Franco Gori - Profile on Academia.edu (original) (raw)

Papers by Franco Gori

Journal of the Optical Society of America, Oct 23, 2008

Thin annular sources, either coherent or completely incoherent from the spatial standpoint, have ... more Thin annular sources, either coherent or completely incoherent from the spatial standpoint, have played a significant role in the synthesis of diffraction-free and J 0 -correlated fields, respectively. Here, we consider thin annular sources with partial correlation. A scalar description is developed under the assumption that the correlation function between two points depends on their angular distance only. We show that for any such source the modal expansion can easily be found. Further, we examine how the correlation properties of the radiated fields change on free propagation. We also give a number of examples and present possible synthesis schemes.

Photonics, Jul 17, 2023

A new class of stationary electromagnetic sources radiating outward from the surface of an infini... more A new class of stationary electromagnetic sources radiating outward from the surface of an infinitely long cylinder is introduced via vectorial coherent mode representation. First, two particular types of such sources are discussed: with either an electric or magnetic field aligned with the cylinder's axis. The former case represents a scalar scenario, while the latter leads to the two-component electric field. The combination of these two types of sources is then considered by forming the three-component electric field vector. An extension to the stationary case is then made in which the electric field correlations are shown to be described by the intrinsically 3 × 3 cross-spectral density matrix. Several known theories of electromagnetic coherence and polarization are then invoked for the analysis of radiation, on and off the source surface. The results for the spectral density, degree of coherence, and degree of polarization are then discussed in detail. The effects of mutual correlation of modes are also outlined. The new family of sources is of importance for any application involving cylindrical sources with controllable radiation.

Fractional Fourier transform and Fresnel transform

Paraxial propagation and kurtosis of fields generated by pseudo-Schell vortex sources

Fourth International Conference on Applications of Optics and Photonics, 2019

In this work, the paraxial evolution of fields generated by pseudo-Schell vortex sources is analy... more In this work, the paraxial evolution of fields generated by pseudo-Schell vortex sources is analyzed through some global parameters. In particular, it is shown that the kurtosis parameter of these fields presents a minimum at the beam waist and a maximum which value and position depends on the coherence characteristics of the source

On an Iterative Method for Super-resolution

Optica Acta: International Journal of Optics, 1975

ABSTRACT A recently proposed iterative method for super-resolution is studied with the aid of pro... more ABSTRACT A recently proposed iterative method for super-resolution is studied with the aid of prolate spheroidal wave functions. Perfect imagery is shown to be achieved in the limit of an infinite number of iterations. The case of a finite number of iterations is examined and possible extensions of the method are mentioned.

Transversely periodic partially coherent electromagnetic sources

The coherence and polarization features of partially coherent fields radiated from transversely p... more The coherence and polarization features of partially coherent fields radiated from transversely periodic electromagnetic sources are investigated in the most general case. Sources of this type are produced, for instance, when a partially polarized plane wave impinges onto an optical element, such as a polarization grating or an anisotropic wedge, which modifies the polarization of the incident field in a periodic way. Experimental results are reported, pertinent to the use of a double-wedge pseudo-depolarizer.

Optica Acta: International Journal of Optics, 1983

This article may be used for research, teaching and private study purposes. Any substantial or sy... more This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Shape invariant propagation of polychromatic fields

Optics Communications, 1984

When a polychromatic field propagates the transverse distribution of the power spectrum generally... more When a polychromatic field propagates the transverse distribution of the power spectrum generally changes from one plane to another. Conditions are found under which the spectrum distribution maintains the same shape in any cross-section. Examples of fields satisfying these conditions are given.

Fusion Engineering and Design, 1995

Numerical studies on the use of a quasi-optical grill to couple lower hybrid waves to a plasma, f... more Numerical studies on the use of a quasi-optical grill to couple lower hybrid waves to a plasma, for current drive in tokamaks, are currently under way. Study of the coupling has been carried out in a rigorous way, through the solution of scattering from cylinders with parallel axes in the presence of a plane of discontinuity for electromagnetic constants. Here we restrict our attention to the case of a plasma with a step density profile and report some results on launched spectra, coupled power and directivity.

