Switching of discrete optical solitons in engineered waveguide arrays

Fractional discrete vortex solitons

We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, to the best of our knowledge, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent $\alpha$, becoming effectively long range at small $\alpha$ values. At long distance, it can be shown that this coupling decreases faster than exponentially: $\sim\exp (- |{\textbf{n}}|)/\sqrt {|n|}$. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower power levels, as the $\alpha$ coefficient diminishes, independently of their topological charge and/or pattern distribution.

Solitons in a modified discrete nonlinear Schrödinger equation

We study the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls-Nabarro barrier, facilitating in this way a degree of soliton steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The qualitative similarity of the results for the mDNLS to the ones obtained for the standard DNLS, suggests that this kind of discrete soliton is an robust entity capable of transporting an excitation across a generic discrete medium that models several systems of interest.

Analytical first-order extension of coupled-mode theory for waveguide arrays

Coupled mode theory for waveguide arrays is extended to next-nearest neighbor interactions using propagation equations. Both lateral diffraction and propagation of Floquet-Bloch waves are altered respectively by extra coupling and non-orthogonality between isolated waveguide modes. The analytical formula describing the distortions of the diffraction relation is validated by direct numerical simulation for weakly coupled InP and GaAs shallow ridge waveguides and for strongly coupled Si-SiO(2) buried strip waveguides. The impact of extended coupled mode theory on propagation and diffraction design in waveguide arrays is discussed with reference to available experimental work.

Confining light flow in weakly coupled waveguide arrays by structuring the coupling constant: towards discrete diffractive optics

Structuring the coupling constant in coupled waveguide arrays opens up a new route towards molding and controlling the flow of light in discrete structures. We show coupled mode theory is a reliable yet very simple and practical tool to design and explore new structures of patterned coupling constant. We validate our simulation and technological choices by successful fabrication of appropriate III-V semiconductor patterned waveguide arrays. We demonstrate confinement of light in designated areas of one-dimensional semi-conductor waveguide arrays.

Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides

We demonstrate that an array of discrete waveguides on a slab substrate, both featuring chi2 nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite soliton are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found, too. In contrast with the usual systems, the intersite-centered fundamental solitons and bound states with the twisted continuous components are stable over almost the entire domain of their existence.

Polarization instability, steering, and switching of discrete vector solitons

We study the dynamics of discrete vector solitons in arrays of weakly coupled birefringent optical waveguides with cubic nonlinear response. We start with a modulational instability analysis, followed by approximate analytical solutions in the form of strongly localized modes. Next, we compute the effective Peierls-Nabarro potential for these modes and obtain the spatial average of the power transfer between both polarizations modes as a function of their relative phase. Finally, we combine the concepts of polarization mode instability with discreteness-induced beam trapping by the array, and demonstrate numerically the amplification of a weak signal by a strong pump of the other polarization, combined with simultaneous discretized all-optical switching.

Discrete light propagation and self-trapping in liquid crystals

We investigate light propagation and self-localization in a voltage-controlled array of channel waveguides realized in undoped nematic liquid crystals. We report on discrete diffraction and solitons, as well as all-optical angular steering and the formation of multiband vector breathers. The results and are in excellent agreement with both coupled mode theory and full numerical simulations.