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Esse artigo busca trazer comentários e a errata da dissertação apresentada à Faculdade de Engenharia Elétrica e de Computação da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenção do título de Mestre em Engenharia Elétrica, na Área de Telecomunicações e Telemática, por Juliano Carvalho Bento, sob o título “Método Analítico para Descrição de Importantes Feixes Ópticos Obstruídos e oSpotde Poisson-Arago”, defendida em 17/07/2016. É possívelacessá-la no site doRepositório da Produção Científica e Intelectual daUnicamp(). Qualquer outro comentário ou errata não hesite em enviar para.

International audience; We present a numerical and experimental demonstration of the emergence of a bright temporal spot in the initial shadow of a fully-coherent temporal signal. Impacts of nonlinearity and dispersion regimes are also investigated.

The purpose of this note is to prove dispersive estimates for the wave and the Schrodinger equations outside strictly convex obstacles in R d . If d = 3 , we show that, for both equations, the linear flow satisfies the (corresponding) dispersive estimates as in R 3 . In higher dimensions d ≥ 4 and if the domain is the exterior of a ball in R d , we show that losses in dispersion do appear and this happens at the Poisson spot.

The history of conceptions of light is among the most exciting scientific adventures. It was Fresnel's theoretical work that made it possible to establish the most solid theoretical basis of wave optics. Two centuries ago, his approach was validated by the observation of a counter-intuitive bright spot appearing at the center of the geometric shadow of an illuminated opaque circular object. This phenomenon has remained known as the Arago spot. We propose here to further extend the spatial/temporal analogy that exists between diffraction and dispersion by revisiting the Arago spot formation in the time domain through the temporal dispersive evolution of light after being briefly stopped by an obstacle. The analytical treatment that is possible for linear propagation as well as the experiments based on telecom optical fibers and fast optoelectronics confirm that we observe the emergence of light where it was initially absent. As the power increases and Kerr nonlinearity affects the propagation, the Arago spot intensity is affected by the sign of the dispersion.

Generation of subwavelength beam sizes is a fascinating challenge with several implications. The observation of a 120 nm laser spot in the visible part of the spectrum is reported here. It has a size variation of less than 10% in a distance of 50 µ m along the axis of propagation. This so-called Arago spot results from the diffraction of the light from a laser diode by the edges of an absorbing disk. Applications are discussed and hollow beams carrying orbital angular momentum with a 400 nm diameter dark spot in the center are evidenced. This paves the way toward atom lithography via atom guiding or new spectroscopy on forbidden transitions.

The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.

We show that structured light can amplify the intensity of an Arago–Poisson bright spot, the cornerstone proof of the wave nature of light, by several orders of magnitude. Specifically, we use a thin annular beam produced by either an axicon–lens combination or two axicons to illuminate an opaque circular obstacle. Experimental results confirm the numerical calculations. By judiciously choosing our scheme’s parameters, the bright spot intensity can be higher than that of the original beam, meaning that structured light facilitates “focusing” of light behind an obstacle. This amplification, in addition to didactic elucidation of this classical effect, can find use in optical alignment/metrology, lithography, aberration measurements, as well as in basic science studies of the Arago–Poisson spot in matter waves.

When a part of an optical wave-front experiences a sharp change in its phase, Fresnel diffraction becomes appreciable. Sharp change in phase occurs as a wave-front strikes with a phase step. The intensity distributions of diffraction patterns of the phase step is formulated by applying Fresnel–Kirchhoff integral. For while the incident light on the step is coherent, the Fresnel–Kirchhoff integral can be solved by using familiar Fresnel integrals. But, when the incident light is partially coherent, one can not express the diffraction integral as the Fresnel integrals and the problem is summarized in solving some unusual integrals. In this report, we propose Fourier transform method for solving the Fresnel–Kirchhoff integral. In this regard we use discrete Fourier transform method and calculate Fresnel diffraction from the 1D phase step by FFT-based algorithms. This method does not have any restriction on the coherence and profile shape of the incident light. We show that the method have appropriate solutions for coherent and partially coherent lights. For the case of the coherent light illumination of the step, the obtained results are in good agreement with the calculated results by using the Fresnel integrals in reported literatures.

