Self-confined Beams Research Articles

Nematonics: from physics to photonics of reorientational solitons

ABSTRACT Nematic Liquid Crystals are birefringent soft matter exhibiting unique nonlocal and nonlinear optical properties. Due to the interaction with finite-size light beams, self-focusing via molecular reorientation can balance out diffraction and result in self-confined beams, namely spatial solitons or nematicons, operating as waveguides for copolarized optical signals. Since nematicon propagation and confinement are determined by material properties that can be tailored by external fields, they allow implementing various photonic functionalities: from signal steering and addressing to bistability, from topological and optical symmetry breaking to beaming of random laser emission, to mention a few. Such proof-of-principle applications make nematic liquid crystals and nematicons a versatile platform for the study of complex light–matter interactions in nonlocal dielectrics and the demonstration of all-optical photonic devices for signal processing.

Nonlinear Self-Confined Plasmonic Beams: Experimental Proof

Controlling low power light beam self-confinement with ultrafast response time opens up opportunities for the development of signal processing in microdevices. The combination of highly nonlinear m...

Effective breaking of the action-reaction principle using spatial solitons

We discuss a class of interactions between self-confined optical beams breaking the action-reaction principle. The effective force intertwining the beams does not satisfy momentum conservation, paving the way to the potential existence of situations where both beams are pushed in the same direction, in turn leading to the so-called diametric drive. In our theoretical proposal the interaction between the two light beams is enabled by optical nonlinearity. The nonlinearity is assumed to change sign with the light polarization, in turn allowing the two light beams to be attracted or repelled by an inhomogeneous region according to the photon polarization. We demonstrate that this exotic type of nonlinear spin-orbit-like interaction can be achieved in nematic liquid crystals (NLCs). In fact, depending on the input polarization, in NLCs a change in temperature corresponds to a focusing or defocusing index change. For the polarization seeing a thermal defocusing response (corresponding to the extraordinary component), the self-confinement is ensured by the simultaneous action of reorientational nonlinearity.

Bistable Beam Propagation in Liquid Crystals

Light-controlling-light is one of the most advanced paradigms in optical signal processing, including light-induced waveguides as well as all-optical switching and routing. Other fundamental aspects of all-optical processing are optical memories and sequential elements, which require responses depending on the evolution history of the system, such as the hysteresis stemming from optical multistability. Hereby, we report on optical bistability and hysteresis in cavityless geometries and in the presence of self-localized beams, i.e., spatial optical solitons, exploiting the nonlocal reorientational nonlinearity of nematic liquid crystals (NLC). When the optic axis of NLC is initially orthogonal to the applied electric field, the molecular dipoles start to rotate above a threshold named after the Freedericksz transition, the latter being usually of the second order. Here, we show that such transition become of the first order via the intrinsic feedback provided by self-focusing, in turn leading to the appearance of a hysteresis loop between diffracting and self-confined beams. We report on hysteresis of the beam size versus input power, as well as hysteresis versus applied voltage at a fixed beam power. Our findings introduce a novel kind of cavity-less optical bistability with propagating light beams and disclose a novel approach to information storage based on light self-localization.

Breather solitons in highly nonlocal media

We investigate the breathing of optical spatial solitons in highly nonlocal media. We use a generalization of the Ehrenfest theorem (1990 Am. J. Phys. 58 742) leading to a fourth-order ordinary differential equation, the latter ruling the beam width evolution in propagation. In actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell (1997 Science 276 1538) cannot accurately describe the dynamics of self-confined beams: 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.

Spatial routing with light-induced waveguides in uniaxial nematic liquid crystals

In reorientational soft-matter with uniaxial character, such as nematic liquid crystals (NLCs), self-confined beams into spatial optical solitons are graded-index waveguides subject to birefringent walkoff. We investigate a router to be realized in a planar cell with an inhomogeneous distribution of the optic axis. Based on the input beam position, the proposed demultiplexer can direct the soliton and the copolarized guided-wave signal(s) to various output ports, enhancing the transverse separation of the exit channels and therefore minimizing crosstalk. Both the soliton and the signal(s) maintain their phasefronts normal to launch and exit wavevectors, allowing for excellent coupling into output channels/fibers at the device exit.

Nematicons and Their Electro-Optic Control: Light Localization and Signal Readdressing via Reorientation in Liquid Crystals

Liquid crystals in the nematic phase exhibit substantial reorientation when the molecules are driven by electric fields of any frequencies. Exploiting such a response at optical frequencies, self-focusing supports transverse localization of light and the propagation of self-confined beams and waveguides, namely “nematicons”. Nematicons can guide other light signals and interact with inhomogeneities and other beams. Moreover, they can be effectively deviated by using the electro-optic response of the medium, leading to several strategies for voltage-controlled reconfiguration of light-induced guided-wave circuits and signal readdressing. Hereby, we outline the main features of nematicons and review the outstanding progress achieved in the last twelve years on beam self-trapping and electro-optic readdressing.

