Photonic potential for TM waves

We discuss the effective photonic potential for TM waves in inhomogeneous isotropic media. The model provides an easy and intuitive comprehension of form birefringence, paving the way for a new approach on the design of graded-index optical waveguides on nanometric scales. We investigate the application to nanophotonic devices, including integrated nanoscale wave plates and slot waveguides.Comment: 4 pages, 7 figure

Breather solitons in highly nonlocal media

We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.Comment: 7 pages, 4 figures, resubmitted to Physical Review

On Modal μ -Calculus and Gödel-Löb Logic

We show that the modal μ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modalμ ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formul

The modal μ-calculus hierarchy over restricted classes of transition systems

We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternation-free fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite model

Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics

We investigate electromagnetic propagation in uniaxial dielectrics with a transversely varying orientation of the optic axis, the latter staying orthogonal everywhere to the propagation direction. In such a geometry, the field experiences no refractive index gradients, yet it acquires a transversely-modulated Pancharatnam-Berry phase, that is, a geometric phase originating from a spin-orbit interaction. We show that the periodic evolution of the geometric phase versus propagation gives rise to a longitudinally-invariant effective potential. In certain configurations, this geometric phase can provide transverse confinement and waveguiding. The theoretical findings are tested and validated against numerical simulations of the complete Maxwell's equations. Our results introduce and illustrate the role of geometric phases on electromagnetic propagation over distances well exceeding the diffraction length, paving the way to a whole new family of guided waves and waveguides which do not rely on refractive index tailoring.Comment: 16 pages, 4 figure

Interplay between multiple scattering and optical nonlinearity in liquid crystals

We discuss the role played by time-dependent scattering on light propagation in liquid crystals. In the linear regime, the effects of the molecular disorder accumulate in propagation, yielding a monotonic decrease in the beam spatial coherence. In the nonlinear case, despite the disorder-imposed Brownian-like motion to the self-guided waves, self-focusing increases the spatial coherence of the beam by inducing spatial localization. Eventually, a strong enhancement in the beam oscillations occurs when power is strong enough to induce self-steering, i.e. in the non-perturbative regime.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Temporal dynamics of light-written waveguides in unbiased liquid crystals

The control of light by light is one of the main aims in modern photonics. In this context, a fundamental cornerstone is the realization of light-written waveguides in real time, resulting in all-optical reconfigurability of communication networks. Light-written waveguides are often associated with spatial solitons, that is, non-diffracting waves due to a nonlinear self-focusing effect in the harmonic regime. From an applicative point of view, it is important to establish the temporal dynamics for the formation of such light-written guides. Here we investigate theoretically the temporal dynamics in nematic liquid crystals, a material where spatial solitons can be induced using continuous wave (CW) lasers with few milliWatts power. We fully address the role of the spatial walk-off and the longitudinal nonlocality in the waveguide formation. We show that, for powers large enough to induce light self-steering, the beam undergoes several fluctuations before reaching the stationary regime, in turn leading to a much longer formation time for the light-written waveguide.Comment: 11 pages, 11 figure

Guiding light via geometric phases

Known methods for transverse confinement and guidance of light can be grouped into a few basic mechanisms, the most common being metallic reflection, total internal reflection and photonic-bandgap (or Bragg) reflection. All of them essentially rely on changes of the refractive index, that is on scalar properties of light. Recently, processes based on "geometric Berry phases", such as manipulation of polarization states or deflection of spinning-light rays, have attracted considerable interest in the contexts of singular optics and structured light. Here, we disclose a new approach to light waveguiding, using geometric Berry phases and exploiting polarization states and their handling. This can be realized in structured three-dimensional anisotropic media, in which the optic axis lies orthogonal to the propagation direction and is modulated along it and across the transverse plane, so that the refractive index remains constant but a phase distortion can be imposed on a beam. In addition to a complete theoretical analysis with numerical simulations, we present a proof-of-principle experimental demonstration of this effect in a discrete element implementation of a geometric phase waveguide. The mechanism we introduce shows that spin-orbit optical interactions can play an important role in integrated optics and paves the way to an entire new class of photonic systems that exploit the vectorial nature of light.Comment: Publication supported by European Union (EU) within Horizon 2020 - ERC-Advanced Grant PHOSPhOR, grant no. 694683. This is the final peer-reviewed manuscript as accepted for publication (including methods and supplementary information

Self-trapping of light using the Pancharatnam-Berry phase

Since its introduction by Berry in 1984, the geometric phase has become of fundamental importance in physics, with applications ranging from solid-state physics to optics. In optics, the Pancharatnam-Berry phase allows the tailoring of optical beams by a local control of their polarization. Here, we discuss light propagation in the presence of an intensity-dependent local modulation of the Pancharatnam-Berry phase. The corresponding self-modulation of the wave front counteracts the natural spreading due to diffraction; i.e., self-focusing takes place. No refractive index variation is associated with the self-focusing: The confinement is uniquely due to a nonlinear spin-orbit interaction. The phenomenon is investigated, both theoretically and experimentally, by considering the reorientational nonlinearity in liquid crystals, where light is able to rotate the local optical axis through an intensity-dependent optical torque. Our discoveries pave the way to the investigation of a new family of nonlinear waves featuring a strong interaction between the spin and the orbital degrees of freedom