In this study, an optical scheme based on the measurement of light intensity and a proper orientation of the Fresnel Rhomb is successfully developed for simultaneous determination of the phase retardation and fast axis of a wave plate. The theoretical analysis of the principle of measuring the reflection-induced retardance of the Fresnel Rhomb and the phase retardation of a wave plate is given taking Stokes–Mueller Formalism as a mathematical tool. In this method, the fast axis position of the wave plate need not be determined in advance. In addition, the measured result is free of the intensity fluctuation of light source. An application example is also demonstrated. The measured result of the example is verified with an experiment. Some of the merits of the method, such as, a simple optical set-up, high stability and high accuracy, low cost and easier operation, are presented, and the validity of the method is demonstrated.

The possibility of X-ray phase contrast imaging using already suggested three-block interferometer consisting of bi-level Fresnel zone plates is considered. The interferometer operates in the amplitude-division mode and does not impose strong requirements to spatial and temporal coherences of an initial radiation. The use of the Fresnel zone plates as the interferometer blocks allows one to obtain an optically magnified image of an object and to condense the radiation incident on the tested object.

Aims. We seek to study the Fresnel diffraction of external occulters that differ from a single mask in a plane. Such occulters have been used in previous space missions and are planned for the future ESA Proba 3 ASPIICS coronagraph. Methods. We studied the shading efficiency of double on-axis disks and generalized results to a 3D occulter. We used standard Fourier optics in an analytical approach. We show that the Fresnel diffraction of two and three disks on axis can be expressed using a Babinet-like approach. Results are obtained in the form of convolution integrals that can be written as Bessel-Hankel integrals; these are difficult to compute numerically for large Fresnel numbers found in solar coronagraphy. Results. We show that the shading efficiency of two disks is well characterized by the intensity of the residual Arago spot, a quantity that is easier to compute and therefore allows an interesting parametric study. Very simple conditions are derived for optimal sizes and positions of two disks to produce the darkest structure around the Arago spot. These conditions are inspired from empirical experiments performed in the sixties. A differential equation is established to give the optimal envelope for a multiple-disk occulter. The solution takes the form of a simple law, the approximation of which is a conical occulter, a shape already used in the SOHO Mission. Conclusions. In addition to quantifying expected results, the present study highlights unfortunate configurations of disks and spurious diffractions that may increase the stray light. Particular attention is paid to the possible issues of the future occulter spacecraft of ASPIICS.

In this chapter I discuss the dependence of image formation on the nature of light itself. Geometrical optics is no longer sufficient to predict the relationship between the object and the image when the object's size approaches the wavelength of light because the object diffracts the incident light. Since diffraction is significant when the details in an object are similar in size to the wavelength of light, we need to understand the interaction of light with matter to predict the relationship between the object and the image formed by diffracted light. This is the realm of physical optics, which is based on the wave theory of light. I discuss the development of the wave theory of light by Huygens, Young, Fresnel, and Maxwell. I also discuss how Ernst Abbe developed a theory of image formation where the diffraction of light limits the resolving power of the light microscope.

The X-ray interferometric Fresnel holography was proposed and theoretically investigated. It was shown that under definite conditions the recorded interference pattern formed at the output surface ofthe analyzer crystal (the third block of interferometer) is the X-ray interferometric hologram (generally the Fresnel one) of the object under investigation. Further reconstruction of an image is performed with the help of visible light or a numerical method. As an example the recording of a Fresnel hologram of the simplest case of one-dimensional object, a narrow slit, and the reconstruction of an image by means of visible light were considered. This method may be used in X-ray microscopy and realized using synchrotron sources ofX-ray radiation, as well as X-ray free electron lasers.