Frequency-Controlled Routing of Self-Confined Beams in Nematic Liquid Crystals

We demonstrate the electro-optic control of self-confined beams via frequency modulation in dual-frequency nematic liquid crystals. Proper design of comb electrodes in a planar cell allows the maximization of the overall steering angle when only walk-off variations are used. A span angle as large as two times the maximum walk-off angle is achieved.

Modeling Nematicon Propagation

We discuss, both theoretically and numerically, the propagation of self-confined beams in uniaxial nematic liquid crystals. Our model accounts for optical anisotropy and goes beyond the perturbative regime, that is, it allows addressing the unique properties of nematicons, including their tunable nonlinearity, high nonlocality, and ability to spatial self-steer.

High intensity behavior of pyroelectric photorefractive self-focusing in LiNbO3

The formation of self-confined beams using pyroelectric effect is numerically and experimentally studied in photorefractive LiNbO3. For a given crystal temperature change, the trapped beam width is shown to be less efficient as intensity is increased. Numerical calculations reveal that the induced refractive-index profile varies along propagation for large intensities due to a nonlinear photovoltaic effect. Moreover, it eventually gives beam splitting for intensities greater than a threshold intensity that depends on LiNbO3 composition.

Electro-Optic Beam Steering with Nematicons

We analyze a novel geometry expressly designed to maximize the bias-controlled deflection of self-confined light beams in nematic liquid crystals (NLC). We use a self-confined beam and a dielectric interface defined by external voltages, ranging from total internal reflection (TIR) to refraction depending on the applied bias. The optimization of the deflection angle is achieved by using comb electrodes in a planar cell employing planarly oriented NLC molecules. We predict a maximum deflection of 70° with the standard mixture E7.

Nematicon waveguides: self-confined beams and their electric control

We investigate the excitation and propagation of self-confined beams and the electric steering of soliton-based optical waveguides in nematic liquid crystalline planar cells. Controlled addressing of a signal is achieved in space by exploiting the electro-optic response of the uniaxial material, employing either uniform or patterned electrodes to alter either the Poynting vector or the wavevector, respectively.

Large electro-optic beam steering with nematicons

We analyze the angular steering of self-confined light beams, i.e., spatial solitons, in nematic liquid crystals exploiting both their electro-optic response and reorientational nonlinearity. A bias-induced interface is obtained with comb electrodes in a planar cell, applying two distinct voltages to control the spatial distribution of the optic axis. The configuration allows spatial solitons to propagate in a plane and maximize their deflection via refraction and total internal reflection, with an overall deflection of 70° in standard E7.

Self-Turning Self-Confined Light Beams in Guest-Host Media

We demonstrate power-dependent steering of self-confined light beams propagating in the nonparaxial regime in a guest-host nonlinear medium. Exploiting the Janossy enhancement in dye-doped liquid crystals with reorientational response, we observe sub-mW spatial soliton self-steering as large as 39 degrees, accompanied by trapping of the light spontaneously emitted by the excited dye. The self-turning is modeled in terms of an effective transverse force stemming from the longitudinal electric field in the tightly confined beams, with good agreement between data and simulations.

Solitons in curved space of constant curvature

We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.

Self-confined beams in erbium-doped lithium niobate

We experimentally investigate the formation of self-confined beams in lithium niobate crystals which are doped in the bulk with erbium. Samples have been grown by the Czochralski method with erbium nominal concentrations varying in the range 0.0–0.7 mol% in the melt. The speeds of beam confinement depend on the applied bias and on the beam intensity, as expected, but on the doping level as well. The erbium incorporation influences both the electro-optic coefficient and the photovoltaic field. A very general dependence of the confined beam waist on the refractive index change was experimentally derived, valid now for every lithium niobate crystal, independent on its growing procedure or doping.

Escaping Solitons from a Trapping Potential

Solitons propagating within a confining potential undergo momentum-dependent scattering and eventually escape for large excitations. We experimentally highlight this phenomenon in the presence of a nonperturbative nonlinear response using self-confined light beams in a reorientational medium.

Tunable refraction and reflection of self-confined light beams

Light filaments or optical spatial solitons are self-confined (non-spreading) beams that originate from the balance between diffraction and self-focusing in nonlinear optical media (those with a response dependent on the level of excitation)1,2,3. Owing to their ability to self-trap as well as to guide weaker signals (even if differing in colour or modulation format) within the waveguides or ‘light-pipes’ they induce, optical spatial solitons could form the basis of future all-optical processing networks4,5. One of the most interesting challenges in soliton propagation and engineering concerns light filaments incident on linear/nonlinear or nonlinear/nonlinear interfaces. Here we report the robust propagation, refraction and reflection of optical spatial solitons at the interface between two regions of a nematic liquid crystal. The ability to independently tune the optical properties of each region enables us to steer the beams by refraction and total internal reflection by as much as −18 and +22 degrees, respectively. Moreover, the extended (nonlocal) and anisotropic response of our system supports polarization healing of the solitons across the interface as well as non-specular filament reflection. Finally, exploiting the inherent and all-optically tunable birefringence, we demonstrate unprecedented nonlinear Goos–Hanchen lateral shifts in excess of 0.5 mm.