It is shown that perfect absorption and giant amplification can be realized when a wave impinges on a special metamaterial layer with zero real parts of the permittivity and permeability. The imaginary parts of the permittivity and permeability remain nonzero, corresponding to finite loss or gain. Perfect absorption and giant magnification can still be achieved even if the thickness of the metamaterial layer is arbitrarily thin and the absolute imaginary parts of the permittivity and permeability are very small. The metamaterial layer needs a total-reflection substrate for perfect absorption, while this is not required for giant magnification.
In this letter, we show how transformation optics makes it possible to design what we call conjugate metamaterials. We show that these materials can also serve as substrates for making a subwavelength-resolution lens. The so-called "perfect lens", which is a lens that could focus all components of light (including propagating and evanescent waves), can be regarded as a limiting case, in which the respective conjugate metamaterials approach the characteristics of left-handed metamaterials, which have a negative refractive index.
Conjugate metamaterials, in which the permittivity and the permeability are complex conjugates of each other, possess the elements of loss and gain simultaneously. By employing a conjugate metamaterial with a purely imaginary form, we propose a mechanism for realizing both coherent perfect absorber (CPA) and laser modes, which have been widely investigated in parity-time symmetric systems. Moreover, the general conditions for obtaining CPA and laser modes, including obtaining them simultaneously, are revealed by analyzing the wave scattering properties of a slab made of purely imaginary conjug…
An infrared perfect absorber based on gold nanowire metamaterial cavities array on a gold ground plane is designed. The metamaterial made of gold nanowires embedded in alumina host exhibits an effective permittivity with strong anisotropy, which supports cavity resonant modes of both electric dipole and magnetic dipole. The impedance of the cavity modes matches the incident plane wave in free space, leading to nearly perfect light absorption. The incident optical energy is efficiently converted into heat so that the local temperature of the absorber will increase. Simulation results show that …
We develop a simple treatment of a metamaterial perfect absorber (MPA) based on grating theory. We analytically prove that the condition of MPA requires the existence of two currents, which are nearly out of phase and have almost identical amplitude, akin to a magnetic dipole. Furthermore, we show that non-zero-order Bragg modes within the MPA may consume electromagnetic energy significantly.
We demonstrate that the metamaterial perfect absorber behaves as a meta-cavity bounded between a resonant metasurface and a metallic thin-film reflector. The perfect absorption is achieved by the Fabry-Perot cavity resonance via multiple reflections between the "quasi-open" boundary of resonator and the "closed" boundary of reflector. The characteristic features including angle independence, ultra-thin thickness and strong field localization can be well explained by this model. With this model, metamaterial perfect absorber can be redefined as a meta-cavity exhibiting high Q-factor, strong fie…
Near perfect infrared light absorption at multi-spectral wavelengths has been experimentally demonstrated by using multiplexed metal square plasmon resonance structures. Optical power absorption over 95% has been observed in dual-band metamaterial absorbers at two separate wavelengths and optical power absorption over 92.5% has been observed in triple-band metamaterial absorbers at three separate wavelengths. The peak absorption wavelengths are primarily determined by the sizes of the metal squares in the multiplexed structures. Electrical field distributions in the middle of the dielectric sp…
A metamaterial perfect absorber consisting of a tri-layer (Al/ZnS/Al) metal-dielectric-metal system with top aluminium nano-disks is fabricated by laser-interference lithography and lift-off processing. The metamaterial absorber had peak resonant absorbance at 1090 nm and showed nonlinear absorption for 600ps laser pulses at 1064 nm wavelength. A nonlinear saturation of reflectance was measured to be dependent on the average laser power incident and not the peak laser intensity. The nonlinear behaviour is shown to arise from the heating due to the absorbed radiation and photo-thermal changes i…
