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We examine a possibility to exploit the nonlinear lens effect-the initial stage of self-focusing to localize initially broad field distribution into the small central area where wave collapse is arrested-the nonlinear beam tapering. We describe two-dimensional localized solitary waves (ring solitons) in a physical system that presents a linear medium in the central core, surrounded by the cladding with the focusing Kerr nonlinearity. The standard variational analysis demonstrates that such solitons correspond to the minimum of the Hamiltonian.
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We report on the thermalization of light carrying orbital angular momentum in multimode optical fibers, induced by nonlinear intermodal interactions. A generalized Rayleigh-Jeans distribution of asymptotic mode composition is obtained, based on the conservation of the angular momentum. We confirm our predictions by numerical simulations and experiments based on holographic mode decomposition of multimode beams. Our work establishes new constraints for the achievement of spatial beam self-cleaning, giving previously unforeseen insights into the underlying physical mechanisms.
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The nonlinear Fourier transform (NFT) is used to characterize the optical combs in the Lugiato-Lefever equation with both anomalous and normal dispersion. We demonstrate that the NFT signal processing technique can simplify analysis of the formation of dissipative dark solitons and regimes exploiting modulation instability for a generation of coherent structures, by approximating the comb with several discrete eigenvalues, providing a platform for the analytical description of dissipative coherent structures.
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We investigate nonlinear transmission regimes of a polarization-multiplexed 16-quadrature amplitude modulation (PDM-16-QAM) orthogonal frequency-division multiplexed (OFDM) signal in a long-haul optical link. We study the dependence between the strength of nonlinear distortion and statistical properties of a PDM-OFDM signal. We also consider the constellation shaping-based solutions that allow to significantly reduce the bit error rate (up to three to 12 times at the cost of 5%-20% signal redundancy) and propose a method to analytically optimize the symbol distribution for higher-order modulation formats using only the initial signal.
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Raman dissipative solitons (RDS) have been investigated numerically. It was found that the area of stable generation is bounded in terms of pump spectral bandwidth and pulse energy. Existing optimum is strongly affected by the net cavity dispersion. The spectral bandwidth of the generated RDS linearly depends on its energy and reaches more than 50 nm in the 5-meters long cavity. Developed numerical model reproduces all the effects observed experimentally. It predicts ability to generate high-quality pulses with energy up to 6 nJ compressible down to â¼100 fs duration. The work shows that RDS generation technique can produce high-energy ultrashort pulses at wavelengths not covered by typical active mediums.
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A two-level iterative algorithm for finding stationary solutions of coupled nonlinear Schrödinger equations describing the propagation dynamics of an electromagnetic pulse in multimode and multicore optical fibers of various structures was developed and tested. Using as an example the proposed analytical soliton solution which is localized in space and time, test calculations were performed, and the convergence of the algorithm was demonstrated.
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Using the cubic Ginzburg-Landau equation as an example, we demonstrate how the inverse scattering transform can be applied to characterize coherent structures in dissipative nonlinear systems. Using this approach one can reduce the number of the effective degrees of freedom in the system when the dynamic is dominated by the coherent structures, even if they are embedded in the dispersive waves and demonstrate unstable behavior.
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We show that Kerr beam self-cleaning results from parametric mode mixing instabilities that generate a number of nonlinearly interacting modes with randomized phases-optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is an analogue to wave condensation that is well known in hydrodynamic 2D turbulence.
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Visualisation of complex nonlinear equation solutions is a useful analysis tool for various scientific and engineering applications. We have re-examined the geometrical interpretation of the classical nonlinear four-wave mixing equations for the specific scheme of a phase sensitive one-pump fiber optical parametric amplification, which has recently attracted revived interest in the optical communications due to potential low noise properties of such amplifiers. Analysis of the phase portraits of the corresponding dynamical systems provide valuable additional insight into field dynamics and properties of the amplifiers. Simple geometric approach has been proposed to describe evolution of the waves, involved in phase-sensitive fiber optical parametric amplification (PS-FOPA) process, using a Hamiltonian structure of the governing equations. We have demonstrated how the proposed approach can be applied to the optimization problems arising in the design of the specific PS-FOPA scheme. The method considered here is rather general and can be used in various applications.
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We propose a general analytical method for estimation of the saturable absorber output energy as a function of the input energy. The method is based on a representation of the saturable absorber output energy as a series of powers of the recovery time. We also derive a simplified expression of the saturable absorber output energy that gives a good approximation for large input energies. The analytical results are verified by the numerical simulation. The results have been applied to the particular cases of an input function that include the Gaussian input pulse and the hyperbolic secant input pulse. We show that the analytical results can improve the prediction of the output energy in the fiber lasers.