Optically induced metal-to-dielectric transition in Epsilon-Near-Zero metamaterials.

Epsilon-Near-Zero materials exhibit a transition in the real part of the dielectric permittivity from positive to negative value as a function of wavelength. Here we study metal-dielectric layered metamaterials in the homogenised regime (each layer has strongly subwavelength thickness) with zero real part of the permittivity in the near-infrared region. By optically pumping the metamaterial we experimentally show that close to the Epsilon-Near-Zero (ENZ) wavelength the permittivity exhibits a marked transition from metallic (negative permittivity) to dielectric (positive permittivity) as a function of the optical power. Remarkably, this transition is linear as a function of pump power and occurs on time scales of the order of the 100 fs pump pulse that need not be tuned to a specific wavelength. The linearity of the permittivity increase allows us to express the response of the metamaterial in terms of a standard third order optical nonlinearity: this shows a clear inversion of the roles of the real and imaginary parts in crossing the ENZ wavelength, further supporting an optically induced change in the physical behaviour of the metamaterial.

Multistability at arbitrary low optical intensities in a metal-dielectric layered structure.

We show that a nonlinear metal-dielectric layered slab of subwavelength thickness and very small average dielectric permittivity displays optical multistable behavior at arbitrary low optical intensities. This is due to the fact that, in the presence of the small linear permittivity, one of the multiple electromagnetic slab states exists no matter how small is the transmitted optical intensity. We prove that multiple states at ultra-low optical intensities can be reached only by simultaneously operating on the incident optical intensity and incidence angle. By performing full wave simulations, we prove that the predicted phenomenology is feasible and very robust.

Highly nonparaxial (1+1)-D subwavelength optical fields.

A general approach for describing (1+1)-D subwavelength optical field whose waist is much smaller than the wavelength is presented. Exploiting the vectorial Rayleigh-Sommerfeld diffraction theory, a suitable expansion in the ratio between the beam waist and the wavelength allows us to prove the a (1+1)D highly nonparaxial field is generally the product of a cylindrical wave carrier and an envelope which is angularly slowly varying. We apply our general approach to the case of highly nonparaxial Hermite-Gaussian beams whose description is fully analytical.

Transverse power flow reversing of guided waves in extreme nonlinear metamaterials.

We theoretically prove that electromagnetic beams propagating through a nonlinear cubic metamaterial can exhibit a power flow whose direction reverses its sign along the transverse profile. This effect is peculiar of the hitherto unexplored extreme nonlinear regime where the nonlinear response is comparable or even greater than the linear contribution, a condition achievable even at relatively small intensities. We propose a possible metamaterial structure able to support the extreme conditions where the polarization cubic nonlinear contribution does not act as a mere perturbation of the linear part.

Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity.

We investigate propagation of a transverse magnetic field through a nonlinear metamaterial slab of subwavelength thickness and with a very small and negative linear dielectric permittivity. We prove that, for a given input intensity, the output intensity is a multivalued function of the field incidence angle so that the transmissivity exhibits angular multistability and a pronounced directional hysteresis behavior. The predicted directional hysteresis is a consequence of the fact that the linear and nonlinear contributions to the overall dielectric response can be comparable so that the electromagnetic matching conditions at the output slab boundary allow more than one field configuration within the slab to be compatible with the transmitted field.

Light-induced dielectric structures and enhanced self-focusing in critical photorefractive ferroelectrics.

We consider the nonlinear dynamics occurring when an optical beam couples to dielectric material polarization in an unbiased photorefractive crystal undergoing a ferroelectric phase transition. The polarization profile produced by the light-induced electric field is evaluated by means of the Landau-Ginzburg approach and is found to manifest new thermodynamical states with their own specific nonlinear optical effects. We show that a temperature T(C), lower than the critical one, exists such that (a) if T>T(C) the optical beam experiences an increasing self-focusing for decreasing temperatures and (b) if T

Collision and fusion of counterpropagating micrometer-sized optical beams in periodically biased photorefractive crystals.

We theoretically investigate collision of optical beams traveling in opposite directions through a centrosymmetric photorefractive crystal biased by a spatially periodic voltage. We analytically predict the fusion of counterpropagating solitons in conditions in which the applied voltage is rapidly modulated along the propagation axis, so that self-bending is suppressed by the "restoring symmetry" mechanism. Moreover, when the applied voltage is slowly modulated, we predict that the modified self-bending allows conditions in which the two beams fuse together, forming a curved light-channel splice.

Electro-activation and electro-morphing of photorefractive funnel waveguides.

We demonstrate the electro-activation of funnel waveguides through the quadratic electro-optic effect in paraelectric potassiumlithium- tantalate-niobate. This allows us to achieve electro-optic intensity modulation in a single optical beam, a 1x2 switch, and finally the electrically controlled morphing of a single waveguide into a 1x2 and a 1x4 divider.

Photorefractive solitons of arbitrary and controllable linear polarization determined by the local bias field.