The iterative Fresnel integrals method (IFIM) has been applied for the simulation and generation of the complete near-field Fresnel diffraction images created by N -apertures for the first time. The simulation can be performed in any PC using a MATLAB program developed by the authors. Necessary formalism was derived for the general N -slit problem, and a simulation algorithm was devised for this application. An interesting combination of interference effects with Fresnel diffraction was observed in the simulated images. Transition to the expected Fraunhofer diffraction pattern from Fresnel diffraction for N -apertures is also observed in the simulations under the appropriate conditions. Principal maxima of the expected Fraunhofer diffraction were observed at their expected positions, as well as the expected minima and the secondary maxima. The program can serve as a useful tool to study the complex phenomenon of Fresnel diffraction from N -apertures, and in addition, to study the near-field Fresnel diffraction from amplitude diffraction gratings.

Focusing characteristics of cross like Fresnel zone plate is well analyzed. This element is composed of two perpendicular linear Fresnel zone plates. Focusing properties of the element is compared to a classic and square Fresnel zone plate. Analysis clarify that focusing of the elements is well corrected in comparison to square Fresnel zone plate. Resolution is noticeably increased, DC noise and diffraction efficiency are substantially reduced and also secondary maxima have been evidently suppressed. Theoretical results have been completely verified by experiment.

We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens for all related audiences. Our solutions are in the analytic form. A general principle of the Talbot effect, which is the optical near-field effect, is the Fresnel diffraction. The Fresnel integral is rather complicated. We therefore introduce an alternative method which is based on the wave propagation through the transmission functions of the grating and the lens. Our method has been proved by a simple experimental setup.

The X-ray interferometer consisting of three Fresnel zone plates with the same optical axis is considered. The interferometer operates in the amplitude-division mode and does not impose the strong requirements on the coherence of initial radiation. The interferometer is the modification of earlier one, with the main difference that the labor-intensive to manufacture multilevel Fresnel zone plates are replaced by the ordinary bi-level ones. The longitudinally and transversely defocused modifications of interferometer were considered by the numerical simulation method.

Phase shifted linear Fresnel zone plates are presented for the first time. These diffractive elements are linear Fresnel zone plates in which their phase are laterally shifted. The impact of the phase shifting on their diffractive and focusing properties are studied. It is demonstrated that by shifting the phase, two parallel linear beams can be generated at the focal plane. Furthermore, as they are propagating, a non-diffractive line-shaped beam is generated at a given distance from the focus. Transverse intensity profile of the beam at different distances as well as its cross section of propagation along the optical axis clearly shows that the intensity profile of the beam is really kept unchanged as it is propagated. All results are completely verified by experiments.

For the observer at infinity, a Schwarzschild black hole serves as an attractive opaque disk with a radius of 3$\sqrt{3} M$ that will produce the diffraction pattern of gravitational waves (GWs). In this study, we demonstrate that a bright spot, which is a diffraction effect analogous to the Poisson-Arago spot in optics, will appear when an ingoing (quasi-) plane GW is diffracted by a Schwarzschild black hole. Here, we propose the diffraction effect of the GWs described by the exact diffraction solution of the GWs using the Heun function. For the first time, the Fresnel half-wave zone method is proposed to calculate the angular part of the GW scattering stripes for the observer at infinity. The prospect of observing the diffraction bright spot is discussed with an eikonal approximation. For normal incidence (quasi)-plane waves with 100 Hz (0.1 Hz) frequency diffracted by the central black hole of the Milky Way, the time delay between the Earth bathed in a bright spot and the minimum of the first dark stripe is 3.86 (3860) days. We will witness the second bright fringe (40% amplitude of the central bright spot) after 6.2 (6200) days. This new diffraction pattern involving the early phase of inspirals and pulsars as continuous gravitational wave sources is a potential scientific target for future space-and ground-based gravitational wave detectors, respectively.

