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In the last years, the unmanned aerial vehicles (UAVs) generated significant innovations in in situ antenna measurements. UAV-mounted test sources have been exploited to characterize the radiation pattern of receiving antennas and arrays for HF radars, radio telescopes in very high-frequency (VHF) band, and up to the $X$ -band for radar characterization. A UAV test source operating in the $Q$ -band has been recently developed within the large-scale polarization explorer (LSPE) project. It will be used for the in situ validation of a ground-based cluster of coherent polarimeters for cosmology observation. This article presents the payload solution that is actually applicable to general UAV-based radiation pattern measurements in the $Q$ -band. It is based on a phase-locked loop synthesizer and an active multiplier coupled with a power detector to compensate for signal power drifts in postprocessing. Relevant system tests have been performed in both laboratory environment and operative conditions. The measured outdoor radiation patterns are in good agreement with both the anechoic chamber measurements and simulated data.

Nonlinear response in a material increases with its index of refraction as $n^4$. Commonly, $n \sim$ 1 so that diffraction, dispersion, and chromatic walk-off limit nonlinear scattering. Ferroelectric crystals with a periodic 3D polarization structure overcome some of these constraints through versatile Cherenkov and quasi-phase-matching mechanisms. Three-dimensional self-structuring can also lead to a giant optical refraction. Here, we perform second-harmonic-generation experiments in KTN:Li in conditions of giant broadband refraction. Enhanced response causes wavelength conversion to occur in the form of bulk Cherenkov radiation without diffraction and chromatic walk-off, even in the presence of strong wave-vector mismatch and highly focused beams. The process occurs with a wide spectral acceptance of more than 100 nm in the near infrared spectrum, an ultra-wide angular acceptance of up to $\pm 40^{\circ}$, with no polarization selectivity, and can be tuned to allow bulk supercontinuum generation. Results pave the way to highly efficient and adaptable nonlinear optical devices with the promise of single-photon-to-single-photon nonlinear optics., 10 pages, 5 figures

Double-loop electric-field vs polarization hysteresis is investigated in a depoled compositionally disordered lithium-enriched potassium tantalate niobate crystal. Comparing electro-optic response and dielectric spectroscopy indicates that the anomalous response occurs for those temperatures in which the sample also manifests a temperature hysteresis in the low-frequency dielectric function. An electric-field hysteresis at concurrent temperatures suggests an underlying role of reorienting mesoscopic polar regions that accompany the nonergodic phase.

Whenever a problem is difficult from the topological, algebraic or functional analytical points of view, a “qualitative theory” arises. The example of choice is the qualitative theory of dynamical systems, founded by Henri Poincar ́e in 1881–1882. In the context of electromagnetics and optics there exist comprehensive accounts on group theoretical methods [1] and on symmetries [2, 3]. This work aims at contributing results in two directions, limited to fixed wavenumber k. 1 - Symmetries and ε-false symmetries in scalar potential scattering at fixed wavenumber. 2 - Approximate propagators in scalar diffraction at fixed wavenumber and related symmetries. The second part of the presentation will focus on group properties and related symmetries of the Helmholtz equation and of its approximations. Aperture diffraction in the halfspace of a scalar wave at fixed k is described by a propagator. A suitable asymptotic approximation yields the Fresnel (≡ paraxial) propagator. Further approximation leads to the Fourier propagator. The related group properties and information contents of both approximation stages will be compared by taking some available results [4–8] into account. REFERENCES 1. Sanchez-Mondragon, J. and K. B. Wolf, Eds., Lie Methods in Optics, Springer, Berlin, 1985. 2. Ramm, A. G., “Symmetry properties of scattering amplitudes and applications to inverse problems,” J. Math. Anal. Appl., Vol. 156, No. 2, 333–340, 1991. 3. Baum, C. E. and H. N. Kritikos, Eds., Electromagnetic Symmetry, Taylor & Francis, Washington, DC, 1995. 4. Grella, R., “Fresnel propagation, diffraction and paraxial wave equation,” J. Optics (Paris), Vol. 13, No. 6, 367–374, 1982. 5. Sudarshan, E. C. G., R. Simon, and N. Mukunda, “Paraxial-wave optics and relativistic front description. I. The scalar theory,” Phys. Rev. A, Vol. 28, 2921–2932, 1983. 6. Crosta, G. F., “On approximations of Helmholtz equation in the halfspace: Their relevance to inverse diffraction,” Wave Motion, Vol. 6, No. 3, 237–246, 1984. 7. Bandres, M. A. and M. Guizar-Sicairos, “Paraxial group,” Opt. Lett., Vol. 34, No. 1, 13–15, 2009. 8. Rodr ́ıguez-Lara, B. M., R. El-Ganainy, and J. Guerrero, “Symmetry in optics and photonics: A group theory approach,” Science Bulletin, Vol. 63, 244–251, 2018, arXiv:1803.00121.

