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Radiation pattern determination from phaseless near field data distributions collected over limited domains on planar surfaces is addressed as a nonlinear inverse problem. Numerical results show the good performances of the considered approach suggesting new possibilities for simplifying measurement setups in near field techniques.

The synthesis of difference patterns via linear arrays, the elements of which are fed with the same amplitude, is proposed as a way to simplify the receiving chain and improve the efficiency of the antenna. The problem is solved by means of suitable analytical procedures based on a ‘density taper’ approach. In particular, two different techniques are introduced and compared on the basis of a set of numerical examples. It is shown that one of them definitely outperforms the other one, and that constraints of practical interest can be satisfactorily fulfilled.

We have developed a numerical code that, starting from far-field intensity measurements, is able to evaluate the excitation coefficients of the transverse modes in a laser system.Both the coherent and incoherent mode cases are addressed, and, while the incoherent case is shown to be equivalent to a linear problem, the coherent case is discussed through its equivalence to the phase-retrieval problem. Problems arising from both ill posedness and the nonlinearity are discussed in detail.The validity of our approach is confirmed by several numerical simulations and some experimental results on the characterization of a Q-switched Nd:YAG laser.

In the solution of inverse scattering problems, support information is useful in order to reduce the degree of nonlinearity of the relationship among the data and the unknowns, as well as the overall computational burden. Moreover, by taking into account the spectral properties of the scattered fields, it can be helpful to reduce the effect of noise on data. Accordingly, a 3D inversion strategy in which one performs a preliminary estimation of the support of the targets is considered in this paper to process the experimental data provided by the Institut Fresnel of Marseille, France. In particular, the imaging problem is tackled in a step-wise fashion, in which one first pursues a morphologic characterization of the targets using a linear sampling method based procedure. Then, the retrieved support is exploited to 'filter' the data and, finally, in the quantitative characterization of the targets. This last step is performed by using the optimized contrast source extended Born inversion method wherein the estimated support is exploited in order to reduce both the investigated domain and the nonlinearity of the inverse problem.

A new method for the estimation of the far field from two amplitude distributions in near zone is presented. The crucial point of the proposed approach relies on the choice of an appropriate function of the data, which is minimised in order to find the solution. It turns out that, although the problem is nonlinear, the global minimum can be found efficiently by a Newton-like minimisation procedure.

The phase retrieval from the knowledge of the amplitude of a complex signals is an interesting problem encountered in many fields of the applied sciences as: astrophysics, electron microscopy, numerical holography, antenna testing, inverse optics, quantum mechanics, etc.. A list of references on such subjects can be found in [1–2]. In this paper we refer to the phase of radiated fields.

Development of accurate numerical methods for the analysis of photonic-bandgap-based devices is a relevant issue in optimizing existing devices and/or developing new design solutions. Within this framework, we present an innovative and general approach for the evaluation of the electromagnetic behavior of two-dimensional finite-extent photonic crystals made of a finite set of parallel rods. The proposed approach is a generalization of the scattering-matrix method introduced by Maystre and co-workers and of its improved version proposed by the present authors, which exploits a suitable aggregation into "macrocells" to achieve a reduction of the number of unknowns. As a matter of fact, both of these approaches can be exploited only in those cases in which particular modal expansions for the fields hold true. In order to overcome this limitation, we propose a suitable exploitation of the method of auxiliary sources to provide a general and reliable method for the numerical computation of the scattering matrix of an object of arbitrary shape. By taking advantage of this, we can then generalize our improved scattering matrix method to further increase its computational effectiveness. A numerical analysis of some square-lattice configurations is reported to confirm the accuracy of the proposed method and the remarkable computational benefit.

Applicability of inverse scattering based imaging procedures can be broadened by developing new approaches exploiting only amplitude data. As a matter of fact, this can open the way to simpler and less expensive measurement set-ups. In this respect, a two-step based procedure for solving electromagnetic nonlinear inverse scattering problems from only amplitude measurements of the total field has been recently proposed [1,2]. However, in these latter both amplitude and phase of the incident field are still required. In this contribution, we show the possibility of achieving this information from the measured amplitude distribution of the incident field on the observation domain. In particular, a three steps imaging technique which exploits only amplitude measurements of the total and incident fields has been developed. The proposed procedure has been tested against benchmark experimental data available in the literature. The obtained results fully confirm the possibility of achieving faithful reconstructions of unknown targets without performing any phase measurements and any approximation on the scattering equations involved in the inverse scattering problems.