Metamaterial-based perfect absorbers promise many applica- tions. Perfect absorption is characterized by the complete suppression of transmission and reflection and complete dissipation of the incident energy by the absorptive meta-atoms. A certain absorption spectrum is usually assigned to a bulk medium and serves as a signature of the respective material. Here we show how to use graphene flakes as building blocks for perfect absorbers. Then, an absorbing meta-atom only consists of a molecular monolayer placed at an appropriate distance from a metallic ground plate. We show that the functiona…
In this article, we have proposed a compact classification of isotropic and homogeneous single negative (SNG) electromagnetic metamaterial based perfect tunneling unit cells. This unified classification has been made by means of the band gap theories and properties of the arrays made up of these unit cells. Based on their reported characteristics, we have proposed new structures that simultaneously show perfect tunneling band and complete band gap (CBG-omni directional stop band for both polarizations). Besides, we have identified a kind of perfect tunneling which can be considered as "phase s…
Metamaterial perfect absorbers from microwaves to optical part of the electromagnetic spectrum has been intensely studied for its ability to absorb electromagnetic radiation. Perfect absorption of light by metamaterials have opened up new opportunities for application oriented functionalities such as efficient sensors and emitters. We present an absorber based sensing scheme at the terahertz frequencies and discuss optimized designs to achieve high frequency and amplitude sensitivities. The major advantage of a perfect metamaterial absorber as a sensor is the sensitive shift in the absorber re…
We investigate the impact of resonator geometry and its coupling with ground plane on the performance of metamaterial perfect absorbers. Using a cross-resonator as an example structure, we find that the absorber thickness can be further reduced through modifying the geometric dimensions of the resonators. Numerical simulations and theoretical calculations reveal that destructive interference of multiple reflections is responsible for the near-unity absorption. The near-field coupling between the resonator array and ground plane can be significant. When this coupling is taken into account, the …
We analyze single and multilayered metamaterials by modeling each layer as a metasurface with effective surface electric and magnetic susceptibility derived through a thin film approximation. Employing a transfer matrix method, these metasurfaces can be assembled into multilayered metamaterials to realize certain functionalities. We demonstrate numerically that this approach provides an alternative interpretation of metamaterial-based perfect absorption, showing that the underlying mechanism is a modified Fabry-Perot resonance. This method provides a general approach applicable for decoupled o…
To overcome the resolution limit of conventional optics, near field imaging techniques using a negative index flat lens (NIFL) have been previously developed that amplify the evanescent components of the incident field. Here, a technique is developed and demonstrated to compensate for losses in a non-ideal NIFL by determining the transfer function of the lens and subsequently applying the inverse to the unresolved raw image. The result is a compensated image with sub-diffraction-limited resolution.
In this work, we theoretically find that coherent perfect absorption (CPA) and laser modes can be realized in a two-dimensional cylindrical structure composed of conjugate metamaterials (CMs). The required phase factors of CMs for achieving CPA and laser modes are determined by the geometric size of the CM cylinder, which is a unique feature compared with other non-Hermitian optical systems. Based on this property, we also demonstrate that CPA and laser modes can exist simultaneously in a CM cylinder with an extremely large size, where the excitations of CPA and laser modes depend on the angul…
In this paper the design for an absorbing metamaterial with near unity absorbance in terahertz region is presented. The absorber's unit cell structure consists of two metamaterial resonators that couple to electric and magnetic fields separately. The structure allows us to maximize absorption by varying dielectric material and thickness and, hence the effective electrical permittivity and magnetic permeability.