We propose an innovative experimental approach to estimate the two-photon absorption (TPA) spectrum of a fluorescent material. Our method develops the standard indirect fluorescence-based method for the TPA measurement by employing a line-shaped excitation beam, generating a line-shaped fluorescence emission. Such a configuration, which requires a relatively high amount of optical power, permits to have a greatly increased fluorescence signal, thus avoiding the photon counterdetection devices usually used in these measurements, and allowing to employ detectors such as charge-coupled device (CCD) cameras. The method is finally tested on a fluorescent isothiocyanate sample, whose TPA spectrum, which is measured with the proposed technique, is compared with the TPA spectra reported in the literature, confirming the validity of our experimental approach.

We demonstrate a steplike optical modulation based on the activation and deactivation of a bistable localized structure using a photoinduced and reconfigurable miniaturized 30 × 30 μm electroactivated funnel waveguide. Control of a single 10-μm-diameter spot in a 200-μm-diameter vertical-cavity surfaceemitting laser at 980 nm is achieved modulating the phase of an exciting beam in the specific position of the spot in the cavity. This localized on-off response can be scaled into arrays and offer a possible route to fast integrated optical logical functions and memory at low intensities at near-infrared wavelengths.

We propose a simplified method to calculate the optical spread function of a paradigmatic system constituted by a pupil-lens with a line-shaped illumination ('line-spread-function'). Our approach is based on decoupling the two transversal directions of the beam and treating the propagation by means of the Fourier optics formalism. This requires simpler calculations with respect to the more usual Bessel-function-based method. The model is discussed and compared with standard calculation methods by carrying out computer simulations. The proposed approach is found to be much faster than the Bessel-function-based one (CPU time % of the standard method), while the results of the two methods present a very good mutual agreement.

Inverse problems aimed at locating cracks and voids inside a dielectric medium by means of electromagnetic waves involve knowledge of transmission eigenvalues. The subject has been actively investigated by many Authors for some years and results have been presented in articles and books. Unfortunately, the frequency dependence of dielectric permittivity and magnetic permeability of the material has not been taken into account. A theorem which provides existence and asymptotic properties of real transmission eigenvalues is shown to be physically inconsistent, because it ignores the Kramers-Kronig relations.

Inverse problems aimed at locating cracks and voids inside a dielectric medium by means of electromagnetic waves involve knowledge of transmission eigenvalues. The subject has been actively investigated by many Authors for some years and results have been presented in articles and books. Unfortunately, the frequency dependence of dielectric permittivity and magnetic permeability of the material has not been taken into account. A theorem which provides existence and asymptotic properties of real transmission eigenvalues is shown to be physically inconsistent, because it ignores the Kramers - Kronig relations.