A new approach for quantitative electromagnetic imaging of scatterers located in free space from phaseless data is proposed and discussed. The procedure splits the problem into two steps. In the first one, we solve a phase-retrieval problem for the total field, thus estimating the amplitude and phase of the scattered field. Careful analysis of properties and possible representations of both scattered and incident fields allow us to introduce a criterion for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step by use of the estimated scattered field. Numerical examples are provided to check the whole chain in the presence of noise-corrupted data.

In several array synthesis problems the lack of a common element pattern among different antennas makes the use of classical synthesis methods based on the array factor questionable. A recently introduced approach to array synthesis is exploited to take account in an exact fashion of the mutual coupling between patches for the synthesis of pencil beams by microstrip arrays. Optimality of the approach allows quantifying the advantages of the method with respect to common approaches, which largely compensates in several cases for its additional computational burden.

The authors present a new approach for determining the excitations of a given set of sources that will produce a maximum field in a given direction subject to arbitrary sidelobe bounds. The approach guarantees attainment of the globally optimal solution for a large class of pencil beam synthesis problems, including possible near field constraints.

The problem of reconstructing an unknown signal starting from the knowledge of only magnitude information about its Fourier transform is addressed. To this end a phase retrieval (PR) method, based on the inversion of a quadratic operator, is proposed, presented, and discussed. The main feature of the approach is the use of a square amplitude distribution rather than an amplitude distribution. In the lack of any a priori information about the phase to be recovered, the success of the method is related to the availability of a sufficiently large ratio between the dimension of data and the dimension of unknowns; the retrieval procedure could converge to a meaningless trap when this ratio is not large enough. It should be noted, however, that the proposed method has a range of global effectiveness wider than that of previous approaches. Moreover, when available, the use of a priori information, such as the knowledge of the support of the scene to be imaged or the knowledge of a part of the scene, allows one to achieve accurate final images starting from a completely random initial guess of the image values. We apply our PR-based method to a synthetic aperture radar (SAR) case. As is well known, random motion of the platform and/or propagation effects in turbulent random media can affect the correct phase synchronization of the received SAR raw data needed for well-focused SAR images. As a matter of fact, even relatively small phase errors greatly impair the quality of the image. Under common conditions phase errors on the received signal affect just the phase of the Fourier transform of the intensity image without impairing its amplitude. The proposed technique is able to compensate these phase errors by retrieving the phase of the Fourier transform of the image intensity. We also present several experiments performed either on numerically simulated data or on actual data relative to an airborne SAR mission that show the effectiveness of the proposed PR method.

This paper describes, analyzes, and implements an approach to far-field determination from phaseless measurements over two planar surfaces. A proper formulation of the problem is considered as a quadratic inverse one whose data is the square amplitude of the near field. A solution is introduced as the global minimum of an appropriate functional. Next, to perform such a minimization procedure, a finite dimensional representation of the field radiated by sources whose plane-wave spectrum becomes negligible outside a fixed angular domain is used. A detailed investigation of the properties of the mapping connecting the unknowns to the data makes it possible to analyze how to escape from the local minima possibly met in the course of the minimization procedure. To this end, the crucial role of the availability of phaseless data over two different sarfa,ces and of appropriate weights in the functional definition is emphasized, and a reliable iterative procedure converging on the solution, regardless of the starting point, is thus obtained. This property is confirmed by experimental results concerning near-zone data from a shaped reflector at 9 Ghz. It can be readily appreciated that when only the field intensity is detected the complexity and the cost of the equipment required for near-field techniques in antenna testing and diagnostics can be reduced to a very large extent.

A new method to accurately reconstruct a synthetic aperture radar complex image starting from raw received data whose phase is affected by propagation in the turbulent atmosphere and/or by motion instability of the platform carrying out the antenna is presented. It is based on the inversion of the, nonlinear relationship between the raw data square amplitude distribution and the unknown complex reflectivity of the scenario. The unknown complex reflectivity is found by minimising a proper functional using the partial phase information carried out by the phase-corrupted raw data as the initial guess of an iterative procedure. The method, which is capable of compensating for both 1-D and 2-D phase errors, has been validated on both simulated data and real data whose phase has been corrupted by a simulated phase error. The considerable accuracy of the final images proves the effectiveness of the proposed procedure.

