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.

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.

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.

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.

Dynamical stability of dipolar Bose-Einstein condensates with temporal modulation of the s-wave scattering length.

We study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.

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.

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.

Deflection and trapping of spatial solitons in linear photonic potentials.

We investigate the dynamics of spatial optical solitons launched in a medium with a finite perturbation of the refractive index. For longitudinally short perturbations of super-Gaussian transverse profile, as the input power varies we observe a transition from a wave-like behavior where solitons break up into multiple fringes to a particle-like behavior where solitons acquire a transverse velocity retaining their shape. For longitudinally long perturbations with an attractive potential solitons get trapped inside the well and propagate with transverse periodic oscillations, resulting in an efficient power-dependent angular steering or deflection. Using the Ehrenfest theorem we derive analytical expressions for soliton trajectory, and achieve excellent agreement between theory and numerical simulations for large powers, that is, narrow solitons.

Soliton self-routing in a finite photonic potential.

We investigate power-dependent routing of one-dimensional Kerr-like spatial solitons in the presence of a finite photonic potential. Large self-deflections can be obtained using a trapping index well of limited length.

Tunable pattern transitions in a liquid-crystal-monomer mixture using two-photon polymerization.

Through two-photon lithographic processes, we report experimentally and numerically a series of photoinduced tunable polymerization patterns in shapes from straight channel, serpentine curve, to periodic grating when an ultrashort femtosecond laser pulse directly writes in a liquid-crystal-monomer mixture along a line for different scanning speeds. Laser beams with polarization perpendicular to the direction of writing and the alignment of liquid crystals, produce snake-shaped patterns at an intermediate scan rate.

Crescent waves in optical cavities.

We theoretically and experimentally generate stationary crescent surface solitons pinged to the boundary of a microstructured vertical cavity surface emission laser by triggering the intrinsic cavity mode as a background potential. Instead of a direct transition from linear to nonlinear cavity modes, we demonstrate the existence of symmetry-breaking crescent waves without any analogs in the linear limit. Our results provide an alternative and general method to control lasing characteristics as well as to study optical surface waves.

Optical solitons and wave-particle duality.

We investigate the propagation of optical solitons interacting with linear defects in the medium. We show that solitons exhibit a wave-particle dualism versus power, i.e., depending on the relative size of soliton and defect, responsible for a soliton trajectory dependent on its waist.