We experimentally demonstrate an electro-optic Gaussian-to-Bessel beam-converter miniaturized down to a 30 × 30 ?m pixel in a potassium-lithium-tantalate-niobate (KLTN) paraelectric crystal. The converter is based on the electro-optic activation of a photoinduced and reconfigurable volume axicon lens achieved using a prewritten photorefractive funnel space-charge distribution. The transmitted light beam has a tunable depth of field that can be more than twice that of a conventional beam with the added feature of being self-healing.

For pt.1 see ibid., vol.41, no.1, p.34-51 (1999). The Ipswich data provide a unique opportunity for the validation of the approximate back-propagation (ABP) methods, which were originally developed to identify the shape of acoustic scatterers in the resonance region. These methods rely on a heuristic relationship, i.e., ABP, between the expansion coefficients that represent the scattered wave in the far zone and those on the obstacle boundary, /spl Gamma/. The unknown is the shape-parameter vector, /spl psi//spl I.oarr//spl isin//spl Psi//sub ad/, the admissible set. The objective function to be minimized is the L/sup 2/(/spl Gamma/)-norm of the boundary defect. In the vertical-polarization case, ABP consists of an affine map, which is easy to derive. Its ingredients are arrays of inner products in L/sup 2/(/spl Gamma/), where outgoing cylindrical wave functions are involved. The corresponding numerical results, based on the IPS001VV data, are satisfactory. The attraction domain of the expected solution, the reference obstacle (a disk), is numerically determined by varying the initial conditions in a wide subset of /spl Psi//sub ad/. Reconstruction seems to be unique, although no uniqueness condition is known for the obstacle. In the horizontal-polarization case, ABP relies on vector harmonic functions in a cylindrical geometry. The complexity of the algorithm is higher. Results based on the TPS001HH set are summarized. Although the numerical solution does not show any focal minimum other than the reference obstacle, the corresponding attraction domain is smaller than in the vertical-polarization case.

We demonstrate experimentally the electro-activation of a localized optical structure in a coherently driven broad-area vertical-cavity surface-emitting laser (VCSEL) operated below threshold. Control is achieved by electro-optically steering a writing beam through a pre-programmable switch based on a photorefractive funnel waveguide., Comment: 5 Figures

We study experimentally the aging of optical spatial solitons in a dipolar glass hosted by a nanodisordered sample of photorefractive potassium-sodium- tantalate-niobate (KNTN). As the system ages, the waves erratically explore varying strengths of the nonlinear response, causing them to break up and scatter. We show that this process can still lead to solitons, but in a generalized form for which the changing response is compensated by changing the normalized wave size and intensity so as to maintain fixed the optical waveform. © 2013 Optical Society of America.

We demonstrate the use of three-dimensional funnel index of refraction patterns analogous to those of retinal Müller cells as support for tunable and multi-functional volume optical component miniaturization and integration. Our experiments in paraelectric photorefractive crystals show how a single funnel can act both as a waveguide and a tunable focusing/defocusing micro-lens. Pairing multiple funnel patterns, we are also able to demonstrate ultra-compact tunable beam-splitting, with distinct guided output modes in under 1mm of propagation. © 2012 Optical Society of America.

We report the simultaneous diffraction cancellation for beams of different wavelengths in out-of-equilibrium dipolar glass. The effect is supported by the photorefractive diffusive nonlinearity and scale-free optics, and can find application in imaging and microscopy. © 2011 Optical Society of America.

Some experimental methods such as TAOS [S. Holler et al., Appl. Optics 43 (33) (2004) 6198-6206] are capable of collecting the light scattered by single airborne particles in the micrometer size range when the latter are illuminated by a triggered LASER source. Data consist of intensity patterns collected in a suitable solid angle and made available at a high rate (\>100 patterns per second). There is no known theoretical method capable of determining the particle size, shape and complex refractive index from such data. As a consequence a heuristic algorithm has been developed, which relies on spectrum enhancement for feature extraction and on multivariate statistics for classification. Spectrum enhancement of an image amounts to the application of a pseudo-differential operator followed by a nonlinear transformation with the aim of separating structure from texture. The classifier has been trained with patterns from two materials (polystyrene spheres and highly irregular elastomer particles). Training has involved the solution of saddle point problems and multiobjective optimization with respect to the parameters which control the algorithm. Recognition has been applied to patterns in the data set originated from different materials. The location, in the principal components plane, of the pattern yielded by a given particle has been related to deviation from the spherical shape, in agreement with findings from scanning electron microscopy. Results show that the classifier has acceptable performance in terms of error rate and has real-time potential, hence is applicable to environmental monitoring.

