Further Comment on 'Encoding many channels on the same frequency through radio vorticity: first experimental test'

We show that the reply by Tamburini et al (2012 New J. Phys. 14 118002) to our previous comment (2012 New J. Phys. 14 118001) on the experiment reported in (2012 New J. Phys. 14 033001) actually does not invalidate any of the issues raised in our initial comment.Comment: 3 pages, 1 figur

Characteristic Functions Describing the Power Absorption Response of Periodic Structures to Partially Coherent Fields

Many new types of sensing or imaging surfaces are based on periodic thin films. It is explained how the response of those surfaces to partially coherent fields can be fully characterized by a set of functions in the wavenumber spectrum domain. The theory is developed here for the case of 2D absorbers with TE illumination and arbitrary material properties in the plane of the problem, except for the resistivity which is assumed isotropic. Sum and difference coordinates in both spatial and spectral domains are conveniently used to represent the characteristic functions, which are specialized here to the case of periodic structures. Those functions can be either computed or obtained experimentally. Simulations rely on solvers based on periodic-boundary conditions, while experiments correspond to Energy Absorption Interferometry (EAI), already described in the literature. We derive rules for the convergence of the representation versus the number of characteristic functions used, as well as for the sampling to be considered in EAI experiments. Numerical examples are given for the case of absorbing strips printed on a semi-infinite substrate.Comment: Submitted to JOSA

Characterization of Power Absorption Response of Periodic 3D Structures to Partially Coherent Fields

In many applications of absorbing structures it is important to understand their spatial response to incident fields, for example in thermal solar panels, bolometric imaging and controlling radiative heat transfer. In practice, the illuminating field often originates from thermal sources and is only spatially partially coherent when reaching the absorbing device. In this paper, we present a method to fully characterize the way a structure can absorb such partially coherent fields. The method is presented for any 3D material and accounts for the partial coherence and partial polarization of the incident light. This characterization can be achieved numerically using simulation results or experimentally using the Energy Absorption Interferometry (EAI) that has been described previously in the literature. The absorbing structure is characterized through a set of absorbing functions, onto which any partially coherent field can be projected. This set is compact for any structure of finite extent and the absorbing function discrete for periodic structures

Statistics of the MLE and Approximate Upper and Lower Bounds - Part 1: Application to TOA Estimation

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accurateness of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation

A beamforming approach to the self-calibration of phased arrays

In this paper, we propose a beamforming method for the calibration of the direction-independent gain of the analog chains of aperture arrays. The gain estimates are obtained by cross-correlating the output voltage of each antenna with a voltage beamformed using the other antennas of the array. When the beamforming weights are equal to the average cross-correlated power, a relation is drawn with the StEFCal algorithm. An example illustrates this approach for few point sources and a 256-element array

Modal characterization of thermal emitters using the Method of Moments

Electromagnetic sources relying on spontaneous emission are difficult to characterize without a proper framework due to the partial spatial coherence of the emitted fields. In this paper, we propose to characterize emitters of any shape through their natural emitting modes, i.e. a set of coherent modes that add up incoherently. The resulting framework is very intuitive since any emitter is regarded as a multimode antenna with zero correlation between modes. Moreover, for any finite emitter, the modes form a compact set that can be truncated. Each significant mode corresponds to one independent degree of freedom through which the emitter radiates power. The proposed formalism is implemented using the Method of Moments (MoM) and applied to a lossy sphere and a lossy ellipsoid. It is shown that electrically small structures can be characterized with a small number of modes, and that this number grows as the structure becomes electrically large.Comment: To be presented in European Conference on Antennas and Propagation (EuCAP 2020

Efficient Tracking of Dispersion Surfaces for Printed Structures using the Method of Moments

The dispersion surfaces of printed periodic structures in layered media are efficiently computed using a full-wave method based on the periodic Method of Moments (MoM). The geometry of the dispersion surface is estimated after mapping the determinant of the periodic MoM impedance matrix over a range of frequencies and impressed phase shifts. For lossless periodic structures in the long-wavelength regime, such as lossless metasurfaces, a tracking algorithm is proposed to represent the dispersion surface as a superposition of parameterized iso-frequency curves. The mapping process of the determinant is accelerated using a specialized interpolation technique with respect to the frequency and impressed phase shifts. The algorithm combines a fast evaluation of the rapidly varying part of the periodic impedance matrix and the interpolation of the computationally intensive but slowly varying remainder. The mapping is further accelerated through the use of Macro basis functions (MBFs). The method has been first tested on lossless metasurface-type structures and validated using the commercial software CST. The specialized technique enables a drastic reduction of the number of periodic impedance matrices that needs to be explicitly computed. In the two examples considered, only 12 matrices are required to cover any phase shift and a frequency band larger than one octave. An important advantage of the proposed method is that it does not entail any approximation, so that it can be used for lossy structure and leaky waves, as demonstrated through two additional examples.Comment: Paper accepted for publication in IEEE Transactions on Antennas and Propagatio

Identification of the absorption processes in periodic plasmonic structures using Energy Absorption Interferometry

Power dissipation in electromagnetic absorbers is a quadratic function of the incident fields. To characterize an absorber, one needs to deal with the coupling that may occur between different excitations. Energy Absorption Interferometry (EAI) is a technique that highlights the independent degrees of freedom through which a structure can absorb energy: the natural absorption modes of the structure. The coupling between these modes vanishes. In this paper, we use the EAI formalism to analyse different kinds of plasmonic periodic absorbers while rigorously accounting for the coupling: resonant golden patches on a grounded dielectric slab, parallel free-standing silver wires and a silver slab of finite thickness. The EAI formalism is used to identify the physical processes that mediate absorption in the near and far field. First, we demonstrate that the angular absorption, which is classically used to characterize periodic absorbers in the far field and which neglects the coupling between different plane waves, is only valid under stringent conditions (subwavelength periodicity, far field excitation and negligible coupling between the two possible polarizations). Using EAI, we show how the dominant absorption channels can be identified through the signature of the absorption modes of the structure, while rigorously accounting for the coupling. We then exploit these channels to improve absorption. We show that long-range processes can be exploited to enhance the spatial selectivity, while short-range processes can be exploited to improve absorptivity over wide angles of incidence. Lastly, we show that simply adding scatterers with the proper periodicity on top of the absorber, the absorption can be increased by more than one order of magnitude