Exploring the impact of longitudinal modulation on the twisting angle in Pancharatnam-Berry phase-based waveguides.

A circularly polarized (CP) beam propagating in a rotated anisotropic material acquires an additional phase delay proportional to the local rotation angle. This phase delay is a particular kind of geometric phase, the Pancharatnam-Berry phase (PBP), stemming from the path of the beam polarization on the Poincaré sphere. A transverse gradient in the geometric phase can thus be imparted by inhomogeneous rotation of the material, with no transverse gradient in the dynamic phase. A waveguide based upon this principle can be induced when the gradient accumulates in propagation, the latter requiring a longitudinal rotation in the optic axis synchronized with the natural rotation of the light polarization. Here, we evaluate numerically and theoretically the robustness of PBP-based waveguides, in the presence of a mismatch between the birefringence length and the external modulation. We find that the mismatch affects mainly the polarization of the quasi-mode, while the confinement is only slightly perturbed.

Second harmonic generation under doubly resonant lattice plasmon excitation.

Second harmonic generation is enhanced at the surface lattice resonance in plasmonic nanoparticle arrays. We carried out a parametric investigation on two-dimensional lattices composed of gold nanobars where the centrosymmetry is broken at oblique incidence. We study the influence of the periodicity, the incidence angle and the direction of the linear input polarization on the second harmonic generation. Excitation of the surface lattice resonance either at the fundamental or second harmonic wavelength, achieved by varying the incidence angle, enhance the conversion efficiency. As a special case, we demonstrate that both the wavelengths can be simultaneously in resonance for a specific period of the lattice. In this double resonant case, maximum second harmonic power is achieved.

Manipulating geometric and optical properties of laser-inscribed nanogratings with a conical phase front.

The formation of volumetric nanogratings in fused silica by femtosecond laser pulses are shown to afford new opportunities for manipulating the physical shape and tailoring the optical properties of the modification zone by harnessing unconventional beam shapes. The nanograting assembly was observed to rigorously follow the beam elongation effects induced with conical-shaped phase fronts, permitting a scaling up of the writing volume. Detailed optical characterization of birefringence, dichroism, and scattering loss pointed to flexible new ways to tune the macroscopic optical properties, with advantages in decoupling the induced phase retardation from the modification thickness by controlling the conical phase front angle. Further insights into an unexpected asymmetric response from Gaussian beams modified with concave and convex phase fronts have been provided by nonlinear propagation simulations of the shaped-laser light.

Enhancement of third harmonic generation induced by surface lattice resonances in plasmonic metasurfaces.

We investigate experimentally third harmonic generation (THG) from plasmonic metasurfaces consisting of two-dimensional rectangular lattices of centrosymmetric gold nanobars. By varying the incidence angle and the lattice period, we show how surface lattice resonances (SLRs) at the involved wavelengths are the major contributors in determining the magnitude of the nonlinear effects. A further boost on THG is observed when we excite together more than one SLR, either at the same or at different frequency. When such multiple resonances take place, interesting phenomena are observed, such as maximum THG enhancement for counter-propagating surface waves along the metasurface, and cascading effect emulating a third-order nonlinearity.

Polarization-insensitive wavefront shaping using the Pancharatnam-Berry phase.

We discuss a method to achieve a polarization-independent modulation of the electromagnetic wavefront based upon the Pancharatnam-Berry phase. When the length of the twisted anisotropic material is equal to the birefringence length (i.e., full-wave plate length), a phase delay proportional to the squared transverse derivative of the twisting angle appears. Physically, the phase delay is associated with the Kapitza effect applied to the Pancharatnam-Berry phase. Our theoretical results are confirmed by finite-difference time-domain (FDTD)-based numerical simulations.

Generation of multiple solitons using competing nonlocal nonlinearities.

We discuss the dynamics of fundamental Gaussian beams launched in saturable and nonlocal nonlinear media. Solely in the presence of a self-focusing saturable nonlinearity, the breathing solitons undergo strong deformation. The addition of a defocusing nonlinearity leads to the generation of couples of solitons. Experimentally, we demonstrate in nematic liquid crystals the formation of multiple spatial solitons starting from a bell-shaped input, with both direction and the number of filaments depending on the input power, confirming the theoretical predictions.

