Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

Chirped self-similar solitary waves for the generalized nonlinear Schrödinger equation with distributed two-power-law nonlinearities

We investigate the propagation characteristics of the chirped self-similar solitary waves in non-Kerr nonlinear media within the framework of the generalized nonlinear Schrödinger equation with distributed dispersion, two-power-law nonlinearities, and gain or loss. This model contains many special types of nonlinear equations that appear in various branches of contemporary physics. We extend the self-similar analysis presented for searching chirped self-similar structures of the cubic model to a more general problem involving two nonlinear terms of arbitrary power. A variety of exact linearly chirped localized solutions with interesting properties are derived in the presence of all physical effects. The solutions comprise bright, kink and antikink, and algebraic solitary wave solutions, illustrating the potentially rich set of self-similar pulses of the model. It is shown that these optical pulses possess a linear chirp that leads to efficient compression or amplification, and thus are particularly useful in the design of optical fiber amplifiers, optical pulse compressors, and solitary wave based communication links. Finally, the stability of the self-similar solutions is discussed numerically under finite initial perturbations.

Excitation of Peregrine-Type Waveforms from Vanishing Initial Conditions in the Presence of Periodic Forcing

We show by direct numerical simulations that spatiotemporally localised waveforms, strongly reminiscent of the Peregrine rogue wave, can be excited by vanishing initial conditions for the periodically driven nonlinear Schrödinger equation. The emergence of the Peregrine-type waveforms can be potentially justified, in terms of the existence and modulational instability of spatially homogeneous solutions of the model and the continuous dependence of the localised initial data for small time intervals. We also comment on the persistence of the above dynamics, under the presence of small damping effects, and justify that this behaviour should be considered as far from approximations of the corresponding integrable limit.

Controlling chaotic spin-motion entanglement of ultracold atoms via spin-orbit coupling

We study the spatially chaoticity-dependent spin-motion entanglement of a spin-orbit (SO) coupled Bose-Einstein condensate with a source of ultracold atoms held in an optical superlattice. In the case of phase synchronization, we analytically demonstrate that (a) the SO coupling (SOC) leads to the generation of spin-motion entanglement; (b) the area of the high-chaoticity parameter region inversely relates to the SOC strength which renormalizes the chemical potential; and (c) the high-chaoticity is associated with the lower chemical potential and the larger ratio of the short-lattice depth to the longer-lattice depth. Then, we numerically generate the Poincaré sections to pinpoint that the chaos probability is enhanced with the decrease in the SOC strength and/or the spin-dependent current components. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. For an appropriate lattice depth ratio, the complete stop of one of (or both) the current components is related to the full chaoticity. The results mean that the weak SOC and/or the small current components can enhance the chaoticity. Based on the insensitivity of chaos probability to initial conditions, we propose a feasible scheme to manipulate the ensemble of chaotic spin-motion entangled states, which may be useful in coherent atom optics with chaotic atom transport.

Solitons in the nonlinear Schrödinger equation with two power-law nonlinear terms modulated in time and space

A nonlinear Schrödinger equation that includes two terms with power-law nonlinearity and external potential modulated both on time and on the spatial coordinates is considered. The model appears in various branches of contemporary physics, especially in the case of lower values of the nonlinearity power. A significant generalization of the similarity transformations approach to construct explicit localized solutions for the model with arbitrary power-law nonlinearities is introduced. We obtain the exact analytical bright and kink soliton solutions of the governing equation for different nonlinearities and potentials that are of particular interest in applications to Bose-Einstein condensates and nonlinear optics. Necessary conditions on the physical parameters for propagating envelope formation are presented. The obtained results can be straightforwardly applied to a large variety of nonlinear Schrödinger models and hence would be of value to understand nonlinear phenomena in a diversity of nonlinear media.

Radiating subdispersive fractional optical solitons

It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.