V. Bagini

Propagation of axially symmetric flattened Gaussian beams

Flattened Gaussian beams are characterized by a waist profile that passes in a continuous way from a nearly flat illuminated region to darkness. The steepness of the transition region is controlled by an integer parameter N representing the order of the beam. Being expressible as a sum of N Laguerre–Gauss modes, a flattened Gaussian beam turns out to be very simple to study as far as propagation is concerned. We investigate the main features of the field distribution pertaining to a flattened Gaussian beam throughout the space and present experimental results relating to the laboratory production of this type of beam.

Generalized Bessel-Gauss beams

In this paper we describe a superposition model for Bessel-Gauss beams, in which higher orders are included. An analogous model leads to a different class of beams, namely the modified Bessel-Gauss beams. Then a generalized set of beams, containing the previous beams as particular cases, is introduced. The behaviour of these beams upon propagation is investigated, both analytically and numerically.

Twisted Gaussian Schell-model Beams: A Superposition Model

Abstract We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given.

Linear Cryptanalysis of Bluetooth Stream Cipher

A general linear iterative cryptanalysis methodfor solving binary systems of approximate linear equations which is also applicable to keystream generators producing short keystream sequences is proposed. A linear cryptanalysis method for reconstructing the secret key in a general type of initialization schemes is also developed. A large class of linear correlations in the Bluetooth combiner, unconditioned or conditionedon the output or on both the output and one input, are found andc haracterized. As a result, an attack on the Bluetooth stream cipher that can reconstruct the 128-bit secret key with complexity about 270 from about 45 initializations is proposed. In the precomputation stage, a database of about 280 103-bit words has to be sorted out.

Extension of the Fresnel transform to ABCD systems

An extension of the Fresnel transform to first-order optical systems that can be represented by an ABCD matrix is analyzed. We present and discuss a definition of the generalized transform, which is recognized to belong to the class of linear canonical transforms. A general mathematical characterization is performed by listing a number of meaningful theorems that hold for this operation and can be exploited for simplyfying the analysis of optical systems. The relevance to physics of this transform and of the theorems is stressed. Finally, a comprehensive number of possible decompositions of the generalized transform in terms of elementary optical transforms is discussed to obtain further insight into this operation.

Propagation of super-Gaussian beams

Abstract A mathematical analysis of propagation in free space of super-Gaussian beams under the paraxial approximation is performed by means of a special “local” expansion in Laguerre-Gauss beams. A new type of beams recently introduced, flattened gaussian beams, is also used.

Theoretical and experimental determination of single round-trip beam parameters in a Xe–Cl laser

The evolution of the main parameters (spot size, radius of curvature, and far-field divergence) of the beam provided by a high-gain, short-pulse Xe–Cl laser equipped with a plane-parallel Gaussian resonator has been investigated both theoretically and experimentally as a function of the number of round trips. It is shown that a theoretical analysis, formerly developed to study the growth of coherence of a Schell–Gauss model beam propagating through a periodic sequence of Gaussian apertures, provides a satisfactory description of the temporal evolution of the Xe–Cl laser beam. A good agreement between theoretical and experimental data has been found.

A new method for measuring the diffusivity of liquid binary mixtures using DSPI

A simple and compact digital speckle pattern interferometer is proposed to measure the isothermal diffusion coefficient in transparent mixtures. The diffusion constant is determined directly from the skeletonized video correlogram. An example of diffusion coefficient measurement of a binary liquid mixture demonstrates the usefulness of the method.

Coherent and Partially Coherent Twisting Beams

We present coherent and partially coherent beams that exhibit transverse pattern expansion and rotation upon free propagation. Coherent twisting beams may be generated by a suitable superposition of Laguerre-Gauss modes, while a model for partially coherent twisting beams is given by a continuous incoherent superposition of lowest order modes.

Expansions of general beams in gaussian beams

Abstract Expansions of beams with a general amplitude distribution in Laguerre-Gauss beams are analyzed in order to find more efficient approximations than the conventional ones based on the Fourier coefficients. Fundamental tools for this elaboration are the local expansions in orthogonal polynomials. Application is also made of a new class of beams recently introduced, flattened gaussian beams.