Discrete Solitons in Waveguide Arrays with Long-Range Linearly Coupled Effect

Abstract

We study the influences to the discrete soliton (DS) by introducing linearly long-range nonlocal interactions, which give rise to the off-diagonal elements of the linearly coupled matrix in the discrete nonlinear schrodinger equation to be filled by non-zero terms. Theoretical analysis and numerical simulations find that the DS under this circumstance can exhibit strong digital effects: the fundamental DS is a narrow one, which occupies nearly only one waveguide, the dipole and double-monopole solitons, which occupy two waveguides, can be found in self-focusing and -defocusing nonlinearities, respectively. Stable flat-top solitons and their stagger counterparts, which occupy a controllable number of waveguides, can also be obtained through this system. Such digital properties may give rise to additional data processing applications and have potential in fabricating digital optical devices in all-optical networks.

Solitary vortices in two-dimensional waveguide matrix

“…According to the standard coupled mode theory, 51,52 if we fix the distance between the two adjacent lattice sites to be 4 µm, the coupling coefficient between them would be 3.6 mm −1 . 52 If we fix this coefficient to 1 in Eq. (2.1), we could estimate the real-scale value for the normalized coupled coefficient C, the unit for the total power.…”

Two-dimensional discrete Anderson location in waveguide matrix

“…[11][12][13][14][15] Guided propagation of light in such arrays emulates electronic wave functions in fundamental periodic and disordered potentials of solid state physics. Therefore, discrete arrays of optical waveguides may be used to implement photonic counterparts of semiconductor devices used in electronic circuits.…”

Dark Solitons and Grey Solitons in Waveguide Arrays with Long-Range Linear Coupling Effects

“…Long-range coupling is different from that of the conventional waveguide arrays, which only consider the coupling between the adjacent waveguides (i.e., the short-range coupling). We have designed such a waveguide array with long-range coupling and studied the formation of bright solitons-see our previous paper in [17]. In this work, we further study the dynamics of dark and grey solitons in such a waveguide array, which was not considered before.…”

“…The relationship between the scaled parameters in Equation (1) and the real-scale parameters are given in [17] in detail.…”

“…In [17], we designed a scheme for an optics experiment to apply our model of long-range linear coupling waveguide arrays. The model is built based on an AlGaAs single-mode waveguide structure.…”