Complete families in a given function space are sets of linearly independent functions, a linear combination of which can approximate any other function with arbitrarily high accuracy. Outgoing cylindrical wave functions are one such family, used to represent the scattered wave in exterior boundary value problems for the scalar Helmholtz equation in two spatial dimensions. When the incident wave is plane and the scattered wave is represented by a series of said functions, which converges up to the boundary of the obstacle, the obstacle is said to be in the Rayleigh class. One shall further distinguish between Dirichlet-Rayleigh and Neumann-Rayleigh obstacles, according to the applicable boundary condition. Discs are trivial obstacles in these classes. Ellipses of eccentricity $\eta$ such that $\eta ^2 < 1/over 2$ were shown to be in the Dirichlet-Rayleigh class by Barantsev et al. in 1971, who used the saddle point method to asymptotically estimate the Fourier scattering coefficients. Herewith, another one parameter family of obstacles is constructed by the same method. It is also shown that the same obstacles are in the Neumann-Rayleigh class. The relevance of these results to the numerical treatment of scattering problems is briefly discussed.

Two-dimensional angular optical scattering (TAOS) is a non destructive means of investigating small particles. Three types of materials are studied: a) polycrystalline tryptophan aggregates, which serve as reference, b) a mixture of tire debris and talc crystals coming from laboratory wear tests, c) dust from a residential, urban area collected by an electrostatic precipitator. Particles are produced from water suspension by an ink-jet aerosol generator and then illuminated by a laser beam. The scattered intensity is recorded within a solid angular sector in the backward domain. The goals of this investigation are 1) to obtain signatures of materials, based on scattering patterns and 2) to justify the experimental results by numerically solving the forward scattering problem.

Approximate backpropagation (ABP) methods are used to identify the shape of acoustic and electromagnetic scatterers in the resonance region from full aperture data. Said methods rely on a heuristic relation i.e., ABP, between the expansion coefficients, which represent the scattered wave in the far zone and, respectively, on the obstacle boundary, Γ. The unknown is the shape parameter vector, ψ, which must be in a suitable admissible set. The objective function to be minimized is the L2(Γ)-norm of the boundary defect. A sample numerical result is given, which comes from the inversion of an IPSWICH data set. In order to justify the well-posedness of ABP some related problems are examined. An error hound is given, which compares the far zone to the least squares boundary coefficients. The approximate forward propagation (AFP) map is defined and its consistency on disks and spheres is stated. Finally, a property of forward propagation in the infinite dimensional case (l2) is provided

