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

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

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

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

New type of guided waves in birefringent media

The existence of waves guided by thin dielectric films deposited over a positive birefringent crystal for waveguide parameters below usual cutoff is discussed. This additional kind of guided wave has a hybrid nature and occurs in properly tailored waveguides when a suitable orientation of the crystal optical axis, relative to the waveguide axis, is taken. The dependence of the allowed orientations on various waveguide parameters has been analyzed. Noticeable fast variations, with potential interest for switching applications, have been found.Peer ReviewedPostprint (published version

Nano Guiding of Light Using Dyakonov Waves

Postprint (published version

Robust ultrashort light bullets in strongly twisted waveguide arrays

We introduce a new class of stable light bullets that form in twisted waveguide arrays pumped with ultrashort pulses, where twisting offers a powerful knob to tune the properties of localized states. We find that, above a critical twist, three-dimensional wave packets are unambiguously stabilized, with no minimum energy threshold. As a consequence, when the higher-order perturbations that accompany ultrashort pulse propagation are at play, the bullets dynamically adjust and sweep along stable branches. Therefore, they are predicted to feature an unprecedented experimental robustness.Peer ReviewedPostprint (published version

Anisotropy-induced photonic bound states in the continuum

Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction1, 2, 3 and early observations in acoustic systems4, such states have been demonstrated recently in photonic structures with engineered geometries5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. Here, we put forward a mechanism, based on waveguiding structures that contain anisotropic birefringent materials, that affords the existence of BICs with fundamentally new properties. In particular, anisotropy-induced BICs may exist in symmetric as well as in asymmetric geometries; they may form in tunable angular propagation directions; their polarization may be pure transverse electric, pure transverse magnetic or full vector with tunable polarization hybridity; and they may be the only possible bound states of properly designed structures, and thus appear as a discrete, isolated bound state embedded in a whole sea of radiative states.Peer ReviewedPostprint (author's final draft

Transition from Dirac points to exceptional points in anisotropic waveguides

We uncover the existence of Dirac and exceptional points in waveguides made of anisotropic materials, and study the transition between them. Dirac points in the dispersion diagram appear at propagation directions where the matrix describing the eigenvalue problem for bound states splits into two blocks, sorting the eigenmodes either by polarization or by inner mode symmetry. Introducing a non-Hermitian channel via a suitable leakage mechanism causes the Dirac points to transform into exceptional points connected by a Fermi arc. The exceptional points arise as improper hybrid leaky states and, importantly, are found to occur always out of the anisotropy symmetry planes.Peer ReviewedPostprint (published version