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A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example., Comment: 38 pages, 16 figures

A capacitor paradox is an electromagnetic problem designed to show the limits of circuit theory which considers the connection of two ideal capacitors, one charged and the second discharged. A blind solution to this problem leads to the non-conservation of energy and, thus, to a paradox. In this text an attempt is made to isolate the inductance part of the problem in the form of wave-guiding phenomenon, providing yet another point of view of this intriguing educational problem., Comment: 2 pages, 3 figures, 1 animation

Existing optimization methods are used to calculate the upper-bounds on radiation efficiency with and without the constraint on self-resonance. These bounds are used for the design and assessment of small electric-dipole-type antennas. We demonstrate that the assumption of lossless, lumped, external tuning skews the true nature of radiation efficiency bounds when practical material characteristics are used in the tuning network. A major result is that, when realistic (e.g., finite conductivity) materials are used, small antenna systems exhibit dissipation factors which scale as $(ka)^{-4}$, rather than $(ka)^{-2}$ as previously predicted under the assumption of lossless external tuning., Comment: 7 pages, 10 figures

Ambiguities in the definition of stored energy within distributed or radiating electromagnetic systems motivate the discussion of the well-defined concept of recoverable energy. This concept is commonly overlooked by the community and the purpose of this communication is to recall its existence and to discuss its relationship to fractional bandwidth. Using a rational function approximation of a system's input impedance, the recoverable energy of lumped and radiating systems is calculated in closed form and is related to stored energy and fractional bandwidth. Lumped circuits are also used to demonstrate the relationship between recoverable energy and the energy stored within equivalent circuits produced by the minimum phase-shift Darlington's synthesis procedure., Comment: 5 pages, 5 figures

A full-wave numerical scheme of polarisability tensors evaluation is presented. The method accepts highly conducting bodies of arbitrary shape and explicitly accounts for the radiation as well as ohmic losses. The method is verified on canonical bodies with known polarisability tensors, such as a sphere and a cube, as well as on realistic scatterers. The theoretical developments are followed by a freely available code whose sole user input is the triangular mesh covering the surface of the body under consideration., Comment: 13 pages, 6 figures

An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain $G$, quality factor $Q$, gain to quality factor ratio $G/Q$, and radiation efficiency $\eta$ of canonical shapes with conduction losses explicitly included. The Rao-Wilton-Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized., Comment: 13 pages, 18 figures, IEEE Transactions on Antennas and Propagation 65, 2017

Artificial diamagnetics are prominent for achieving extraordinarily strong diamagnetism in a wide frequency range. However, as far as the magnetic fields outside the artificial medium are concerned, bulk conductors show a very similar pattern. The question arises whether the complicated internal structure of artificial diamagnetics can, to this end, be replaced by a simpler object. We analyse the figure of merit for the application of diamagnetics in magnetic levitation, and show that for an electrically small body, any internal structuring makes the figure of merit worse than that of a simple conducting object., Comment: 5 pages, 5 figures

This paper describes an analytical evaluation of the quality factor Qz in a separable system in which the vector potential is known. The proposed method uses a potential definition of active and reactive power, implicitly avoiding infinite entire space integration and extraction of radiation energy. As a result, all the used quantities are finite, and the calculated Qz is always non-negative function of frequency. The theory is presented on the canonical example of the currents flowing on a spherical shell. The Qz for the dominant spherical TM and TE mode and their linear combination are found in closed forms, including both internal and external energies. The proposed analytical method and its results are compared to previously published limits of the quality factor Q., Comment: 8 pages, 9 figures, full paper (IET-MAP)

New expressions are derived to calculate the Q factor of a radiating device. The resulting relations link Q based on the frequency change of the input impedance at the input port (Qx, Qz) with expressions based solely on the current distribution on an radiating device. The question of which energies of a radiating system are observable is reviewed, and then the proposed Q factor as defined in this paper is physical. The derivation is based on potential theory rather than fields. This approach hence automatically eliminates all divergent integrals associated with electromagnetic energies in infinite space. The new formulas allow us to study the radiation Q factor for antennas without feeding (through e.g. Characteristic Modes) as well as fed by an arbitrary number of ports. The new technique can easily be implemented in any numerical software dealing with current densities. To present the merits of proposed technique, three canonical antennas are studied. Numerical examples show excellent agreement between the measurable Qz derived from input impedance and the new expressions., Comment: 8 pages, 9 figures, full paper (IEEE TAP)

