconstruction. With this procedure, the continuous-wave tone that accompanies the received signal is reduced by 5 dB to 6 dB compared to the requirement of a KK receiver alone.

Statistical distribution of polarization-dependent loss in systems characterized by the hinge model.

We study the statistics of polarization-dependent loss in systems, where this phenomenon is dominated by discrete optical components. Exact expressions for the probability distribution of the polarization-dependent loss and of the overall link attenuation are reported here for the first time, to the best of our knowledge.

Experimental characterization of nonlinear interference noise as a process of intersymbol interference.

We demonstrate a method for experimentally characterizing the second order statistics of nonlinear interference noise (NLIN) as an intersymbol interference (ISI) process. The method enables measurement of the properties of high-order ISI coefficients, which have been largely overlooked in the past. The ability of measuring these statistics is imperative for designing effective NLIN mitigation schemes. The variance, temporal correlation times, and cross correlations of the various ISI coefficients are evaluated in several system implementations.

Coherent detection with an incoherent local oscillator.

We demonstrate the feasibility of fully coherent reconstruction of the complex envelope of arbitrary optical fields while using an incoherent source as a local oscillator (LO). The reconstruction relies on a signal processing procedure that we describe, and the only requirement from the system is that the receiver's electrical bandwidth and sampling rate are at least twice as high as the bandwidth of the received signal and of the LO. The proposed scheme is particularly attractive in spectral regions where no high-quality lasers are available.

Nonlinear interference noise in space-division multiplexed transmission through optical fibers.

We study the nonlinear interference noise (NLIN) generated in SDM systems, and generalize the NLIN model introduced in the context of single-mode fibers to the multi-mode case. The generalized model accounts for the modulation-format dependence of the NLIN, and gives the scaling of the NLIN power with the number of transmitted modes. It also provides the tools for extending the results of the NLIN Wizard to SDM. Unlike in the case of single-mode systems, the effect of MD cannot in general be ignored in the SDM case. We show that inclusion of MD erases the contribution of FWM effects, and significantly suppresses the effect of XPM.

The delay spread in fibers for SDM transmission: dependence on fiber parameters and perturbations.

Contrary to single mode fibers, where random imperfections are responsible for polarization-mode dispersion, modal dispersion (MD) in multi-mode fiber structures for space-division multiplexed (SDM) transmission, originates chiefly from the intrinsic non-degeneracy of the propagating modes, also known as modal birefringence. The presence of random imperfections in such fibers has a positive aspect, as it reduces the intrinsic MD, and in the limit of strong coupling it causes the signal delay spread to increase with the square root of the propagation distance, rather than linearly, as would be the case in an ideal fiber. In this paper we derive a formula that relates the signal delay spread to the fiber geometry and to the statistical properties of the structural fiber perturbations. The derived formula provides insight into the MD phenomenon and facilitates the design of low-MD multi-mode fiber structures.

Modeling and performance metrics of MIMO-SDM systems with different amplification schemes in the presence of mode-dependent loss.

Mode-dependent loss (MDL) is a major factor limiting the achievable information rate in multiple-input multiple-output space-division multiplexed systems. In this paper we show that its impact on system performance, which we quantify in terms of the capacity reduction relative to a reference MDL-free system, may depend strongly on the operation of the inline optical amplifiers. This dependency is particularly strong in low mode-count systems. In addition, we discuss ways in which the signal-to-noise ratio of the MDL-free reference system can be defined and quantify the differences in the predicted capacity loss. Finally, we stress the importance of correctly accounting for the effect of MDL on the accumulation of amplification noise.

Intensity impulse response of SDM links.

We study the response of space-division multiplexed fiber links to an excitation by a short impulse of the optical intensity. We show that, in the presence of full mixing, the intensity impulse response is Gaussian, confirming recently reported experimental observations, and relate its variance to the mean square of the mode dispersion vector of the link τ(->). The good agreement between our theory and the previously published experiments provides solid foundations to the random coupling model of SDM fiber links, and provides a tool for efficient design of MIMO-DSP receivers.

Accumulation of nonlinear interference noise in fiber-optic systems.

Through a series of extensive system simulations we show that all of the previously not understood discrepancies between the Gaussian noise (GN) model and simulations can be attributed to the omission of an important, recently reported, fourth-order noise (FON) term, that accounts for the statistical dependencies within the spectrum of the interfering channel. We examine the importance of the FON term as well as the dependence of NLIN on modulation format with respect to link-length and number of spans. A computationally efficient method for evaluating the FON contribution, as well as the overall NLIN power is provided.

New bounds on the capacity of the nonlinear fiber-optic channel.

We revisit the problem of estimating the nonlinear channel capacity of fiber-optic systems. By taking advantage of the fact that a large fraction of the nonlinear interference between different wavelength-division-multiplexed channels manifests itself as phase noise, and by accounting for the long temporal correlations of this noise, we show that the capacity is notably higher than what is currently assumed. This advantage translates into nearly doubling of the link distance for a fixed transmission rate.

Properties of nonlinear noise in long, dispersion-uncompensated fiber links.

