Adrian Ankiewicz

Stable soliton pairs in optical transmission lines and fiber lasers

Optical-fiber transmission of pulses can be modeled with the complex Ginzburg–Landau equation. We find novel stable soliton pairs and trains, which are relevant in this case, and analyze them. We suggest that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations, rather than by equations of standard perturbation theory. We present a two-dimensional phase plane (interaction plane) for analyzing the stability properties and general dynamics of two-soliton solutions of the Complex Ginzburg–Landau equation.

Coupling between parallel optical fiber cores--Critical examination

The well-known perturbation theory for weakly guiding couplers of the polished kind is compared with exact numerical results, and found to be highly accurate, even when the cores touch. An investigation is made into the form birefringence of this type of coupler and various properties of its normal modes, including the fraction of modal power propagating within the cores.

Does the nonlinear Schrodinger equation correctly describe beam propagation

The parabolic equation (nonlinear Schrödinger equation) that appears in problems of stationary nonlinear beam propagation (self-focusing) is reconsidered. It is shown that an additional term, which involves changes of the propagation constant along the propagation direction, should be taken into account. The physical consequences of this departure from the standard approximation, which uses the parabolic equation, are discussed. A numerical simulation showing the difference between the new approach and the standard nonlinear Schrödinger equation is given as an example.

Rogue waves, rational solutions, the patterns of their zeros and integral relations

The focusing nonlinear Schrodinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.

Geometric optics approach to light acceptance and propagation in graded index fibres

The methods of geometric optics are applied to light acceptance and propagation in graded index fibres. The symmetry of the basic ray equations reveals ray path invariants. Rays are classified into bound, tunnelling and refracting rays. The role of source properties in exciting different ray types is analysed. Pulses are considered in terms of absolute widths, r.m.s. widths and complete shape detail. Optimization formulae are obtained. The incorporation of attenuation mechanisms is described and the effects of an absorbing core are analysed in detail.

Optical fiber couplers-optimum solution for unequal cores

A concise scalar theory is developed for parallel fibers that are weakly coupled through their evanescent fields, providing the simplest description of optical crosstalk. The scalar theory is the most accurate framework possible because the weak coupling approximation is inconsistent unless restricted to couplers that are weakly guiding. The optimum solution is found using a standard variational method and this solution is shown to be identical to that of conventional perturbation or coupled-mode methods. Expressions are given for lossy couplers and for crosstalk between significantly different cores. >

Dissipative soliton resonances in laser models with parameter management

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. We have found that the DSR phenomenon is robust and does not disappear when perturbations are introduced into the model. In particular, parameter management is benign to DSR: the resonance property remains intact even when a pulse experiences periodic changes of system parameters in a laser cavity. We also show that high energy pulses emerging from a laser cavity can be compressed to shorter durations with the help of linear dispersive devices.

Generalized Gaussian approximation for single-mode fibers

A variational method is presented that generalizes well-known Gaussian method for single-mode fibers. This method uses only simple elementary functions to approximate the fundamental mode fields. By applying it to practical cases such as step index and clad parabolic index fibers, where exact solutions can be found, it is demonstrated that the method is essentially simple and that it is accurate for the analysis of single-mode fibers and devices. This approximation provides much better eigenvalues and, in particular, evanescent fields than the traditional Gaussian. Significantly, the present approximations range of applicability covers the whole single-mode range, while being only slightly more complicated than the modified Gaussian method. >

ULTRASHORT PULSES GENERATED BY MODE-LOCKED LASERS WITH EITHER A SLOW OR A FAST SATURABLE-ABSORBER RESPONSE

We present a new exact solution for ultrashort pulses generated by passively mode-locked lasers, taking into account the slow and the fast parts of the semiconductor saturable-absorber response in the nonsaturated limit.

Multi-soliton complexes

In this paper we introduce the concept of multi-soliton complexes (MSC). A particular example of a MSC is an incoherent soliton in a multimode fiber or in a photorefractive crystal, but there are many examples in other areas of physics. We discuss a variety of profiles of MSCs, their unusual collisional properties, the possibility of a MSC on a background and some other interesting properties of MSCs. Some of their features are also shared by single solitons, but there are many differences between the properties of the two types. (c) 2000 American Institute of Physics.