The analogy between electromagnetic waves and ballistic electrons within the Kane's model is developed and subsequently applied to a theoretical description of a quantum version of a metamaterial planar lens. Restrictions imposed on the perfect lens and the poor man's lens by available semiconductor band structures are discussed. A realistic implementation is proposed for the quantum poor man's lens, which uses specific properties of the HgTe compound. The properties of the lens are presented on the basis of a calculated transmission of oblique electrons through the lens structure., Comment: 4 figures

This paper presents a study of the body orientation of domestic cattle on free pastures in several European states, based on Google satellite photographs. In sum, 232 herds with 3412 individuals were evaluated. Two independent groups participated in our study and came to the same conclusion that, in contradiction to the recent findings of other researchers, no alignment of the animals and of their herds along geomagnetic field lines could be found. Several possible reasons for this discrepancy should be taken into account: poor quality of Google satellite photographs, difficulties in determining the body axis, selection of herds or animals within herds, lack of blinding in the evaluation, possible subconscious bias, and, most importantly, high sensitivity of the calculated main directions of the Rayleigh vectors to some kind of bias or to some overlooked or ignored confounder. This factor could easily have led to an unsubstantiated positive conclusion about the existence of magnetoreception., Comment: Added electronic supplement with source data

In this paper we are using formal analogy of electromagnetic wave equation and Schrodinger equation in order to study the phenomenon of perfect tunneling (tunneling with unitary transmittance) in 1D semiconductor heterostructure. Using the Kane model of semiconductor we are showing that such phenomenon can indeed exist, resembling all the interesting features of the analogous phenomenon in classical electromagnetism in which metamaterials (substances with negative material parameters) are involved. We believe that these results can open up the way to interesting applications in which the metamaterial ideas are transfered into semiconductor domain.

We describe an efficient rigorous model suitable for calculating the properties of finite metamaterial samples, which takes into account the discrete structure of metamaterials based on capacitively loaded ring resonators. We illustrate how this model applies specifically to a metamaterial lens employed in magnetic resonant imaging. We show that the discrete model reveals the effects which can be missed by a continuous model based on effective parameters, and that the results are in close agreement with the experimental data., Comment: 6 pages, 6 figures

It is shown that artificial magnetism with relatively large frequency bandwidth can be obtained from periodic arrangements of dielectric rings. Combined with dielectric rods, dielectric rings can provide 3D isotropic left-handed metamaterials being an advantageous alternative to metallic split ring resonators and/or metallic wires when un-detectability by low frequency external magnetic fields is desired. Furthermore it is shown that dielectric rings can be also combined with natural plasma-like media to obtain a left-handed metamaterial., Comment: 4 pages, 8 figures

Bi-isotropic and isotropic negative refractive index (NRI) 3D metamaterials made from periodic arrangements of chiral split ring resonators (SRRs) are proposed and demonstrated. An analytical theory for the characterization and design of these metamaterials is provided and validated by careful full-wave electromagnetic simulations. The reported results are expected to pave the way to the design of practical 3D bi-isotropic and isotropic NRI metamaterials made from a single kind of inclusions., Comment: Submmitted to Phys. Rev. Lett

Some novel quasi-planar chiral inclusions, feasible from standard photo-etching techniques, are proposed. It is shown that such inclusions can be designed in order to present balanced electric, magnetic and magneto-electric polarizabilities. Using these inclusions, random and periodic bi-isotropic artificial metamaterials exhibiting a balanced positive/negative refractive index can be build up. These metamaterials would exhibit reasonable bandwidths and excellent matching to free space., Comment: 4 pages, 2 figures, Metamaterials 2007, Rome 22-24 October 2007

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations., Comment: 4 pages, 3 figures

In this paper a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The role of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose it is assumed that the metamaterial is composed by cubic SRR resonators, arranged in a cubic lattice. The minimum symmetries needed to ensure an isotropic behavior are analyzed, and some particular configurations are proposed. Besides, an equivalent circuit model is proposed for the considered cubic SRR resonators. Experiments are carried out in order to validate the proposed theory. We hope that this analysis will pave the way to the design of bulk metamaterials with strong isotropic magnetic response, including negative permeability and left-handed metamaterials., Comment: Submitted to Physical Review B, 23 pages

This letter proposes a quasi-planar chiral resonator suitable for the design of negative refractive index matamaterial. It is presented an analytical model for the determination of its polarizabilities, and the viability of negative refraction in chiral and racemic arrangements with the proposed inclusions is analyzed. The present analysis is expected to pave the way to the design of negative refractive index matamaterials made of a single kind of inclusions feasible from standard photo-etching techniques., Comment: Submitted to Applied Physics Letters