Approximate backpropagation (ABP) methods have been used to identify the shape of axially symmetric acoustic scatterers in the resonance region from full aperture data [C1]. More recently one such method has been applied to the electromagnetic case [C2], where the Ipswich data [MK1] are available. ABP methods have relied on a heuristic relation between the expansion coefficients, which represent the scattered wave in the far zone and, respectively, on the obstacle boundary, $\Gamma$, and have led to minimization algorithms. In spite of satisfactory computational results, the well - posedness of ABP remains an open problem. A pertaining result, which may justify the method, is the following. Let $\lambda, \mu$ be multi-indices, $\{ v_{\mu} \}$ be e.g., the family of outgoing cylindrical (n = 2) wave functions and $\{ f_{\mu} \}:= {\bf f }$ be the sequence of far field scattering coefficients. Denote outward differentiation on $\Gamma$ by $\partial_N$. Assume both series $ \sum_{\mu} f_{\mu} v_{\mu} $, and $ \sum_{\mu} f_{\mu} \partial_N v_{\mu} $ converge uniformly on $ \Gamma $. Let $ {\bf b } $ be a sequence of inner products in $ L^2( \Gamma ) $, which depend on the incident wave, $ u $, and consider the operator $ {\cal R}{\bf L} := - (i/4)[ \langle u_{\lambda} |_{\Gamma} \partial_N v_{\mu} \rangle ] $, where $ u_{\lambda} := \real [v_{\lambda}] $. Also, let $ L $ be the approximation order and $ \Lambda [L] $ the corresponding set of indices. Denote e.g., by $ {\bf b}^{(L)} $ the finite sequence derived from $ {\bf b} $ and by $ {\bf c}^{(L)} $ the vector of least squares boundary coefficients, which solve $ || u + \sum_{\lambda \in \Lambda [L]} c_{\lambda}^{(L)} v_{\lambda}||_{L^2 (\Gamma)} ^2 = {\rm min} $. \textsc{Theorem}. Assume $ {\bf f}, {\bf b}\in \ell^2 $ and $ {\cal R}{\bf L} : \ell^2 \rightarrow \ell^2 $ is bounded. Let the spectral radius $ r_{\sigma} $ of $ {\cal R}{\bf L} $ satisfy $ r_{\sigma} < 1 $. Then a) $ \forall{\bf b}\in\ell^2 $ there exists a unique fixed point $ {\bf f} $ for the map $ {\bf p} [t+ l] = {\bf b} + {\cal R}{\bf L}\cdot{\bf p} [t], t = 0, 1, 2,... $, obtained by successive approximations, started with an arbitrary $ {\bf p}[0] \in\ell^2 $; b) let $ \bar{\bf c}^{(L)} $ be the fixed point of $ {\bf p}^{(L)} [ t+1] = {\bf b}^{(L)}+{\cal R}{\bf L}^{(L)}\cdot{\bf p}^{(L)}[ t ] $, with $ {\bf p}^{(L)}[0] \equiv {\bf c}^{(L)} $ and $ {\bf p}^{(L)}[ 1 ] = {\bf p}^{(L)} $; if $ | f_\lambda - \bar c_\lambda ^{(L)} | < \epsilon_1 | \bar c_\lambda ^{(L)} | $ and $ | c_\lambda ^{(L)} - \bar c_\lambda | - | p_\lambda ^{(L)} - \bar c_\lambda ^{(L)} | > 2 \epsilon_1 | \bar c_\lambda ^{(L)} |, \forall \lambda \in \Lambda [L] $ then forward propagation is effective i.e., $| f_\lambda ^{(L)} - p_\lambda ^{(L)} | < | f_\lambda ^{(L)} - c_\lambda ^{(L)} |, \forall \lambda \in \Lambda [L] $. These results will be applied to a class of numerical problems and their practical repercussions on shape identification will be discussed. References [Cl] G F CROSTA, The Backpropagation Method in Inverse Acoustics, in Tomography, Impedance Imaging and Integral Geometry, LAM 30 (Edited by M CHENEY, P KUCHMENT, E T QUINTO) pp 35 - 68, AMS: Providence, RI (1994). [C2] G F CROSTA, Scalar and Vector Backpropagation Applied to Shape Identification from Experimental Data: Recent Results and Open Problems to appear in Inverse Problems/Tomography and Image Processing, (Edited by A G Ramm) Plenum: New York, NY [MK1] R V McGahan, R E Kleinman, Special Session on Image Reconstruction Using Real Data, IEEE Antennas and Propagation Magazine 38 39 - 40 (1996)

The wave scattered by the unknown obstacle is approximated by two different representations, one in the far zone, the other on the obstacle boundary. Each of these representations contains expansion coefficients which can be related by an approximate back propagator (ABP). The latter depends non-linearly on the parameters which describe the obstacle shape, and yields the boundary scattered wave from knowledge of the far field data. Reconstruction is carried out by minimising the L^2 norm of the boundary defect with respect to the shape parameters and other auxiliary unknowns. A numerical reconstruction from the Ipswich data is presented. A convergence propert of the approximate forward propagator is stated.