The “Association de Satellites Pour l'Imagerie et l'Interferometrie de la Couronne Solaire”, ASPIICS, selected by ESA for the PROBA-3 mission, heralds the next generation of coronagraph for solar research, exploiting formation flying to gain access to the inner corona under eclipse-like conditions for long periods of time. A detailed description of the ASPIICS instrument and of its scientific objectives can be found in [1]. ASPIICS is distributed on the two PROBA 3 spacecrafts (S/C) separated by 150 m. The coronagraph optical assembly is hosted by the “coronagraph S/C” protected from direct solar disk light by the occulting disk on the “occulter S/C”. The most critical issue in the design of a solar coronagraph is the reduction of the stray light due to the diffraction and scattering of the solar disk light by the occulter, the aperture and the optics. In the present article, we deal with two of these issues: - The analysis of the stray light inside the telescope. - The optimization of the external occulter edge, in order to eliminate the Poisson spot behind the occulter and to lower the stray light level going through the entrance pupil of the telescope. This work was performed in the framework of the ESA STARTIGER program which took place at the Laboratoire d’Astrophysique de Marseille (LAM) during a 6-month period from September 2009 to March 2010. In general, it is a very complicated task to combine the above two stray light issues together in the simulation and design phase as it requires to consider the propagation inside the telescope of the light diffracted by the external occulter. Actually, the present literature only reports diffraction calculations performed for simple occulting systems (i.e., two disks and serrated disk). A more pragmatic approach, also driven by the tight schedule of the STARTIGER program, is to separate the two contributions, and perform two different stray light analyses. This paper is dedicated to the description of both analyses: in particular, the first part is dedicated to the evaluation of the stray light inside the telescope, assuming a simple disk as occulter, and a preliminary baffle design is presented; the second part describes the investigation on the geometry of the external occulter, with a detailed description of the laboratory setup that has been designed and implemented to compare together several types of occulting systems.

The vector diffraction of linearly polarized plane wave passing through a thin circular plate with a sub-wavelength radius is investigated by the finite element method. The transverse distribution and propagating evolution of the diffracted field with different intensity expressions are analyzed and compared. It shows that there are not only the component of the incident polarization, but also those of other two vertical directions in the near-field diffracted region. Regardless of the relationship between the wavelength and the radius of the circular plate, the diffracted field could evolve into a steady annular diffracted pattern, in which there is a central bright spot (so-called Poisson spot). There is an obvious difference of the diffracted properties between two intensity expressions from the square of electric field and the average magnitude of the Poynting vector as the propagation distance is very small, while they can be considered same with a large propagation distance (e.g. more than a wavelength).

There are many 3D data structures for computing diffraction field, the description based on 3D point-cloud is the elemental method of other descriptions, the diffraction field of 3D scene can be thought as the superposition of the diffraction field of each sampled light point and other descriptions can be thought as grouping with point-cloud by different way. The paper focuses on devising a computation method of 3D Fresnel field which is based on Fresnel diffraction field propagation reversibility. The proposed method combines the reversibility of Fresnel propagation and the requirement of sampling spacing by Nyquist criterion, i.e. to find the best space positions to optimize the number of sampling points and the reconstruction for the 3D Fresnel field. The method can be applied to reduce the computational complexity and improve computational efficiency.

In this work, we propose and analyze a novel kind of binary Fresnel zone plate with single focus. It consists of a Fresnel zone plate whose zones have rough edges. We give analytical results for the intensity along the optical axis and demonstrate that lateral roughness of the zones produces the disappearance of secondary foci as a blurring of the edges. Besides, we corroborate its behavior by numerical simulations and experiments. This kind of Fresnel zone plate can be useful in a wide range of photonic applications, even for focusing with soft and hard X-rays or extreme ultraviolet radiation.

Recently there have been experimental results on Poisson spot matter wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for the Poisson's spot with matter waves based on Babinet principle in which we use the results for a free propagation and single slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium ($D_{2}$) molecules., 8 pages, 5 figures

The intensity distribution in the vicinity of the focus of circular Fresnel zone plate formed by Bessel-Gauss beam is studied. Dark hollow beams are obtained near focus under the illumination of high order Bessel-Gauss beam, the width and the length of central hollow depends on the order of the beam and the number of plate zones. These beams with special intensity distribution in the field of laser processing and trapping particles have potential application value.