We analytically investigate transverse magnetic (TM) spatial bright solitons, as exact solutions of Maxwell's equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the considered medium, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two novel self-trapping mechanisms able to support two-peaked and flat-top solitons, respectivel…
We derive periodic multilayer absorbers with effective uniaxial properties similar to perfectly matched layers (PML). This approximate representation of PML is based on the effective medium theory and we call it an effective medium PML (EM-PML). We compare the spatial reflection spectrum of the layered absorbers to that of a PML material and demonstrate that after neglecting gain and magnetic properties, the absorber remains functional. This opens a route to create electromagnetic absorbers for real and not only numerical applications and as an example we introduce a layered absorber for the w…
We study metamaterials with an anisotropic effective permittivity tensor in which one component is near zero. We find that such an anisotropic metamaterial can be used to control wave propagation and construct almost perfect bending waveguides with a high transmission rate (>95%). This interesting effect originates in the power flow redistribution by the surface waves on the input and output interfaces, which smoothly matches with the propagating modes inside the metamaterial waveguide. We also find that waves in such anisotropic epsilon-near-zero materials can be reflected by small-sized perf…
Black phosphorus (BP) as a promising two-dimensional material with extraordinary optical properties constitutes an excellent building block in multilayer hyperbolic metamaterials. In this work, we design a multilayer structure composed of BP/dielectric layer stacking unit cells patterned on a gold mirror and theoretically demonstrate the tunable anisotropic absorption in the infrared regime. The electric dipole resonance between the adjacent unit cells drives the structure in the critical coupling state, and impedance of the structure matches to that of free space, showing the perfect absorpti…
We experimentally demonstrate that a thin (~150 nm) film of vanadium dioxide (VO2) deposited on sapphire has an anomalous thermal emittance profile when heated, which arises due to the optical interaction between the film and the substrate when the VO2 is at an intermediate state of its insulator-metal transition (IMT). Within the IMT region, the VO2 film comprises nanoscale islands of metal- and dielectric-phase, and can thus be viewed as a natural, disordered metamaterial. This structure displays "perfect" blackbody-like thermal emissivity over a narrow wavelength range (~40 cm-1), surpassin…
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 metam…
The impedance matching in metamaterial perfect absorbers has been believed to involve and rely on magnetic resonant response, with a direct evidence from the anti-parallel directions of surface currents in the metal structures. Here we present a different theoretical interpretation based on interferences, which shows that the two layers of metal structure in metamaterial absorbers are linked only by multiple reflections with negligible near-field interactions or magnetic resonances. This is further supported by the out-of-phase surface currents derived at the interfaces of resonator array and …
Above-light-line surface plasmon polaritons can arise at the interface between a metal and epsilon-near-zero metamaterial. This unique feature induces unusual fast-wave non-radiative modes in a epsilon-near-zero material/metal bilayer. Excitation of this peculiar mode leads to wide-angle perfect absorption in low-loss ultrathin metamaterials. The ratio of the perfect absorption wavelength to the thickness of the epsilon-near-zero metamaterial can be as high as 10^4; the electromagnetic energy can be confined in a layer as thin as λ/10000. Unlike conventional fast-wave leaky modes, these fast-w…
We describe the properties of birefringent left-handed metamaterials and introduce the concept of a birefringent perfect lens. We demonstrate that, in a sharp contrast to the conventional left-handed perfect lens at $ε=μ=-1$, where $ε$ is the dielectric constant and $μ$ is the magnetic permeability, the birefringent left-handed lens can focus either TE or TM polarized waves or both of them, allowing a spatial separation of the TE and TM images. We discuss several applications of the birefringent left-handed lenses such as the beam splitting and near-field diagnostics at the sub-wavelength scal…
We present experimental demonstration of electronically tunable metamaterial perfect absorbers in the terahertz regime. By incorporation of active liquid crystal into strategic locations within the metamaterial unit cell we are able to modify the absorption by 30 percent at 2.62 THz, as well as tune the resonant absorption over 4 percent in bandwidth. Numerical full-wave simulations match well to experiments and clarify the underlying mechanism, i.e. a simultaneous tuning of both the electric and magnetic response that allows for the preservation of the resonant absorption. These results show …
We propose a design for an universal absorber, characterized by a resonance frequency that can be tuned from visible to microwave frequencies independently of the choice of the metal and the dielectrics involved. An almost resonant perfect absorption up to 99.8 % is demonstrated at resonance for all polarization states of light and for a very wide angular aperture. These properties originate from a magnetic Fabry-Perot mode that is confined in a dielectric spacer of $λ/100$ thickness by a metamaterial layer and a mirror. An extraordinary large funneling through nano-slits explains how light ca…
We investigate the absorption properties of graphene-based anisotropic metamaterial structures where the metamaterial layer possesses an electromagnetic response corresponding to a near-zero permittivity. We find that through analytical and numerical studies, near perfect absorption arises over an unusually broad range of beam incidence angles. Due to the presence of graphene, the absorption is tunable via a gate voltage, providing dynamic control of the energy transmission. We show that this strongly enhanced absorption arises due to a coupling between light and a fast wave-mode propagating a…
We propose a thin, compact, broadband, polarization and angle insensitive metamaterial absorber based on a tungsten reflector, silicon spacer and a top pattern composed of a double square-like ring resonator utilizing nickel(Ni). In such a structure, a high absorption (above 80 %) bandwidth ~ 4.8 μm from 3.52 up to 8.32 μm corresponding to the relative bandwidth ~81% can be achieved with deeply subwavelength unit cell dimensions. Here the physical origin of the broadband absorption is associated with low Q-factor dipole modes of the top pattern inner and outer sides functioning as rectangular …
A simple metamaterial-based wide-angle plasmonic absorber is introduced, fabricated, and experimentally characterized using angle-resolved infrared spectroscopy. The metamaterials are prepared by nano-imprint lithography, an attractive low-cost technology for making large-area samples. The matching of the metamaterial's impedance to that of vacuum is responsible for the observed spectrally selective "perfect" absorption of infrared light. The impedance is theoretically calculated in the single-resonance approximation, and the responsible resonance is identified as a short-range surface plasmon…
Left-handed metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two conducting plates may turn from attraction to repulsion if a perfect lens is sandwiched between them. For optical left-handed metamaterials this repulsive force of the quantum vacuum may levitate ultra-thin mirrors.