The inverse problem considered herewith consists of determining the shape of a two dimensional, perfectly conducting obstacle from knowledge of the incident monochromatic plane electromagnetic wave and of a set of laboratory measurements related to the scattered wave: the Ipswich data. The solution algorithm and its numerical implementation rely on approximate back propagation (ABP). The latter is an algebraic transformation, which is deduced from the properties of complete families of base functions and relates the far field scattering coefficients to those on the obstacle boundary. The features presented herewith for the first time are: a) a consistency result for a forward propagator, which transforms least squares boundary coefficients into far field scattering coefficients; b) the development and testing of a scalar ABP method for two dimensional electromagnetic problems, where polarization is vertical; c) the outline and the implementation of a vector ABP method for horizontal polarization; d) the application of both methods to the inversion of experimental data. Since general conditions for the well posedness of ABP methods are still unknown, the main related open problems are also stated.

The inverse electromagnetic problem for a perfectly conducting obstacle is stated in two spatial dimensions. Part One of the talk deals with the heuristics of shape reconstruction. Two classes of algorithms are presented, ABP and AFP. The former, known as the approximate back propagation algorithm, minimises the boundary defect; the latter, known as the approximate forward propagation algorithm, minimises the far-zone defect. Numerical results are provided for both. Part Two attempts at justifying the algorithms. The least-squares boundary coefficients are investigated in relation to error bounds and the Rayleigh hypothesis. The affine-least squares scheme is investigated in relation to the approximate forward propagator. The convergence of said propagator holds, provided the spectral radius of a Gram matrix is less than one.

The approximate forward propagation (AFP) algorithm is a new shape reconstruction method, which consists of the minimization of the far zone defect norm with respect to the unknown shape parameters. AFP relies on an algebraic relation between least square coefficients, which represent the scattered electric field on the obstacle boundary, and the far zone scattering coefficients. The algorithm is applied to the inversion of a set of the experimental Ipswich data. In order to justify the effectiveness of AFP, a preliminary convergence result is stated for obstacles which comply with the Rayleigh hypothesis and other, more restrictive conditions.

Approximate backpropagation (ABP) methods have been used by the author to identify the shape of simple scatterers in the resonance region from full aperture data both in the acoustic and electromagnetic case. ABP methods rely on a relation between the expansion coefficients, which represent the scattered wave in the far zone and, respectively, on the obstacle boundary, $\Gamma$, and lead to minimization algorithms. In spite of satisfactory computational results, the well-posedness of ABP generally remains an open problem. A related result, which may eventually justify the method, pertains to a forward propagator i.e., to the affine map ${\bf N}[.]:= {\cal R}{\bf L} [.]+ {\bf b}$, which appears in the solution of the direct scattering problem. Very briefly, if both the scattered wave and its normal derivative on $\Gamma$ are represented by uniformly converging series according to a suitable basis in $L^2 (\Gamma)$, if ${\bf N}[.]$ is bounded and maps $\ell_2$ sequences of scattering coefficients into $\ell_2$ sequences and if the spectral radius $r_{\sigma [ {\cal R]{\bf L} ]$ satisfies $r_{\sigma [ {\cal R]{\bf L} ]

Complete families of linearly independent solutions to the scalar Helmholtz equation introduced by Vekua (1953) and further studied by Kleinman et al. (1984), Ramm (1986), provide a unified view over a class of direct and inverse scattering problems and have an impact over solution algorithms. They are shown to improve the understanding of two known direct scattering algorithms and to suggest a new solution method for an imaging problem: the reconstruction of an impenetrable obstacle in the resonance region from knowledge of the incident field and the scattering amplitude and from prior information.