Alessandro Ciattoni

Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond

We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwells equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.

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.

Propagation of cylindrically symmetric fields in uniaxial crystals.

We investigate the paraxial propagation along the optical axis of a uniaxially anisotropic crystal of a general paraxial beam whose boundary Cartesian components possess cylindrical symmetry. This property allows us to obtain expressions whose dependence on the azimuth angle phi (in cylindrical coordinates) is fully described and very simple. We also find that the beam loses its boundary cylindrical symmetry during propagation, as a consequence of medium anisotropy. Further, these expressions elucidate the way in which the anisotropy changes the state of polarization. As an example, we discuss the case of a Gaussian beam focused into the crystal by a thin spherical lens.

Circularly polarized beams and vortex generation in uniaxial media

We deduce the expressions for the two circularly polarized components of a paraxial beam propagating along the optical axis of a uniaxial crystal. We find that each of them is the sum of two contributions, the first being a free field and the second describing the interaction with the opposite component. Moreover, we expand both components as a superposition of vortices of any order, thus obtaining a complete physical picture of the interaction dynamics. Consequently, we argue that a left-hand circularly polarized incoming beam, endowed with a circular symmetric profile, gives rise, inside the crystal, to a right-hand circularly polarized vortex of order 2. The efficiency of this vortex generation is investigated by means of a power exchange analysis. The Gaussian case is fully discussed, showing the relevant features of the vortex generation.

Laguerre–Gauss and Bessel–Gauss beams in uniaxial crystals

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index n(o) and n(e)2/n(o), where n(o) and n(e) are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre-Gauss and Bessel-Gauss beams propagating through an anisotropic crystal are given.

Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity

We consider a subwavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small, thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by interesting features such as the transverse power flow reversing. In order to probe this regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and show that these waves are allowed to propagate even in media with

Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis

\ensuremath{\epsilon}l0

Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation

and

Terahertz active spatial filtering through optically tunable hyperbolic metamaterials

\ensuremath{\mu}g0

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

since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyperfocusing induced by the phase difference between the field components.