There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

Cylindrical vector beams: from mathematical concepts to applications

Unified theory of coherence and polarization of random electromagnetic beams

Want to get experience? Want to get any ideas to create new things in your life? Read methods of numerical integration now! By reading this book as soon as possible, you can renew the situation to get the inspirations. Yeah, this way will lead you to always think more and more. In this case, this book will be always right for you. When you can observe more about the book, you will know why you need this.

Methods of Numerical Integration

The choice of the mathematical form of spatial correlation functions for optical fields is restricted by the constraint of nonnegative definiteness. We discuss a sufficient condition for ensuring the satisfaction of such a constraint.

/pdf/devising-genuine-spatial-correlation-functions-1b995cozty.pdf

Devising genuine spatial correlation functions

We consider a class of beams that are both partially polarized and partially coherent from the spatial standpoint. They are characterized by a correlation matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that would appear identical to ordinary Gaussian Schell-model beams in a scalar treatment. After establishing some inequalities that limit the choice of the matrix parameters, we study the main effects of propagation. Starting from the source plane, in which the beam is assumed to be uniformly polarized, we find that in the course of propagation the degree of polarization generally becomes non-uniform across a typical section of the beam. Furthermore, we find that the intensity distribution at the output of an arbitrarily oriented linear polarizer is Gaussian shaped at the source plane whereas it can be quite different at other planes.

/pdf/partially-polarized-gaussian-schell-model-beams-1tn1rk5u1q.pdf

Partially polarized Gaussian Schell-model 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.

Propagation of axially symmetric flattened Gaussian beams

For an electromagnetic stochastic beam, the choice of the mathematical structure of the cross-spectral density matrix is limited by the constraint of non-negative definiteness. We present a sufficient condition for building these matrices in such a way that this constraint is automatically satisfied. This allows us to put into evidence that electromagnetic beams can exhibit very peculiar correlation properties, some of which would not be encountered in scalar treatments. These results are illustrated by means of a number of examples.

http://webusers.fis.uniroma3.it/~ottica/sant/pubs/Max104.pdf

On genuine cross-spectral density matrices

We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint It is based on the use of a single matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities This approach, which can be viewed as an approximate form of Wolf's general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach A peculiar interference law applying to mutual intensities is derived We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description Hints for extensions are given

/pdf/beam-coherence-polarization-matrix-197senfugb.pdf

Massimo Santarsiero

Papers

Devising genuine spatial correlation functions

Partially polarized Gaussian Schell-model beams

Propagation of axially symmetric flattened Gaussian beams

On genuine cross-spectral density matrices

Beam coherence-polarization matrix