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Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions. Employing the residue-pole expansion, we describe the relation between field components as a system of ODEs solvable through the auxiliary differential equation approach. Not only can be used in Finite difference methods, the approach can be also employed to model complex surface structures.

An Electrodynamics solver for moving sources is introduced. The main challenges and formulation are highlighted. The solver enables the simulation of fields for sources undergoing arbitrary motion. Two examples of uniformly moving current sources are provided to correlate the numerical solver computations with theory, based on the solution of Maxwell's equations and the relativistic transformation of the electromagnetic fields.

An ab-initio analysis based on coupled mode theory (CMT) is applied to describe the interaction dynamics of high dielectric resonators (DRs) with its containing aqueous solution. We prove that the coupling mechanism is reciprocal. Such property is exploited to find closed form and accurate expressions of the coupling coefficient, the main factor characterizing the system performance. Based on such expressions, it is shown that, for wireless power transfer (WPT) applications, up sizing the DRs relaxes the need of using ultra high dielectric constant materials. The nature of interaction is captured by the coupling matrix, which shows that the behaviour of the system is identical to the ones studied extensively in the literature when the contained aqueous solution is replaced by an enclosing cavity. It follows, as in a typical three coupled resonators setting, that when two DRs are inserted in the aqueous solution a non-bonding mode emerges; hence enabling efficient wireless power transfer (WPT) via the opening of an electromagnetic induced transparency like window. Due to the inevitable situations where the DRs are not symmetrically placed inside the solution, the general eigenvalue problem, with asymmetrically placed DR inserts is solved and the eigenvectors representing the coupled modes are depicted by vectors in a 3D mathematical space where the uncoupled modes represent its basis. Moreover, the strong coupling between the DR inserts and the aqueous medium allows the proposed WPT system to tolerate intrinsic aqueous solution losses and the presence of extraneous objects. Additionally, the value of the load at maximum efficiency is independent of the aqueous solution loss tangent, thus tolerating the variation of the medium salinity. The Proposed EIT like scheme can find applications for mid/short range power transfer in/through swimming pools, chemical reactors, fish tanks, etc., Comment: 10 pages, 11 figures

The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an eigenvalue problem form, the equivalency between solutions at different positions along the structure is demonstrated. It is shown that the underlying mathematical machinery is identical to the one used in the analysis of linear time invariant periodic structures, where a two step eigen-decompositions is performed. The first decomposition is in the temporal eigenfunctions basis, which is followed by the decomposition of the translation operator in the spatial domain. The two step process results in the well-known dispersion relation. We also prove that all points in the ($\beta$,$\omega$) plane parallel to the modulation velocity are equivalent in the sense that the eigenvectors are related by a shift operator. Additionally, the wave propagation inside the space time periodic circuit and the terminal characteristics are rigorously determined via the expansion of the total solution in terms of the eigenmodes. To validate the developed framework, two examples are provided. In the first, a space time modulated composite right left handed transmission line is studied and results are compared with time domain simulation. The second example is concerned with the characterization of the non-reciprocal behaviour observed on a nonlinear transmission line that was manufactured in our lab. Using the developed machinery it is shown that the passive interaction between different harmonics results in an observed giant non-reciprocity, where the difference between the forward and backward transmission coefficients can be greater than 30 dB. The frequencies at which non-reciprocity occurs and its strength agree with time domain simulation and measurements., Comment: 10 pages, 15 figures

Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating and modulation wavelengths. In the limit of infinitesimal unit cell, the dispersion relation reduces identically to its continuous counterpart. For homogeneous space-time modulated media, the time periodic circuit approach allows the extension of the well-known telegraphist's equations. The time harmonics are coupled together to form an infinite system of coupled differential equations. At the scattering centres, where the interaction is mediated via the modulation (pump wave), the telegraphist's equations reduce to the interaction of two waves only: the signal and idler. The interaction can then be described using three wave mixing, satisfying the phase matching condition. It is demonstrated that the time periodic S parameters provide an alternative and appealing visualization of the modal conversion and the emergence of non-reciprocity inside the bandgaps., Comment: 9 pages, 10 figures

