The (n+1)/2 rule for dealiasing in the split-step Fourier methods for n-wave interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (n+1)/2, where n is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(n+1) fraction of each spectral dimension

Nonlinear propagation of an optical speckle field

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010) ].. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates

Stationary scattering from a nonlinear network

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multi-stability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.Comment: 4 pages, 4 figure

Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state

Invited Article: Visualisation of extreme value events in optical communications

Fluctuations of a temporal signal propagating along long-haul transoceanic scale fiber links can be visualised in the spatio-temporal domain drawing visual analogy with ocean waves. Substantial overlapping of information symbols or use of multifrequency signals leads to strong statistical deviations of local peak power from an average signal power level. We consider long-haul optical communication systems from this unusual angle, treating them as physical systems with a huge number of random statistical events, including extreme value fluctuations that potentially might affect the quality of data transmission. We apply the well-established concepts of adaptive wavefront shaping used in imaging through turbid medium to detect the detrimental phase modulated sequences in optical communications that can cause extreme power outages (rare optical waves of ultra-high amplitude) during propagation down the ultra-long fiber line. We illustrate the concept by a theoretical analysis of rare events of high-intensity fluctuations—optical freak waves, taking as an example an increasingly popular optical frequency division multiplexing data format where the problem of high peak to average power ratio is the most acute. We also show how such short living extreme value spikes in the optical data streams are affected by nonlinearity and demonstrate the negative impact of such events on the system performance

Nonlinear spectral management:linearization of the lossless fiber channel

Using the integrable nonlinear Schrodinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called eigenvalue communication idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed

Temporal solitonic crystals and non-Hermitian informational lattices

Clusters of temporal optical solitons—stable self-localized light pulses preserving their form during propagation—exhibit properties characteristic of that encountered in crystals. Here, we introduce the concept of temporal solitonic information crystals formed by the lattices of optical pulses with variable phases. The proposed general idea offers new approaches to optical coherent transmission technology and can be generalized to dispersion-managed and dissipative solitons as well as scaled to a variety of physical platforms from fiber optics to silicon chips. We discuss the key properties of such dynamic temporal crystals that mathematically correspond to non-Hermitian lattices and examine the types of collective mode instabilities determining the lifetime of the soliton train. This transfer of techniques and concepts from solid state physics to information theory promises a new outlook on information storage and transmission