Diffraction of matter-waves is an important demonstration of the fact that objects in nature possess a mixture of particle-like and wave-like properties. Unlike in the case of light diffraction, matter-waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of indium atoms is diffracted around a silicon dioxide sphere. The result is an amplification of the on-axis bright feature which is the matter-wave analogue of the well-known `Poisson spot' from optics. Our treatment confirms that the diffraction patterns resulting from our complete account of the sphere Casimir-Polder potential are indistinguishable from those found via a large-sphere non-retarded approximation in the discussed experiments, establishing the latter as an adequate model., 13 pages, 10 figures

The presence of a bright (Poisson) spot in the geometrical shadow of circular/spherical shapes has been known for the past two centuries. A broad class of telescopes that involve simultaneous transmit and receive require suppression of the reflected light from the secondary mirror on the detector. For instance, the on-axis design of optical telescope for the evolved Laser Interferometric Space Antenna (eLISA), a re-scoped version of the baseline LISA mission concept, requires suppression of reflected laser light from the secondary mirror on the detector. In the past few years, the hypergaussian functions with petal-shaped realization have been shown to significantly suppress intensity along the optical axis. This work reports on fabrication of a series of petal-shaped masks using a variety of techniques such as 3D printing, photolithography, and wire Electro Discharge Machining. These masks are designed and fabricated to operate in the range of Fresnel numbers between 4 and 120. This paper discusses the challenges, successes, and failures of each fabrication technique and the optical performance of typical masks with suggestions for potential follow up work.

A novel formulation of the problem of wave diffraction by abrupt and volume discontinuities in a waveguide is presented in this chapter. In the context of this formulation, the authors succeeded in solving a number of the long-discussed problems concerning mathematical properties of matrix models of the mode-matching technique. In particular, they rigorously justified the possibility to use the truncation technique, unconditionally converging in the norm of a space of infinite sequences, for numerical implementation of the developed matrix models. The operator-matrix analysis of the mode-matching technique has shown that the proposed approach leads to the operator Fresnel formulas, which generalize properly the well-known Fresnel formulas to the scattering operators.

This appendix explains complex Fresnel integrals. Several forms of Fresnel integrals have been defined by various authors, and as a result, the definition often depends on the application. The complex Fresnel integral is related to the cosine and integral functions. Another function used in diffraction theory is the modified Fresnel integral. This book is intended as an advanced text for courses in antennas, with a focus on the mature but vital background field of aperture antennas. It is is useful for students of final year, MSc, PhD and Post‐Doctoral, as well as readers who are moving from academia into industry, beginning careers as wireless engineers, system designers, in R&D, or for practising engineers.

The Fresnel lens arrays, which can be used as the alternative of microlens arrays for integral imaging, were designed and fabricated. Their imaging properties for different colors were investigated, and a design based on the Fresnel lens arrays with chromatic dispersion is proposed.

The Arago-Poisson spot played an important role in the discovery of the wave nature of light. We demonstrate a novel way to shape the Arago-Poisson spot by partially twisting the phase fronts of the incident light beam. We use a spatial light modulator to generate the holographic gratings both for mimicking the circular opaque objects and for modulating the spiral phase profiles. For incomplete spiral phase of five- and tenfold symmetry, we observe the gradual formation of the on-axis bright spots upon propagation. Our results show that two fundamental but seemingly independent optical phenomena, namely, the Arago-Poisson spot and the orbital angular momentum (OAM) of light, can be well connected by changing the phase height ϑ gradually from 0 to 2π. The experimental results are well interpreted visually by plotting the Poynting vector flows. In addition, based on the decomposed OAM spectra, the observations can also be understood from the controllable mixture of a fundamental Gaussian beam and an OAM beam. Our work is an elegant demonstration that spiral phase modulation can add to the optical tool to effectively shape the diffraction of light and may have potential applications in the field of optical manipulations.

We have reported the present status in the development of a position measurement unit (PMU) for a flying inertial fusion energy (IFE) target. The PMU, which uses Arago spot phenomena, is designed to have a measurement accuracy smaller than 1 μm. By employing divergent, pulsed orthogonal laser beam illumination, we can measure the time and the target position at the pulsed illumination. The two-dimensional Arago spot image is compressed into one-dimensional image by a cylindrical lens for real-time processing. The PMU are set along the injection path of the flying target. The local positions of the target in each PMU are transferred to the controller and analysed to calculate the target trajectory. Two methods are presented to calculate the arrival time and the arrival position of the target at the reactor centre.