Wireless power transfer via a dielectric loaded multi-moded split cavity resonator (SCR) is proposed. Unlike conventional inductive resonant coupling, the scheme enables the control of both the real and imaginary parts of the transfer impedance. It is demonstrated through measurements that the inclusion of dielectric resonators (DRs) tuned to the SCR $TE_{012}$ mode, significantly enhances the system figure of merit and optimal efficiency. The effect of the DRs is shown to be related to the resonant coupling of the DRs $TE_{01\delta}$ and SCR modes, resulting in an electromagnetic induced transparency-like window. An efficiency of 70% is achieved when the transfer distance is 7 cm, or half wavelength. Additionally, it was shown that the efficiency is above 40% over a relatively wide bandwidth and a wide range of optimum load impedance., Comment: 15 pages

The properties of space-time modulated media operating in the sub-sonic regime are discussed based on rigorous Bloch-Floquet theory. A geometrical description in the frequency-wavenumber plane is developed to provide insight into the possible interactions and their nature. It is shown that the secular equation has a singularity, which results in a weak/passive second harmonic generation process. Additionally bandgaps arising from the strong/active parametric interaction between an incident wave and its space-time harmonic, result in an inelastic Brillouin like scattering process. Hence when the incident frequency is inside a forward (backward) bandgap, a Stokes' (Anti-Stokes') scattered wave bounces back to the source. Although the forward and backward bandgaps do not generally occur at the same frequency bands, the insertion loss and gap width are equal. Requiring that both gaps do not overlap, enforces a lower bound on the modulation speed. It is shown that although an increase in the modulation index is desirable, as it enhances the non-reciprocal behaviour, it also limits the range of possible modulation speeds. The effective complex refractive index is calculated over a wide frequency range. It is shown that peaks appear in the extinction coefficient, indicating scattering to Stokes' and Anti-Stokes' waves. Finally, a comprehensive numerical analysis based on the Finite Difference Time Domain method is developed to verify and demonstrate the intriguing properties of space-time modulated media., Comment: 15 pages

Similar to the hybridization of three atoms, three coupled resonators interact to form bonding, anti-bonding and non-bonding modes. The non-bonding mode enables an electromagnetic induced transparency like transfer of energy. Here the non-bonding mode, resulting from the strong electric coupling of two dielectric resonators and an enclosure, is exploited to show that it is feasible to transfer power over a distance comparable to the operating wavelength. In this scheme, the enclosure acts as a mediator. The strong coupling permits the excitation of the non-bonding mode with high purity. This approach is different from resonant inductive coupling which works in the sub-wavelength regime. Optimal loads and the corresponding maximum efficiency are determined using two independent methods: Coupled Mode Theory and Circuit modelling. It is shown that, unlike resonant inductive coupling, the figure of merit depends on the enclosure quality and not on the load, which emphasizes the role of the enclosure as a mediator. Briefly after the input excitation is turned on, the energy in the receiver builds up via all coupled and spurious modes. As time elapses, all modes except the non-bonding cease to sustain. Due to the strong coupling between the dielectrics and the enclosure, such systems have unique properties such as high and uniform efficiency over large distances; and minimal fringing fields. These properties suggest that electromagnetic induced transparency like schemes which rely on the use of dielectric resonators can be used to power autonomous systems inside an enclosure or find applications when exposure to the fields needs to be minimal. Finite Element computations are used to verify the theoretical predictions by determining the transfer efficiency, fields profile and coupling coefficients for two different systems., Comment: 10 pages, 14 figures

There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an eigenvalue problem, is derived. The solution of the master equation gives the coupled frequencies and fields in terms of the uncoupled modes. By doing so, the problem size is limited to the number of modes rather than the, usually large, discretized spatial and temporal domains obtained by fullwave solvers. Therefore, the method can be considered as a numerical recipe which determines the behavior of a complex system once its simpler ingredients are known. Besides quantitative analysis, the coupled mode equation proposes a pictorial view of the split rings hybridization. It can be regarded as the electromagnetic analog of molecular orbital theory. The solution of the eigenvalue problem for different configurations gives valued information and insight about the coupling of metamaterials unit cells. For instance, it is shown that the behavior of split rings as a function of the relative position and orientation can be systematically explained. This is done by singling out the effect of each relevant parameter such as the coupling coefficient and coupled induced frequency shift coefficients.