NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.

Nonlinear inverse synthesis technique for optical links with lumped amplification

The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless pathaveraged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital backpropagation.

On the theory of autosoliton propagation in optical fibers guided by in-line nonlinear devices

A theoretical model is developed to describe the propagation of ultra-short optical pulses in fiber transmission systems in the quasi-linear regime, with periodically inserted in-line lumped nonlinear optical devices. Stable autosoliton solutions are obtained for a particular application of the general theory.

Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Modeling of CW Yb-doped fiber lasers with highly nonlinear cavity dynamics

We develop a theoretical framework for modeling of continuous wave Yb-doped fiber lasers with highly nonlinear cavity dynamics. The developed approach has shown good agreement between theoretical predictions and experimental results for particular scheme of Yb-doped laser with large spectral broadening during single round trip. The model is capable to accurately describe main features of the experimentally measured laser outputs such as power efficiency slope, power leakage through fibre Bragg gratings, spectral broadening and spectral shape of generated radiation. © 2011 Optical Society of America.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Perception of global image contrast is predicted by the same spatial integration model of gain control as detection and discrimination

How are the image statistics of global image contrast computed? We answered this by using a contrast-matching task for checkerboard configurations of ‘battenberg’ micro-patterns where the contrasts and spatial spreads of interdigitated pairs of micro-patterns were adjusted independently. Test stimuli were 20 × 20 arrays with various sized cluster widths, matched to standard patterns of uniform contrast. When one of the test patterns contained a pattern with much higher contrast than the other, that determined global pattern contrast, as in a max() operation. Crucially, however, the full matching functions had a curious intermediate region where low contrast additions for one pattern to intermediate contrasts of the other caused a paradoxical reduction in perceived global contrast. None of the following models predicted this: RMS, energy, linear sum, max, Legge and Foley. However, a gain control model incorporating wide-field integration and suppression of nonlinear contrast responses predicted the results with no free parameters. This model was derived from experiments on summation of contrast at threshold, and masking and summation effects in dipper functions. Those experiments were also inconsistent with the failed models above. Thus, we conclude that our contrast gain control model (Meese & Summers, 2007) describes a fundamental operation in human contrast vision.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.

Modeling 2R regenerator based on High Nonlinear Dispersion Imbalanced Loop Mirror (HN-DILM)

The model of Reshaping and Re-amplification (2R) regenerator based on High Nonlinear Dispersion Imbalanced Loop Mirror (HN-DILM) has been designed to examine its capability to reduce the necessary of fiber loop length and input peak power by deploying High Non linear Fiber (HNLF) compared to Dispersion Shifted Fiber (DSF). The simulation results show by deployed a HNLF as a nonlinear element in Dispersion Imbalanced Loop Mirror (DILM) requires only 400mW peak powers to obtain a peak of transmission compared to DSF which requires a higher peak power at 2000mW to obtain a certain transmissivity. It also shows that HNLF required shorter fiber length to achieve the highest transmission. The 2R regenerator also increases the extinction ratio (ER) of the entire system. © 2010 IEEE.