Sampling in Optics

Springer texts in electrical engineering, 1993

Illuminate an object with laser light and look at it through a diffraction grating. You will see ... more Illuminate an object with laser light and look at it through a diffraction grating. You will see a set of mutually displaced copies of the object. If the lateral extent of the object is small enough, the various copies do not overlap. You can easily devise a method for selecting a single copy of the object. For example, you can replace your own optical system, i.e., your eye, by a converging lens and let the multiple images that were impressing your retina be produced on a screen. Then, a hole on the screen will suffice to isolate a single image. You can even dispense with the laser light and repeat the observation in a more domestic environment by looking at a distant street lamp through a piece of fine fabric. In this case, all of the object copies except the central one will appear iridescent, but the basic phenomena will be the same.

Journal of the Optical Society of America, Nov 24, 2015

We describe the new tutorial article type in detail and give some background on the reasons for i... more We describe the new tutorial article type in detail and give some background on the reasons for its introduction.

Nonambiguous determination of optical constants for absorbing materials

Applied optics, 1991

A recently proposed method for determining the optical constants of absorbing materials starting ... more A recently proposed method for determining the optical constants of absorbing materials starting from reflectance measurements is analytically treated. The conditions for a nonambiguous determination of the optical constants are established. The values of the parameters satisfying these conditions are explicitly evaluated.

Journal of the Optical Society of America, Apr 18, 2012

Journal of the Optical Society of America, Jul 27, 2015

Journal of Modern Optics, 1998

On the basis of the modal theory of coherence, we study partially coherent sources whose modes be... more On the basis of the modal theory of coherence, we study partially coherent sources whose modes belong to the class of Laguerre-Gauss functions for which the Laguerre polynomial has zero order. These modes present a phase profile with a helicoidal structure, which is responsible for notable phenomena, such as the propagation of optical vortices, beam twisting, and the presence of dislocations in interference patterns. By suitably choosing the eigenvalues associated with such modes, different partially coherent sources are obtained: sources with a flattened Gaussian profile, twisted Gaussian Schell-model sources with a saturated twist, and a new class of sources having an annular profile. Owing to the shape-invariance property of the underlying modes, the fields radiated by these sources do not change their transverse profile through propagation, except for scale and phase factors. We also prove that, if any such source is covered by a circularly symmetric filter, the new modal structure can he found in a straightforward manner.

Photonics

A new class of stationary electromagnetic sources radiating outward from the surface of an infini... more A new class of stationary electromagnetic sources radiating outward from the surface of an infinitely long cylinder is introduced via vectorial coherent mode representation. First, two particular types of such sources are discussed: with either an electric or magnetic field aligned with the cylinder’s axis. The former case represents a scalar scenario, while the latter leads to the two-component electric field. The combination of these two types of sources is then considered by forming the three-component electric field vector. An extension to the stationary case is then made in which the electric field correlations are shown to be described by the intrinsically 3×3 cross-spectral density matrix. Several known theories of electromagnetic coherence and polarization are then invoked for the analysis of radiation, on and off the source surface. The results for the spectral density, degree of coherence, and degree of polarization are then discussed in detail. The effects of mutual corre...

On-axis polarization of beams radiated by electromagnetic circularly coherent sources

Optics Letters, Jun 28, 2022

Tailoring on-axis spectral density with circularly coherent light beams

Optics Letters

The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circula... more The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source’s degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.

Propagation of cross-spectral densities from spherical sources

Optics Letters, 2012

We show that the cross-spectral density in the far zone of a homogeneous spherical source can be ... more We show that the cross-spectral density in the far zone of a homogeneous spherical source can be described as a low-pass filtered version of that existing across the source surface. We prove that, to an excellent approximation, the corresponding filter with respect to a (normalized) spatial frequency ξ has a functional structure of the form √(1-ξ2), for 0≤ξ≤1. The cases of spatially incoherent and Lambertian sources are treated as significant examples.

Christoffel–Darboux sources

Optics Letters, 2021

A new, to the best of our knowledge, class of partially coherent sources is introduced on the bas... more A new, to the best of our knowledge, class of partially coherent sources is introduced on the basis of the Christoffel–Darboux (CD) formula read as the expression of a possible cross-spectral density. It will be seen that such an interpretation is possible because the CD formula gives the reproducing kernel of a suitable Hilbert space. After discussing general properties of CD kernels, a specific example is worked out using Hermite polynomials. A connection with the density matrix will be highlighted.