A quantitative measurement of laser-beam quality can be performed by determination of the presence of multiple transverse modes of the laser oscillator and by calculation of their power content. Along this line of argument, we discuss a new approach that, starting from near-field and far-field intensity measurements, can evaluate the complex excitation coefficients of the transverse modes in a laser beam. The exploitation of near-field measurements sharply improves the performances of the technique in those cases in which only far-field measurements are used. The validity of the method is confirmed by several accurate numerical simulations and by some experimental results relative to a multimode Q-switched Nd:YAG laser.

The experimental feasibility of testing a radiating source by a method requiring only amplitude data is shown in the cylindrical scanning technique. The proposed innovative approach is applied to a set of measured near field data of a parabolic reflector antenna. The presence of a real probe antenna is also considered. No a priori assumption about the missing phase information is required; the solution is found by starting from a completely random first guess. The applied technique, especially at millimeter wavelengths, provides a powerful tool for dealing with several applications, such as f.i. reflector or array testing and diagnostics. It has high precision and employs less expensive and simpler setups.

A new method for recovering the complex near and far field from amplitude distributions collected over two near zone surfaces is proposed. By exploiting the mathematical properties of the radiated fields and choosing an appropriate functional of the data, the solution is found through the minimisation of the introduced functional. All details of the resulting iterative procedure are worked out for the cylindrical scanning in the three dimensional vector case where the implementation turns out to be effective thanks to a proper use of the FFT algorithm. It is shown that this new approach allows the solution to be obtained starting from a completely arbitrary point, so avoiding the local minima problem.

After briefly reviewing the properties of the squared amplitudes of radiated fields, a simple and effective necessary condition to test if a source of given size and structure can radiate or not a power pattern lying in a given mask is furnished. The criterion is shown to be also sufficient for linear arrays, thus allowing to reduce the overall problem to the synthesis of a nominal pattern.Then, new synthesis procedures, strongly relying on the properties of squared amplitude distributions and on the quadraticity of the operator relating the source to the power pattern, are introduced. They are implemented and tested in the cases of linear and planar uniform arrays, showing that thanks to a full exploitation of the properties of quadratic operators and of those of squared amplitude distributions, they allow one to achieve very efficient solutions to mask constrained synthesis problems.

Within the framework of inverse scattering problems, the quantifying of the degree of nonlinearity of the problem at hand provides an interesting possibility for evaluating the validity range of the Born series and for quantifying the difficulty of both forward and inverse problems. With reference to the two-dimensional scalar problem, new tools are proposed that allow the determination of the degree of nonlinearity in scattering problems when the maximum value, dimensions, and spatial-frequency content of the unknown permittivity are changed at the same time. As such, the proposed tools make it possible to identify useful guidelines for the solution of both forward and inverse problems and suggest an effective solution procedure for the latter. Numerical examples are reported to confirm the usefulness of the tools introduced and of the procedure proposed.

In Chiappinelli et al. (1999) we have shown the usefulness of wavelet expansions in linearized inverse scattering problems. In this communication we motivate the use of wavelet expansions and show their usefulness in the non-linearized case through numerical examples. Two different approaches, which we call fixed and adaptive multiresolution respectively, are dealt with.

This paper presents a simple and innovative deterministic approach to the synthesis of uniformaly excited thinned arrays able to fulfill constraints concerning both the sidelobe level and the value of the radiated far field (and/or of the directivity) in a set of given directions. Starting from a reference regular (periodic or even aperiodic) lattice and from an optimal continuous reference source fulfilling at best the required specifications, the proposed approach finds out both the number and the location of the isophoric (i.e., equi-amplitude) radiating elements to withdraw in a fast and effective fashion. In fact, it is based on a deterministic best-fitting procedure which takes inspiration from existing density taper techniques. Examples are provided with reference to the synthesis of large circular arrays and confirm the interest of the proposed procedure.

The problem of SAR imaging when only phase corrupted raw data are available is addressed. Results on real data, when polynomial phase errors are used, are also presented. The presented method is able to compensate for both 1D and 2D phase errors.