We discuss and experimentally demonstrate a scheme to achieve photorefractive solitons of arbitrary linear polarization using the quadratic electro-optic effect and describe the observation of the self-trapping of a set of linear polarized beams in different positions of a paraelectric photorefractive crystal of potassium-lithium-tantalate-niobate (KLTN) biased by the inhomogeneous field produced by two miniaturized top electrodes. The polarization of the single solitons of the set is determined by the local electrostatic configuration and the underlying tunable anisotropy, which is detected through zero-field electro-activation.

Wiggling and bending-free micron-sized solitons in periodically biased photorefractives.

Considering nonlinear optical propagation through photore-fractive crystals in which the bias voltage is periodically modulated along the propagation direction, we are able to identify the conditions in which a beam forms a soliton in a straight line down to micron-sized widths. The effect, which is numerically investigated considering the full (3+1)D spatio-temporal light-matter dynamics, emerges when the period of modulation of the bias is smaller than the beam diffraction length. In conditions in which the two scales are comparable, the soliton follows a characteristic wiggling trajectory, oscillating in response to the oscillating bias. The finding indicates a method to achieve highly miniaturized soliton-based photonic applications that do not require specific off-axis alignment.

Counterpropagating spatial solitons in reflection gratings with a longitudinally modulated Kerr nonlinearity.

We investigate quasi-Bragg-matched counterpropagating spatial solitons in a reflection grating in the presence of a longitudinally modulated Kerr nonlinearity. The physical interplay of linear reflection and Kerr self-focusing with the modulation in the nonlinearity yields a variety of elaborate self-action mechanisms. We first analytically predict the existence of symmetric soliton pairs supported by a pure Kerr-like effective nonlinearity. We then analytically derive two families of solitons, associated with the linear grating eigenmodes, supported by an effective "incoherent" Kerr-like coupling arising from the exact balance between the modulation in the nonlinearity and the Kerr interaction due to beam interference.

Counterpropagating nondiffracting beams through reflection gratings.

We investigate the counterpropagation of paraxial non-diffracting optical beams through a medium hosting a bulk reflection grating in the quasi-Bragg matching condition. The impact of the relative magnitude of the Bragg detuning parameter and the grating depth on the plane wave dispersion relation allows us to identify three distinct regimes where counterpropagation and interaction of nondiffracting beams show qualitatively different features, encompassing longitudinally invariant, periodic or exponential intensity profiles. In one of the identified regimes the dispersion relation is not monotonic and the consequent "longitudinal degeneracy" allows the investigation of new class of nondiffracting beams characterized by a double spectral ring profile.

Separating polarization components through the electro-optic read-out of photorefractive solitons.

Analyzing the propagation dynamics of a light beam of arbitrary linear input polarization in an electro-activated photorefractive soliton we are able to experimentally find the conditions that separate its linear polarization components, mapping them into spatially distinct regions at the crystal output. Extending experiments to the switching scheme based on two oppositely biased solitons, we are able to transform this spatial separation into a separation of two distinct guided modes. The result is a miniaturized electro-optic polarization separator.

Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior.

Experimental and theoretical results indicate that miniaturized micron-sized nonlinear beam phenomenology in photorefractives leads to a regime qualitatively distinct from solitonlike propagation on consequence of the specific role of space-charge saturation. In the highly modulated conditions typical of beams, this contribution amounts to an effective electron self-action.

Polarization and energy dynamics in ultrafocused optical Kerr propagation.

Developing a complete vectorial description of optical nonparaxial propagation of highly focused beams in Kerr media, we disclose a family of new phenomena. These phenomena appear to emerge as a consequence of the mutual coupling of all three components of the optical field. This circumstance, which is intrinsic to the very nature of Kerr propagation, was previously discarded on the basis of the conjecture that a reduced system is possible in which only one transverse field component interacts with the longitudinal component.

Vectorial theory of propagation in uniaxially anisotropic media.

We describe propagation in a uniaxially anisotropic medium by relying on a suitable plane-wave angular-spectrum representation of the electromagnetic field. We obtain paraxial expressions for both ordinary and extraordinary components that satisfy two decoupled parabolic equations. As an application, we obtain, for a particular input beam (a quasi-Gaussian beam), analytical results that allow us to identify some relevant features of propagation in uniaxial crystals.

Distortion correction by phase conjugation of nonparaxial vectorial beams: a general proof.

We present a general proof of the distortion-correction theorem, that is, of the possibility of correcting wave distortion by the technique of optical phase conjugation. The proof is valid for fully vectorial nonparaxial propagation in the presence of a tensorial refractive-index perturbation and backscattering of the incident field.

Anisotropic charge displacement supporting isolated photorefractive optical needles.

Strong asymmetry in the charge distribution supporting a single noninteracting spatial needle soliton in a paraelectric photorefractive is directly observed by means of electroholographic readout. Whereas in trapping conditions a quasi-circular wave is supported, the underlying double-dipolar structure can be made to support two distinct propagation modes.

A one- and two-dimensional nonlinear pulse interaction

The peculiar intergrability of the Davey-Stewartson equation allows us to analytically find solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted phenomenology allows us to address the issue of interaction of solitons of different dimensionality that may serve as a starting point for the understanding of hybrido-dimensional collisions recently observed in nonlinear optical media.