Propagation Of Single Pulse Research Articles

The quadratically cubic Burgers equation: an exactly solvable nonlinear model for shocks, pulses and periodic waves

A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and generality of this QC nonlinearity are illustrated here by several examples and experimental results. The QC equation can be linearized and it describes the experimentally observed phenomena. Some of its exact solutions are given. It is shown that in a QC medium not only shocks of compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Single-pulse propagation is studied by computer modeling. The nonlinear evolutions of N- and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed.

Nonlinear Silicon Photonics: Analytical Tools

Since the recent demonstration of chip-scale, silicon-based, photonic devices, silicon photonics provides a viable and promising platform for modern nonlinear optics. The development and improvement of such devices are helped considerably by theoretical predictions based on the solution of the underlying nonlinear propagation equations. In this paper, we review the approximate analytical tools that have been developed for analyzing active and passive silicon waveguides. These analytical tools provide the much needed physical insight that is often lost during numerical simulations. Our starting point is the coupled-amplitude equations that govern the nonlinear dynamics of two optical waves interacting inside a silicon-on-insulator waveguide. In their most general form, these equations take into account not only linear losses, dispersion, and the free-carrier and Raman effects, but also allow for the tapering of the waveguide. Employing approximations based on physical insights, we simplify the equations in a number of situations of practical interest and outline techniques that can be used to examine the influence of intricate nonlinear phenomena as light propagates through a silicon waveguide. In particular, propagation of single pulse through a waveguide of constant cross section is described with a perturbation approach. The process of Raman amplification is analyzed using both purely analytical and semianalytical methods. The former avoids the undepleted-pump approximation and provides approximate expressions that can be used to discuss intensity noise transfer from the pump to the signal in silicon Raman amplifiers. The latter utilizes a variational formalism that leads to a system of nonlinear equations that governs the evolution of signal parameters under the continuous-wave pumping. It can also be used to find an optimum tapering profile of a silicon Raman amplifier that provides the highest net gain for a given pump power.

Coherent propagation of polaritons in the nonlinear optical regime

The propagation of light pulses through semiconductor heterostructures is studied under the combined influence of polariton effects and optical nonlinearities. For the investigated heterostructures, the light field strongly interacts with the excitonic resonances of the material which leads to a series of polariton resonances. Even in the linear optical regime, the theoretical description is distinctly complicated by the presence of surfaces and interfaces which prevents an analytical solution of the polariton problem. In the coherent nonlinear regime, dynamical changes of the polariton resonances and contributions of biexcitons will be addressed. For this purpose, we combine a microscopic treatment of the boundary problem for the optical interband excitations and the propagating light field in a sample of finite thickness with a description of excitonic and biexcitonic nonlinearities. A practicable scheme is developed to provide a self-consistent solution of generalized Schr\"odinger and Heitler-London equations for the excitonic and biexcitonic excitations, respectively, together with Maxwell's equations under strict consideration of the boundary conditions. To study the influence of excitonic and biexcitonic nonlinearities on single-pulse propagation, pump and probe transmission experiments, and four-wave mixing spectra, the dependence of the results on the light polarization is analyzed.

The effect of quintic nonlinearity on the propagation characteristics of dispersion managed optical solitons

The role of quintic nonlinearity on the propagation characteristics of optical solitons in dispersion managed optical communication systems has been presented in this paper. It has been shown that quintic nonlinearity has only marginal influence on single pulse propagation. However, numerical simulation has been undertaken to reveal that quintic nonlinearity reduces collision distance between neighbouring pulses of the same channel. It is found that for lower map strength the collapse distance between intra channel pulses is very much sensitive to the dispersion map strength.

Temporal and spectral properties of contra-propagating picosecond optical pulses in SOA

A useful analysis of contra-propagating optical pulses in semiconductor optical amplifier (SOA) is presented. Pulse temporal and spectral evolutions are investigated by resolving coupled equations describing pulse field propagation and SOA gain dynamics. With reference to the case of single pulse propagation, collision between pulses tends to maintain a good time-bandwidth product of amplified pulse and could provide a temporal compression by about 10% compared to pulse’s initial width.