Presents an iterative method, based on the use of a phase retrieval technique, for the accurate processing of SAR images starting from phase errors affected raw data.

By taking inspiration from (1), a synthesis strategy is proposed for the case of planar arrays and ring shaped patterns which does not require the exploitation of global optimization procedures. In particular, the approach is able to determine a priori (that is, without solving the overall design problem) whether the given power pattern design constraints can be fulfllled or not, and, in the adflrmative case, to determine the needed excitation coe-cients in a fast deterministic manner. Although the approach does not apply to generic planar arrays and generic constraints, it applies to a large number of problems of actual interest, and outperforms some recently published synthesis procedures. Moreover, it may serve both as a reference solution for more general synthesis procedures, and as an elementary brick for more cumbersome synthesis problems.

The Linear Sampling Method (LSM) is an efiective method to tackle the prob- lem of reconstructing the shape of unknown metallic or dielectric scatterers from the knowledge of single frequency multi-view/multi-static data. Notably, as it just requires to solve a linear problem, its implementation is straightforward and its computational burden almost negligible. However, no results are available in the literature to explain under which operating conditions (e.g., the number of incident waves and receivers which has to be considered) LSM properly works. With respect to the case of dielectric scatterers, in this communication, starting from the physical interpretation of LSM, we provide some guidelines for its successful application. These results are then conflrmed processing experimental data from the \Marseille" data-set.

A hybrid approach to the synthesis of the excitations and locations of non-uniformly spaced arrays, in order to achieve optimal focusing in any given direction, is proposed and discussed. The approach takes definite advantage from the convexity of the problem with respect to the excitation variables, and exploits a simulated annealing procedure as far as the location variables are concerned. The corresponding synthesized patterns outperform previously known results in standard benchmark problems.

This paper presents an innovative Direct Radiating Array (DRA) architecture exploiting aperiodic tilings of the plane. In particular, a pinwheel tiling has been selected in order to flx positions of the difierent radiating sources, which are constituted by properly shaped elements. Such a choice allows to achieve a good aperture e-ciency and very low pseudo-grating lobes while using only two difierent kinds of radiating elements. Preliminary results are shown and discussed with reference to both cases wherein the single tiles are not fully populated and wherein ad-hoc sub-array radiators are used. The very encouraging results achieved leave open the way for further interesting possibilities.

In a large number of applications, including communica- tions from satellites, an optimal exploitation of the available power is of the outmost importance. As a consequence, isophoric array archi- tectures, i.e., arrays using the same power in all the difierent entry points and achieving the ampliflers' maximum e-ciency, are of great interest. At the same time, the easy reconflgurability of the power patterns results fundamental in order to get a full exploitation of the payload. In this paper, an innovative and deterministic approach is proposed for the optimal synthesis of linear phase-only reconflgurable isophoric sparse arrays able to commute their pattern amongst an arbi- trary number of radiation modalities. The introduced perspective leads to an efiective solution procedure for the fast design of antennas with high performance, and does not recur to computationally expensive global-optimization techniques. Numerical results concerning applica- tions of actual interest and employing realistic element patterns are provided in support of the given theory.

Simulation of 3D structures requires large memory and CPU time, which may then forbid realistic simulations of complex structures. Computational requirements can be dramatically reduced using the Transmission matrix T of the structure elements. The T matrix of the whole structure is in fact the product of the T matrices of the constituting elements. The model is proposed and tested in 2D with some specific examples. Possible critical points, such as radiation modes effects and multimode guided propagation are commented.

The PRIN 2009 Project SAPPHIRE has created the first national infrastructure for a shared access to a silicon photonic foundry. The goal has been accomplished developing dedicated design kits of silicon photonic building blocks together with software tools for high-level circuit design of Photonic Integrated Circuits (PICs). Here, we present successful examples of silicon photonic PICs fabricated in multi project wafers in the framework of the SAPPHIRE platform, demonstrating the flexibility and the viability of the generic foundry model for silicon photonics.

Mode Division Multiplexing is currently investigated as a possible way to increase fiber system capacity. With this approach, different modes of the same fiber carry distinct information. One of the problems to be solved in these systems concerns coupling/decoupling of the various modes to/from the same fiber. In this presentation, the mode features of a mode mux/demux based on holey fibers are investigated, with particular emphasis on optimal device design. Some preliminary experimental results will also be presented.