All known methods for transverse confinement and guidance of light rely on modification of refractive index, that is, on the scalar properties of electromagnetic radiation 1-11 . Here we disclose a concept of dielectric waveguide which exploits vectorial spin-orbit interactions of light and the resulting geometric phases [12][13][14][15][16][17] . The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. Besides theoretical analysis we present an experimental demonstration of the guiding using a series of discrete geometric-phase lenses made from liquid-crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.Published in Nature Photonics, vol. 10, 571-575 (2016). DOI: 10.1038/NPHOTON.2016 Waveguides are central to modern photonics and optical communications. Besides the standard optical fibres -based on total internal reflection (TIR) and gradedindex (GRIN) refractive potential-and the hollow-metalpipes for microwaves 1 , several more complex structures have been investigated, ranging from photonicbandgap systems 2-5 to "slot" waveguides 6 , plasmonic waveguides 7 , coupled-resonators 8,9 , grating-mediated 10 and Kapitza-effect waveguides 11 . Despite such variety, all light-guiding mechanisms investigated hitherto rely on variations, sudden or gradual, of the refractive index or -generally-the dielectric permittivity. Even when anisotropic materials are employed to realize waveguides, as for example in liquid crystals 18 , light confinement is based on the transverse modulation of the refractive index experienced by extraordinary waves through the nonuniform orientation of the optic axis with respect to the wave-vector. A fundamental question is whether the guided propagation of light can be achieved at all in structures without perturbations of the refractive index. As we shall prove, this is indeed possible provided that the transverse trapping is purely based on vectorial effects, that is, it relies on spin-orbit interactions between wave propagation and polarization states of light 12,13 : otherwise stated, an entirely new mechanism for light confinement.Spin-orbit photonic interactions are strictly related to geometric Berry phases [14][15][16][17] . In the context of optics, the latter are phase retardations linked exclusively to the geometry of the transformations imposed to light by the medium and independent of the optical path length 12 . This concept has been already implemented in optical elements with various architectures, including patterned dielectric gratings, liquid crystals and metasurfaces [19][20][21][22][23] . These devices exploit the medium a...
We investigate spatial solitons in nonlocal media with a nonlinear index well modeled by a diffusive equation. We address the role of nonlocality and its interplay with boundary conditions, shedding light on the behavior of accessible solitons in real samples and discussing the accuracy of the highly nonlocal approximation. We find that symmetric solitons exist only above a power threshold, with an existence region that grows larger and larger with nonlocality in the plane width power.
Geometric phase is a unifying and central concept in physics, including optics. As a matter of fact, optics played a pivotal role from the inception of this new paradigm, as some of the first experimental demonstrations have been carried out in optics. A specific type of geometric phase was first introduced by Pancharatnam while investigating interference effects between different polarizations. This specific type of geometric phase, nowadays called the Pancharatnam–Berry phase, is related to the variation of light polarization, encompassing exotic properties when compared with the dynamic phase associated with the optical path. The most widespread manifestation of the Pancharatnam–Berry phase occurs in the presence of a twisted anisotropic material, yielding a point‐wise phase modulation proportional to the local rotation angle of the material. Here the basic mechanism behind the Pancharatnam–Berry phase is discussed. The various applications of this relatively original concept in photonics are then reviewed, presenting both the most important results and manufactured devices reported in literature. The interplay between geometric phase and diffraction occurring in bulk structures is discussed in detail. In the latter case it is shown how geometric phase can be harnessed to generate a new kind of optical waveguide without the necessity of any index gradient.
We theoretically investigate the propagation of bright spatial solitary waves in highly nonlocal media possessing radial symmetry in a three-dimensional cylindrical geometry. Focusing on a thermal nonlinearity, modeled by a Poisson equation, we show how the profile of the light-induced waveguide strongly depends on the extension of the nonlinear medium in the propagation direction as compared to the beamwidth. We demonstrate that self-trapped beams undergo oscillations in size, either periodically or aperiodically, depending on the input waist and power. The-usually neglected-role of the longitudinal nonlocality as well as the detrimental effect of absorptive losses are addressed.
Existence and stability of PT -symmetric gap solitons in a periodic structure with defocussing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable in the presence of an imaginary potential. The instability manifests itself as a lateral drift of solitons due to an unbalanced particle flux. We also demonstrate that the perturbation growth rate is proportional to the amount of gain (loss), thus predicting the observability of stable gap solitons for small imaginary potentials.
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