We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the results of the Gaussian noise (GN) model (according to which NLIN is additive Gaussian) and a recently published time-domain analysis, which attributes drastically different properties to the NLIN. Upon reviewing the two approaches we identify several unjustified assumptions that are key in the derivation of the GN model, and that are responsible for the discrepancy. We derive the true NLIN power and verify that the NLIN is not additive Gaussian, but rather it depends strongly on the data transmitted in the channel of interest. In addition we validate the time-domain model numerically and demonstrate the strong dependence of the NLIN on the interfering channels' modulation format.

Random coupling between groups of degenerate fiber modes in mode multiplexed transmission.

We study random coupling induced crosstalk between groups of degenerate modes in spatially multiplexed optical transmission. Our analysis shows that the average crosstalk is primarily determined by the wavenumber mismatch, by the correlation length of the random perturbations, and by the coherence length of the degenerate modes, whereas the effect of a deterministic group velocity difference is negligible. The standard deviation of the crosstalk is shown to be comparable to its average value, implying that crosstalk measurements are inherently noisy.

Raman amplification in multimode fibers with random mode coupling.

We present the theory of Raman amplification in long multimode optical fibers, where strong random mode coupling within groups of quasi-degenerate modes is unavoidable. In such fibers, the signal components in modes that belong to the same strongly coupled group experience the same Raman amplification, where the differential gain is linearly dependent on the aggregate powers of the pump in each of the mode groups. The equations that we derive significantly facilitate the numerical and analytical study of Raman amplification in long multimode fibers.

Optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss.

We propose a space-time coding scheme designed to increase the tolerance of fiber-optic communications systems to polarization-dependent loss (PDL). A notable increase in the tolerable amount of average link PDL is achieved without affecting the complexity of the overall optical communications link. Other advantages include seamless integration with the broadly deployed blind equalization modules relying on the constant modulus algorithm.

Beneficial use of spectral broadening resulting from the nonlinearity of the fiber-optic channel.

We discuss the possibility of exploiting spectral broadening resulting from fiber nonlinearity for the transmission of information. The spectral broadening induced by nonlinearity combined with the appropriate waveform can turn quadrature amplitude modulation-like constellations into frequency-shift-keying constellations over a much larger dimension. Thus, the Kerr effect can be thought of as a large dimensional mapper/modulator. A simple single-span fiber-optic link implemented over dispersion shifted fiber is assumed for the demonstration of the principle. It is shown that for a particular constellation the achievable data rates in the presence of nonlinearity can be significantly higher than the capacity characterizing a linear channel with the same input bandwidth.

Coupled Manakov equations in multimode fibers with strongly coupled groups of modes.

We derive the fundamental equations describing nonlinear propagation in multi-mode fibers in the presence of random mode coupling within quasi-degenerate groups of modes. Our result generalizes the Manakov equation describing mode coupling between polarizations in single-mode fibers. Nonlinear compensation of the modal dispersion is predicted and tested via computer simulations.

Modeling the evolution of spatial beam parameters in parabolic index fibers.

We analyze the evolution of beam quality when propagating through a parabolic index (PI) fiber. The deterioration in beam quality is expressed in terms of the fiber parameters, and a methodology for minimizing the deterioration is presented. The fiber optimization procedure is evaluated numerically for an application where the PI fiber is used to deliver the signal produced by a tapered fiber-bundle beam combiner. It was demonstrated that delivery with no beam quality deterioration can be achieved with proper fiber design.

The underaddressed optical multiple-input, multiple-output channel: capacity and outage.

We study an optical space-division multiplexed system where the number of modes that are addressed by the transmitter and receiver is allowed to be smaller than the total number of optical modes supported by the fiber. This situation will be of relevance if, for instance, fibers supporting more modes than can be processed with current multiple-input, multiple-output technology are deployed with the purpose of future-proof installation. We calculate the ergodic capacity and the outage probability of the link and study their dependence on the number of addressed modes at the transmitter and receiver.

Nonlinear propagation in multi-mode fibers in the strong coupling regime.

We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.

Stokes-space analysis of modal dispersion in fibers with multiple mode transmission.

Modal dispersion (MD) in a multimode fiber may be considered as a generalized form of polarization mode dispersion (PMD) in single mode fibers. Using this analogy, we extend the formalism developed for PMD to characterize MD in fibers with multiple spatial modes. We introduce a MD vector defined in a D-dimensional extended Stokes space whose square length is the sum of the square group delays of the generalized principal states. For strong mode coupling, the MD vector undertakes a D-dimensional isotropic random walk, so that the distribution of its length is a chi distribution with D degrees of freedom. We also characterize the largest differential group delay, that is the difference between the delays of the fastest and the slowest principal states, and show that it too is very well approximated by a chi distribution, although in general with a smaller number of degrees of freedom. Finally, we study the spectral properties of MD in terms of the frequency autocorrelation functions of the MD vector, of the square modulus of the MD vector, and of the largest differential group delay. The analytical results are supported by extensive numerical simulations.