Kapitza light guiding in photonic mesh lattice.

We experimentally demonstrate the transverse confinement of light in the presence of a longitudinally periodic photonic potential with vanishing average. In agreement with Kapitza's original findings in classical mechanics, we confirm that light undergoes a transverse localization due to the action of an effective potential proportional to the square of the first derivative of the potential. Experiments are performed based on (1+1) D synthetic dimensions realized in a fiber loop system, allowing for complete control of the transverse and longitudinal distributions of the potential.

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.

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.

Paraxial light beams in structured anisotropic media.

We discuss the paraxial approximation for optical waves propagating in a uniaxial anisotropic medium inhomogeneously twisted on the plane normal to the wave vector, with the latter being parallel to one of the two principal axes normal to the optic axis. Such geometry implies a continuous power transfer between the ordinary and extraordinary components, regardless of the input beam polarization. We pinpoint that this peculiar feature, generalizable to any inhomogeneous linear birefringent material, strongly affects the application of the paraxial approximation due to the simultaneous presence of two different phase velocities. We eventually show that a local coordinate transformation permits a correct application of the paraxial approximation.

Spin-orbit interactions in optically active materials.

We investigate the inherent influence of light polarization on the intensity distribution in anisotropic media undergoing a local inhomogeneous rotation of the principal axes. Whereas, in general, such a configuration implies a complicated interaction between the geometric and the dynamic phase, we show that, in a medium showing an inhomogeneous circular birefringence, the geometric phase vanishes. Due to the spin-orbit interaction, the two circular polarizations perceive reversed spatial distribution of the dynamic phase. Based on this effect, polarization-selective lenses, waveguides, and beam deflectors are proposed.

Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects.

We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.

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 in 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 that do not rely on refractive index tailoring.

Nonlinear competition in nematicon propagation.

We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping.

Parity-time-symmetric solitons in trapped Bose-Einstein condensates and the influence of varying complex potentials: A variational approach.

Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.

Beam hysteresis via reorientational self-focusing.

We theoretically investigate light self-trapping in nonlinear dielectrics with a reorientational response subject to threshold, specifically nematic liquid crystals. Beyond a finite excitation, two solitary waves exist for any given power, with an hysteretic dynamics due to feedback between beam size, self-focusing and the nonlinear threshold. Soliton stability is discussed on the basis of the system free energy.

Power-controlled transition from standard to negative refraction in reorientational soft matter.

Refraction at a dielectric interface can take an anomalous character in anisotropic crystals, when light is negatively refracted with incident and refracted beams emerging on the same side of the interface normal. In soft matter subject to reorientation, such as nematic liquid crystals, the nonlinear interaction with light allows tuning of the optical properties. We demonstrate that in such material a beam of light can experience either positive or negative refraction depending on input power, as it can alter the spatial distribution of the optic axis and, in turn, the direction of the energy flow when traveling across an interface. Moreover, the nonlinear optical response yields beam self-focusing and spatial localization into a self-confined solitary wave through the formation of a graded-index waveguide, linking the refractive transition to power-driven readdressing of copolarized guided-wave signals, with a number of output ports not limited by diffraction.

Accessible solitons in diffusive media.

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.

Bistability with optical beams propagating in a reorientational medium.

We investigated bistability with light beams in reorientational nematic liquid crystals. For a range of input powers, beams can propagate as either diffracting or self-trapped, the latter corresponding to spatial solitons. The first-order transition in samples exhibiting abrupt self-focusing with a threshold is in agreement with a simple model.

Nematicons in planar cells subject to the optical Fréedericksz threshold.

We investigate, both theoretically and experimentally, self-trapping of light beams in nematic liquid crystals arranged so as to exhibit the optical Fréedericksz transition in planar cells. The resulting threshold in the nonlinear reorientational response supports a bistable behavior between diffracting and self-localized beam states, leading to the appearance of a hysteretic loop versus input excitation. Our results confirm the role of nematic liquid crystals in the study of non-perturbative nonlinear photonics.