Robustness of Quadratic Solitons with Periodic Gain

We address the robustness of quadratic solitons with periodic non-conservative perturbations. We find the evolution equations for guiding-center solitons under conditions for second-harmonic generation in the presence of periodic multi-band loss and gain. Under proper conditions, a robust guiding-center soliton formation is revealed.Comment: 5 pages, 5 figures, submitted to Optics Communicatio

Vortex nucleation and evolution in parametric wave mixing

We predict a variety of new phenomena, that includes the spontaneous nucleation of multiple vortex twins, vortex rotation and drift, vortex-antivortex interaction and annihilation, and formation of quasi-aligned patterns of single-charge vortices. We consider cw light propagation in a bulk quadratic nonlinear crystal under conditions for type I second-harmonic generation. We restrict ourselves to up-conversion geometries with material and light conditions that yield negligible depletion of the pump fundamental frequency (FF) beam. Then, the second-harmonic (SH) beam is dictated by an inhomogeneous linear partial differential equation whose general solution can be obtained by means of the Green function approach. In the case of un-seeded geometries (i.e., no SH input light), and in absence of Poynting vector walk-off between the FF and SH beams, sum- and difference-charge arithmetic operations have been predicted and observed experimentally. However, a new range of phenomena is discovered in seeded geometries and with Poynting vector walk-off. In particular, in the case of seeded schemes without walk-off, our numerical and experimental investigations show the spontaneous nucleation of multiple-vortex twins. In such case, the number of vortices present in the SH beam and its total topological charge varies with the propagation distance inside the crystal.Peer ReviewedPostprint (published version

Similarity rules for nonlinear Kerr-like slab optical waveguides

It is shown that the stationary waveguiding properties of TE guided waves in a slab optical waveguide with a nonlinear Kerr-like bounding medium can be described in a compact way by means of the usual normalized effective modal index (b) and a set of only four independent normalized parameters: the well-known normalized thickness (V) and asymmetry measure (a) of the waveguide, the generalized aspect ratio between film and substrate refractive indexes, and a guided power measure. From an analysis starting on Buckingham's II-theorem, the similarity rules existing between the above waveguiding structures have been investigated. Allowed and forbidden regions in (b,V,a)-space in order that a guided solution exists have been recognized and classified, with the marginal loci separating different regions being a function of only V and a.Peer ReviewedPostprint (published version

Engineering of spatial solitons in two-period QPM structures

We report on a scheme which might make it practically possible to engineer the effective competing nonlinearities that on average govern the light propagation in quasi-phase-matching (QPM) gratings. Modulation of the QPM period with a second longer period, introduces an extra degree of freedom, which can be used to engineer the effective quadratic and induced cubic nonlinearity. However, in contrast to former work here we use a simple phase-reversal grating for the modulation, which is practically realizable and has already been fabricated. Furthermore, we develop the theory for arbitrary relative lengths of the two periods and we consider the effect on solitons and the bandwidth for their generation. We derive an expression for the bandwidth of multicolor soliton generation in two-period QPM samples and we predict and confirm numerically that the bandwidth is broader in the two-period QPM sample than in homogeneous structures.Comment: V1: 15 pages, 8 figures. V2: Accepted for publication in Optics Communications.16 pages, 10 figures. New soliton content figures, confirming the theoretically predicted peak splitting in 2-period QPM, have been include

Universal diagrams for te waves guided by thin films bounded by saturable nonlinear media

It is shown that universal V-b diagrams provide a powerful tool when analyzing the stationary waveguiding properties of the TE waves guided by a thin film bounded by a saturable nonlinear substrate or cladding. For a wide class of nonlinearities, the allowed and forbidden regions of these diagrams, for a stationary guided propagation to occur, display a universal pattern, the marginal loci separating different allowed regions from the forbidden ones being simple functions of only the asymmetry measure of the waveguide and the saturation value of the nonlinear permittivity. Relevant information for device design purposes is summarized on a few diagrams, so general waveguiding properties can be immediately read-off from them, and threshold power-independent values of the normalized thickness of the waveguide for a particular kind of guided wave to be allowed are obtained. Qualitative information concerning both the guided power and the stability of guided waves is also included in the diagrams.Peer ReviewedPostprint (published version

Solitary waves due to x(2):x(2) cascading

Solitary waves in materials with a cascaded x(2):x(2) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the x(2):x(2) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrödinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrödinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrödinger-equation solitons, which are a two-parameter family of solutions. Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.Peer ReviewedPostprint (published version

Vector mixed-gap surface solitons

We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from different gaps of lattice spectrum and their mutual trapping results in the formation of stable vector states. The unstable soliton component is stabilized by the cross-coupling with the stable component. We show that vector mixed-gap surface solitons exhibit a new combination of properties of vectorial surface waves and gap solitons.Comment: 7 pages, 4 figures, to appear in Optics Expres

Highly-asymmetric soliton complexes in parabolic optical lattices

We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry-breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.Comment: 12 pages, 4 figures, to appear in Optics Letter

Light beam dynamics in materials with radially-inhomogeneous thermal conductivity

We study the properties of bright and vortex solitons in thermal media with nonuniform thermal conductivity and homogeneous refractive index, whereby the local modulation of the thermal conductivity strongly affects the entire refractive index distribution. While regions where the thermal conductivity is increased effectively expel light, self-trapping may occur in the regions with reduced thermal conductivity, even if such regions are located close to the material boundary. As a result, strongly asymmetric self-trapped beams may form inside a ring with reduced thermal conductivity and perform persistent rotary motion. Also, such rings are shown to support stable vortex solitons, which may feature strongly non-canonical shapes.Comment: 4 pages, 5 figures, to appear in Optics Letter