Journal of the Optical Society of America, Oct 23, 2008

Thin annular sources, either coherent or completely incoherent from the spatial standpoint, have ... more Thin annular sources, either coherent or completely incoherent from the spatial standpoint, have played a significant role in the synthesis of diffraction-free and J 0 -correlated fields, respectively. Here, we consider thin annular sources with partial correlation. A scalar description is developed under the assumption that the correlation function between two points depends on their angular distance only. We show that for any such source the modal expansion can easily be found. Further, we examine how the correlation properties of the radiated fields change on free propagation. We also give a number of examples and present possible synthesis schemes.

Photonics, Jul 17, 2023

A new class of stationary electromagnetic sources radiating outward from the surface of an infini... more A new class of stationary electromagnetic sources radiating outward from the surface of an infinitely long cylinder is introduced via vectorial coherent mode representation. First, two particular types of such sources are discussed: with either an electric or magnetic field aligned with the cylinder's axis. The former case represents a scalar scenario, while the latter leads to the two-component electric field. The combination of these two types of sources is then considered by forming the three-component electric field vector. An extension to the stationary case is then made in which the electric field correlations are shown to be described by the intrinsically 3 × 3 cross-spectral density matrix. Several known theories of electromagnetic coherence and polarization are then invoked for the analysis of radiation, on and off the source surface. The results for the spectral density, degree of coherence, and degree of polarization are then discussed in detail. The effects of mutual correlation of modes are also outlined. The new family of sources is of importance for any application involving cylindrical sources with controllable radiation.

Fractional Fourier transform and Fresnel transform

Paraxial propagation and kurtosis of fields generated by pseudo-Schell vortex sources

Fourth International Conference on Applications of Optics and Photonics, 2019

In this work, the paraxial evolution of fields generated by pseudo-Schell vortex sources is analy... more In this work, the paraxial evolution of fields generated by pseudo-Schell vortex sources is analyzed through some global parameters. In particular, it is shown that the kurtosis parameter of these fields presents a minimum at the beam waist and a maximum which value and position depends on the coherence characteristics of the source

On an Iterative Method for Super-resolution

Optica Acta: International Journal of Optics, 1975

ABSTRACT A recently proposed iterative method for super-resolution is studied with the aid of pro... more ABSTRACT A recently proposed iterative method for super-resolution is studied with the aid of prolate spheroidal wave functions. Perfect imagery is shown to be achieved in the limit of an infinite number of iterations. The case of a finite number of iterations is examined and possible extensions of the method are mentioned.

Transversely periodic partially coherent electromagnetic sources

The coherence and polarization features of partially coherent fields radiated from transversely p... more The coherence and polarization features of partially coherent fields radiated from transversely periodic electromagnetic sources are investigated in the most general case. Sources of this type are produced, for instance, when a partially polarized plane wave impinges onto an optical element, such as a polarization grating or an anisotropic wedge, which modifies the polarization of the incident field in a periodic way. Experimental results are reported, pertinent to the use of a double-wedge pseudo-depolarizer.

Optica Acta: International Journal of Optics, 1983

This article may be used for research, teaching and private study purposes. Any substantial or sy... more This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Shape invariant propagation of polychromatic fields

Optics Communications, 1984

When a polychromatic field propagates the transverse distribution of the power spectrum generally... more When a polychromatic field propagates the transverse distribution of the power spectrum generally changes from one plane to another. Conditions are found under which the spectrum distribution maintains the same shape in any cross-section. Examples of fields satisfying these conditions are given.

Fusion Engineering and Design, 1995

Numerical studies on the use of a quasi-optical grill to couple lower hybrid waves to a plasma, f... more Numerical studies on the use of a quasi-optical grill to couple lower hybrid waves to a plasma, for current drive in tokamaks, are currently under way. Study of the coupling has been carried out in a rigorous way, through the solution of scattering from cylinders with parallel axes in the presence of a plane of discontinuity for electromagnetic constants. Here we restrict our attention to the case of a plasma with a step density profile and report some results on launched spectra, coupled power and directivity.

