William C. K. Mak

Slowdown and splitting of gap solitons in apodized bragg gratings

Abstract We study the motion of gap solitons in two models of apodized nonlinear fibre Bragg gratings (BGs), with the local reflectivity k varying along the fibre. A single step of k, and a periodic array of alternating steps with opposite signs (a ‘Bragg superstructure’) are considered. These structures may be used in the design of various optical elements employing the gap solitons. A challenging possibility is to slow down and eventually halt the soliton by passing it through a step of increasing reflectivity; thus capturing a pulse of standing light. First, we develop an analytical approach, assuming adiabatic evolution of the soliton, and making use of the energy conservation and balance equation for the momentum. Comparison with simulations shows that the analytical approximation is quite accurate, unless the inhomogeneity is too narrow, or the step is too high: the soliton is either transmitted across the step or bounces back from it. If the step is narrow, systematic simulations demontrate that the soliton splits into transmitted and reflected pulses (splitting of a BG soliton which hits a chirped grating was observed in experiments). Moving through the periodic ‘superstructure’, the soliton accumulates distortion and suffers radiation loss if the structure is composed of narrow steps. The soliton moves without any loss or irreversible deformation through the array of sufficiently broad steps.

Solitary waves in asymmetric coupled waveguides with quadratic nonlinearity

Abstract By means of direct numerical methods, we study spatial solitons and their stability in a pair of asymmetric linearly coupled waveguides with intrinsic quadratic nonlinearity. Two cases are considered in detail, viz., when the coupling constants at the fundamental and second harmonics are equal, and when the coupling at the second harmonic is absent. These cases correspond to the physical situations in which the coupled waveguides are, respectively, closely or widely separated. Two different kinds of the asymmetry between the waveguides are considered. The first corresponds to a difference in the phase mismatch between the fundamental and second harmonics in the two cores. Unfoldings of the previously known bifurcation diagrams for the symmetric coupler are studied in detail, and the stability of different branches of the solutions are tested. Simulations of dynamical evolution of unstable solitons demonstrate a trend of their rearrangement into stable solitons coexisting with them. The second kind of asymmetry is the special case when one waveguide is linear, while the other one possesses quadratic nonlinearity. In contrast to the case when both waveguides are nonlinear, in this case the soliton solutions for the two limiting cases of closely and widely separated waveguides are not much different. All the solitons in this system are found to be stable. The obtained results, and especially bifurcations between solitons of different types, suggest straightforward applications to all-optical switching.

Analsysis of soliton interaction with local defects in fiber Bragg grating

The interaction of a fiber Bragg grating point like soliton with local defects has been thoroughly analyzed. The stability of trapped solitons has also been discussed. The main finding reveals the reversal of the sign of interaction from attraction to repulsion. It is also observed that the attraction depends on the accuracy of the numerical simulations.