A Numerical Study of the Light Bullets Interaction in the (2+1) Sine-Gordon Equation

The propagation and interaction in more than one space dimension of localized pulse solutions (so-called light bullets) to the sine-Gordon [SG] equation is studied both asymptotically and numerically. Similar solutions and their resemblance to solitons in integrable systems were observed numerically before in vector Maxwell systems. The simplicity of SG allows us to perform an asymptotic analysis of counterpropagating pulses, as well as a fully resolved computation over rectangular domains. Numerical experiments are carried out on single pulse propagation and on two pulse collision under different orientations. The particle nature, as known for solitons, persists in these two space dimensional solutions as long as the amplitudes of initial data range in a finite interval, similar to the conditions on the vector Maxwell systems.

Stable propagation of ultrashort optical pulses in modified higher-order nonlinear Schroedinger equation

Stable propagation of single ultrashort (subpicosecond or femtosecond) optical pulses and pulse trains is obtained in numerical solutions of a higher-order nonlinear Schroedinger equation with bandwidth limited amplification and nonlinear gain. It is shown that stable single pulse propagation can be achieved for a broad class of pulses with different initial shapes, and that pulse trains can propagate stably without interaction under certain conditions.

Single-channel transmission in dispersion management links in conditions of very strong pulse broadening: application to 40 Gb/s signals on step-index fibers

The dynamic behavior of single-channel transmission on standard fibers with strong dispersion management has been theoretically and numerically analyzed. A single pulse and a pseudorandom pulse sequence have been compared in order to highlight the relevant role played by pulse interaction. A semianalytical theory of the bandwidth evolution demonstrates that the introduction of prechirp is very important for controlling the single pulse propagation and numerical results show that such a chirp also permits to limit the nonlinear pulse interaction when other pulses are present. Simulations of a 40 Gb/s return-to-zero (RZ) system operating in links encompassing step-index fibers, by adopting a periodical compensation of the chromatic dispersion have been performed and results show that a record distance of 1300 km can be achieved with an amplifier spacing of 100 km. A compensation of the fiber third order dispersion would extend the transmission to 1800 km, which corresponds to the limits imposed by the amplified spontaneous emission (ASE) noise of the optical amplifiers.

Ultrafast Spectroscopy of Semiconductor Devices

In this work we present an experimental technique for investigating ultrafast carrier dynamics in semiconductor optical amplifiers at room temperature. These dynamics, influenced by carrier heating, spectral hole-burning and two-photon absorption, are very important for device applications in information processing at high data transfer rates. The technique is based on single pulse propagation through the device, with pulse duration tunable from 150fs to 11ps, and the characterization of the pulse at the output of the device by measuring the total pulse energy, the real time profile and the frequency spectrum. Results on a InGaAsP bulk amplifier are shown as an example.

Volterra series transfer function of single-mode fibers

A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems.

Pulse propagation in a randomly perturbed ocean: Single pulse statistics

A statistical theory of broadband single pulse propagation in a random ocean is presented. The mutual coherence function of the received signal is derived using an analysis based upon coupled mode theory. As propagation range increases, the combined effects of modal dispersion and random fluctuations spread the pulse and decompose it into a series of multiple arrivals.

Coupled Solitary Waves in Neurophysics

An analytic description of single pulse propagation on a single myelinated fiber is presented and multiple pulse solutions on a single fiber are described. A structural perturbation technique is developed to study the formation of "condensed pulse states" on fiber bundles. It is suggested that such condensed states may serve as a mechanism for the interaction of neural systems with weak (non-ionizing) electromagnetic fields.

Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses

We consider a reaction–diffusion system far from chemical equilibrium, with kinetics on multiple time scales and the capacity of attaining one or multiple homogeneous stable steady states. For such systems we present a theory of the structure (concentration profile) and velocity of fronts based on a matched asymptotic solution of the singular perturbation problem. We analyze single front (wave) propagation as a transition occurs from one stable stationary state to another; show the possibility of multiple mode front propagation; and discuss single pulse propagation in systems with one stable stationary state. For each process we confirm the theory by comparison with numerical solutions of the coupled differential equations for a model system. Finally, by application of the theory we discuss a reduction of the complexity of the stability analysis of these fronts.