Biomedical subjects

Alessandro Ciattoni

Publications and source records attributed to Alessandro Ciattoni.

13 recordsLinked to original sources

PubMed2004

Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media.

We introduce a scheme for describing electromagnetic nondiffracting pulses propagating in isotropic and lossless media characterized by a plasma-like refractive index. A family of nondiffracting waves in a dispersive medium is analytically derived in the form of a generalization of X waves propagating in vacuum. It is also shown how the ratio between pulse width and plasma length has a crucial effect on the pulse dynamics.

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PubMed2004

One-dimensional nondiffracting pulses.

A general expression describing nondiffracting pulses whose transverse profile is a one-dimensional image is presented. The pulse turns out to be expressed as a superposition of two fields, possessing a purely translational dynamics, whose profiles are related to the field distribution on the the waist plane through an Hilbert transformation. The space-time structure of the generally X-shaped pulse is investigated and a simple relation connecting its transverse and the longitudinal widths is established. Specific analytical examples are considered and, in particular, the fundamental one-dimensional X waves are deduced and compared to their two-dimensional counterparts.

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PubMed2004

Vector electromagnetic X waves.

A vector propagation scheme for describing electromagnetic nondiffracting beams (X waves) is introduced. In particular we show that, from the knowledge of the transverse field components on a given transverse plane and at a fixed instant, it is possible to predict the whole electric field everywhere which in particular allows us to investigate the imaging properties of nondiffracting beam. Furthermore, we show that the longitudinal field component crucially depends on the pulse velocity and that it can be neglected only if the velocity is slightly greater than c. The proposed formalism is tested by means of two examples, the vector fundamental and Gaussian X waves which admit analytical treatment. As an application of the propagation scheme, we derive in closed form the expressions for the field propagator showing that its transverse component formally coincides with one of the scalar fundamental X wave.

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PubMed2004

Universal space-time properties of X waves.

Exact results concerning spatiotemporal universal features of three-dimensional propagation-invariant solutions of the wave equation (X waves) are derived. In particular, relations connecting the pulse transverse extension to the longitudinal coordinate and the propagation velocity to the spatial field distribution are obtained for the whole class of X waves.

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PubMed2003

Angular momentum dynamics of a paraxial beam in a uniaxial crystal.

The conservation law governing the dynamics of the radiation angular momentum component along the optical axis (z axis) of a uniaxial crystal is derived from Maxwell's equations; the existence of this law is physically related to the rotational invariance of the crystal around the optical axis. Specializing the obtained general expression for the z component of the angular momentum flux to the case of a paraxial beam propagating along the optical axis, we find that the expression is the same as the corresponding one for a paraxial beam propagating in an isotropic medium of refractive index n(o) (ordinary refractive index of the crystal); besides, we show that the flux is conserved during propagation and that it decomposes into the sum of an intrinsic and an orbital contribution. Investigating their dynamics we demonstrate that they are coupled and, during propagation, an exchange between them exists. This exchange asymptotically exhibits a saturation process leading, for z--> infinity, the intrinsic part to vanish and the orbital one equates the total amount of angular momentum flux. As an example, the evolution of the intrinsic and the orbital contributions to the flux is investigated in the case of circularly polarized beams. Besides, the radiation angular momentum stored in the crystal is also investigated, in the paraxial regime, showing that it is simply given by the product of the total angular momentum flux by the time the radiation takes in passing through the crystal.

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PubMed2003

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.

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PubMed2003

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 Maxwell's 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.

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PubMed2002

Paraxial propagation along the optical axis of a uniaxial medium.

An approach for describing paraxial propagation of light along the optical axis of a uniaxial medium is introduced. Contrary to previous theoretical schemes, our approach directly deals with the propagation of the whole optical field without resorting to the standard decomposition into ordinary and extraordinary parts, thus avoiding some related mathematical difficulties. A paraxial equation governing the field propagation has been derived, and its formal solution has been deduced. The structure of this solution allows us to think of the optical field in the crystal as the corresponding one propagating in vacuum "dressed" by the effect of anisotropy. This relationship is used to derive two analytical techniques for evaluating the propagated field. Starting from the formal solution, the closed-form expression of the anisotropic propagator is also derived. The proposed approach is used to predict the evolution of an astigmatic Gaussian beam through a calcite crystal, which has been also experimentally investigated. The agreement between theory and experiment is good.

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PubMed2002

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.

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PubMed2002

Exact axial electromagnetic field for vectorial Gaussian and flattened Gaussian boundary distributions.

The exact expressions of the electromagnetic field pertinent to Gaussian and flattened Gaussian linearly polarized boundary distributions have been derived in closed-form terms for any point lying on the axis. The obtained results allow the fields to be predicted for an arbitrary transverse beam size. Numerical results showing the differences between the exact results and those obtained within the paraxial framework are also presented.

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PubMed2002

Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal.

Angular spectra of reflected and transmitted fields, induced by an arbitrary electromagnetic beam passing through the planar interface between a homogeneous medium and a uniaxially anisotropic medium, are derived and related to the incident medium. By using these formulas, we obtain the expressions for paraxial and slightly nonparaxial fields. The reflected paraxial field is related to the incident one by means of Fresnel relations; the transmitted paraxial field is the superposition of an ordinary and an extraordinary beam, multiplied by the Fresnel coefficient. We find that the nonparaxial corrections, owing to the medium discontinuity, are larger than their free-propagation counterparts and that they are very simply related to the paraxial solutions of the incident beam. The case of two homogeneous media with different refractive indices is also discussed. The general expressions obtained are applied to the case of a nonparaxial Gaussian beam.

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PubMed2002

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.

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PubMed2002

Energy exchange between the Cartesian components of a paraxial beam in a uniaxial crystal.

The evolution of the optical power associated with the Cartesian components of a paraxial beam propagating along the optical axis in a uniaxial crystal is investigated. The energy exchange is found to undergo a saturation that is due to both diffraction and coupling between the chi- and gamma-field components; for linearly polarized circularly symmetric input beams, the asymptotic power exchange always amounts to a quarter of the total power. The general results are applied to the case of astigmatic Gaussian beams, which admits of a fully analytical description. The case of finite length crystals is also considered.

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