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In this paper, picosecond laser inscription of segmented waveguides in crystalline silicon based on a deterministic single-pulse modification process is demonstrated.Pulses of 43 ps duration at 1.55 ${\mu}$m wavelength are used to transversely inscribe periodic structures with a pulse-to-pulse pitch of around 2 ${\mu}$m. Infrared shadowgraphy images and Raman spectroscopy measurements indicate that the modifications exhibit a spherical shape. Characterization of waveguide performance at 1.55 ${\mu}$m for various pulse energies and periods is carried out. Direct comparison with numerical simulations confirms the presence of graded index waveguides, encompassing a micrometer core size and a maximum refractive index change of around $7\times 10^{-3}$. This short-pulse inscription approach can pave the way for three-dimensional integrated photonic devices in the bulk of silicon.

A fundamental brick of light-matter interaction at large optical intensities is the generation of a plasma. The optically-induced plasma in turn plays a fundamental role in determining the optical propagation. The plasma generation is a result of the interplay between multi-photon, tunnel and avalanche ionization. Here we use the basic rate equations to discuss an analytical model for the interaction between these physical effects. After defining a nonlinear impulse response for the system, we describe how the interplay depends on the features of the optical pulses. Our approach strongly simplifies the modelling of the propagation of ultrashort-pulses, paving the way to a much easier and faster interpretation of experimental observations, with potential impact on the broad fields of ultrafast light-matter interaction and laser micro-machining., Comment: 8 pages, 6 figures. Submitted to PRB

We investigate experimentally Third Harmonic Generation (THG) from plasmonic metasurfaces consisting of two-dimensional rectangular lattices of centrosymmetric gold nano-bars. 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 frequencies. 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., Comment: 6 pages, 5 figures, accepted in Optics Letters-Optica

We theoretically and numerically investigate the properties of waveguides based on the Pancharatnam-Berry phase, obtained by a longitudinally periodic rotation of the optic axis in a transversely-twisted birefringent medium. In this paper we study the case where the period of the longitudinal modulation is chosen so that a net accumulation of geometric phase in propagation occurs. First, the interplay between different contributions to the optical potential is addressed. Second, a continuous evolution of the polarization structure of the quasi-modes is observed in the numerical simulations. We explain it by a combination of plane-wave-based models and gauge transformations. We discover that, beyond the longitudinal oscillations, the polarization of the quasi-mode also varies through its cross-section. The analogies with respect to charged particles moving in a magnetic field are outlined., Comment: 16 pages, 11 figures

We discuss the semi-classical transverse trapping of waves by means of an inhomogeneous gauge field. In the proposed scheme a temporally-periodic perturbation is shifted in time, the imparted delay being dependent on the transverse direction. We show that, due to the Kapitza effect, an effective potential proportional to the square of the transverse derivative of the delay arises. On a more physical ground, the delay induces a transversely-varying periodic force acting on the wave, in turn providing a phase delay owing to the local modulation of the kinetic energy. Our results are quite generic and can find application in several fields, ranging from cold atoms to optics: accordingly, an experimental proof-of-principle is provided using an optical set-up based upon fiber loops., Comment: 15 pages, 11 figures

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., Comment: 19 pages, 18 figures

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 figures

Existence and stability of PT-symmetric gap solitons in a periodic structure with defocusing 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., Comment: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.013812

Since its introduction by Sir Michael Berry in 1984, geometric phase became of fundamental importance in physics, with applications ranging from solid state physics to optics. In optics, 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 wavefront 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, 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., Comment: 9 pages, 5 figures

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 figures

Thanks to their unique properties, nematic liquid crystals feature a variety of mechanisms for light-matter interactions. For continuous-wave optical excitations, the two dominant contributions stem from reorientational and thermal nonlinearities. We thoroughly analyze the competing roles of these two nonlinear responses 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 and continuous-wave beams at two distinct wavelengths in order to adjust the relative weights of the two responses. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation and compared to experimental results., Comment: 13 pages, 12 figures, submitted to PRE

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 configuration implies a complicated interaction between geometric and 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 upon this effect, polarization-selective lens, waveguides and beam deflectors are proposed., Comment: 5 pages, 4 figures

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 figures

We discuss the propagation of an electromagnetic field in an inhomogeneously anisotropic material where the optic axis is rotated in the transverse plane but is invariant along the propagation direction. In such a configuration, the evolution of an electromagnetic wavepacket is governed by the Pancharatnam-Berry phase (PBP), responsible for the appearance of an effective photonic potential. In a recent paper [A. Alberucci et al., "Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics", ACS Photonics \textbf{3}, 2249 (2016)] we demonstrated that the effective potential supports transverse confinement. Here we find the profile of the quasi-modes and show that the photonic potential arises from the Kapitza effect of light. The theoretical results are confirmed by numerical simulations, accounting for the medium birefringence. Finally, we analyze in detail a configuration able to support non-leaky guided modes., Comment: 14 pages, 13 figures

We demonstrate that light is subject to anomalous (i.e., negative) diffraction when propagating in the presence of hyperbolic dispersion. We show that light propagation in hyperbolic media resembles the dynamics of a quantum particle of negative mass moving in a two-dimensional potential. The negative effective mass implies time reversal if the medium is homogeneous. Such property paves the way to diffraction compensation, spatial analogue of dispersion compensating fibers in the temporal domain. At variance with materials exhibiting standard elliptic dispersion, in inhomogeneous hyperbolic materials light waves are pulled towards regions with a lower refractive index. In the presence of a Kerr-like optical response, bright (dark) solitons are supported by a negative (positive) nonlinearity., Comment: 10 pages, 10 figures; accepted for publication in Physical Review A

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 A

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)

The reorientational nonlinearity of nematic liquid crystals enables a self-localized spatial soliton and its waveguide to be deflected or destroyed by a control beam propagating across the cell. We demonstrate a simple all-optical readdressing scheme by exploiting the lens-like perturbation induced by an external beam on both a nematicon and a co-polarized guided signal of different wavelength. Angular steering as large as 2.2 degrees was obtained for control powers as low as 32mW in the near infrared.