Sampling in Optics

Springer texts in electrical engineering, 1993

Illuminate an object with laser light and look at it through a diffraction grating. You will see ... more Illuminate an object with laser light and look at it through a diffraction grating. You will see a set of mutually displaced copies of the object. If the lateral extent of the object is small enough, the various copies do not overlap. You can easily devise a method for selecting a single copy of the object. For example, you can replace your own optical system, i.e., your eye, by a converging lens and let the multiple images that were impressing your retina be produced on a screen. Then, a hole on the screen will suffice to isolate a single image. You can even dispense with the laser light and repeat the observation in a more domestic environment by looking at a distant street lamp through a piece of fine fabric. In this case, all of the object copies except the central one will appear iridescent, but the basic phenomena will be the same.

Journal of the Optical Society of America, Nov 24, 2015

We describe the new tutorial article type in detail and give some background on the reasons for i... more We describe the new tutorial article type in detail and give some background on the reasons for its introduction.

Nonambiguous determination of optical constants for absorbing materials

Applied optics, 1991

A recently proposed method for determining the optical constants of absorbing materials starting ... more A recently proposed method for determining the optical constants of absorbing materials starting from reflectance measurements is analytically treated. The conditions for a nonambiguous determination of the optical constants are established. The values of the parameters satisfying these conditions are explicitly evaluated.

Journal of the Optical Society of America, Apr 18, 2012

Journal of the Optical Society of America, Jul 27, 2015

Journal of Modern Optics, 1998

On the basis of the modal theory of coherence, we study partially coherent sources whose modes be... more On the basis of the modal theory of coherence, we study partially coherent sources whose modes belong to the class of Laguerre-Gauss functions for which the Laguerre polynomial has zero order. These modes present a phase profile with a helicoidal structure, which is responsible for notable phenomena, such as the propagation of optical vortices, beam twisting, and the presence of dislocations in interference patterns. By suitably choosing the eigenvalues associated with such modes, different partially coherent sources are obtained: sources with a flattened Gaussian profile, twisted Gaussian Schell-model sources with a saturated twist, and a new class of sources having an annular profile. Owing to the shape-invariance property of the underlying modes, the fields radiated by these sources do not change their transverse profile through propagation, except for scale and phase factors. We also prove that, if any such source is covered by a circularly symmetric filter, the new modal structure can he found in a straightforward manner.

Photonics

A new class of stationary electromagnetic sources radiating outward from the surface of an infini... more A new class of stationary electromagnetic sources radiating outward from the surface of an infinitely long cylinder is introduced via vectorial coherent mode representation. First, two particular types of such sources are discussed: with either an electric or magnetic field aligned with the cylinder’s axis. The former case represents a scalar scenario, while the latter leads to the two-component electric field. The combination of these two types of sources is then considered by forming the three-component electric field vector. An extension to the stationary case is then made in which the electric field correlations are shown to be described by the intrinsically 3×3 cross-spectral density matrix. Several known theories of electromagnetic coherence and polarization are then invoked for the analysis of radiation, on and off the source surface. The results for the spectral density, degree of coherence, and degree of polarization are then discussed in detail. The effects of mutual corre...

On-axis polarization of beams radiated by electromagnetic circularly coherent sources

Optics Letters, Jun 28, 2022

Tailoring on-axis spectral density with circularly coherent light beams

Optics Letters

The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circula... more The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source’s degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.

Propagation of cross-spectral densities from spherical sources

Optics Letters, 2012

We show that the cross-spectral density in the far zone of a homogeneous spherical source can be ... more We show that the cross-spectral density in the far zone of a homogeneous spherical source can be described as a low-pass filtered version of that existing across the source surface. We prove that, to an excellent approximation, the corresponding filter with respect to a (normalized) spatial frequency ξ has a functional structure of the form √(1-ξ2), for 0≤ξ≤1. The cases of spatially incoherent and Lambertian sources are treated as significant examples.

Christoffel–Darboux sources

Optics Letters, 2021

A new, to the best of our knowledge, class of partially coherent sources is introduced on the bas... more A new, to the best of our knowledge, class of partially coherent sources is introduced on the basis of the Christoffel–Darboux (CD) formula read as the expression of a possible cross-spectral density. It will be seen that such an interpretation is possible because the CD formula gives the reproducing kernel of a suitable Hilbert space. After discussing general properties of CD kernels, a specific example is worked out using Hermite polynomials. A connection with the density matrix will be highlighted.