We investigate the interaction of polarized electromagnetic waves with hyperbolic metamaterial structures, whereby the in-plane permittivity component $ε_x$ is opposite in sign to the normal component $ε_z$. We find that when the thickness of the metamaterial is smaller than the wavelength of the incident wave, hyperbolic metamaterials can absorb significantly higher amounts of electromagnetic energy compared to their conventional counterparts. We also demonstrate that for wavelengths leading to $\Re(ε_z) \approx 0$, near-perfect absorption arises and persists over a range of frequencies and s…
This paper shows that customised broadband absorption of electromagnetic waves having arbitrary polarisation is possible by use of lossy cut-wire (CW) metamaterials. These useful features are confirmed by numerical simulations in which different lengths of CW pairs are combined as one periodic metamaterial unit and placed near to a perfect electric conductor (PEC). So far metamaterial absorbers have exhibited some interesting features, which are not available from conventional absorbers, e.g. straightforward adjustment of electromagnetic properties and size reduction. The paper shows how with …
In nature, the beetle Chrysina gloriosa derives its iridescence by selectively reflecting left-handed circularly polarized light only. Here, for the first time, we introduce and demonstrate the optical analogue based on an ultrathin metamaterial, which we term circular dichroic metamirror. A general method to design the circular dichroic metasmirror is presented under the framework of Jones calculus. It is analytically shown that the metamirror can be realized by two layers of anisotropic metamaterial structures, in order to satisfy the required simultaneous breakings of n-fold rotational (n>2…
Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are approximated by at metamaterial layers that can be implemented by standard fabrication and stacking techniques. We illustrate the approximation approach for the specific example of a cylindrical invisibility cloak. First, we introduce a numerical method for the design of cloaks with arbitrary boundary shapes, and apply it to faceted shapes. Subsequently, we red…
We present a superconducting metamaterial saturable absorber at terahertz frequencies. The absorber consists of an array of split ring resonators (SRRs) etched from a 100nm YBaCu3O7 (YBCO) film. A polyimide spacer layer and gold ground plane are deposited above the SRRs, creating a reflecting perfect absorber. Increasing either the temperature or incident electric field (E) decreases the superconducting condensate density and corresponding kinetic inductance of the SRRs. This alters the impedance matching in the metamaterial, reducing the peak absorption. At low electric fields, the absorption…
A tri-layer metamaterial perfect absorber of light, consisting of (Al/ZnS/Al) films with the top aluminium layer patterned as an array of circular disk nanoantennas, is investigated for resonantly enhancing Raman scattering from C-60 fullerene molecules deposited on the metamaterial. The metamaterial is designed to have resonant bands due to plasmonic and electromagnetic resonances at the Raman pump frequency (725 nm) as well as Stokes emission bands. The Raman scattering from C60 on the metamaterial with resonantly matched bands is measured to be enhanced by an order of magnitude more than fr…
Using metamaterial absorbers, we have shown that metallic layers in the absorbers do not necessarily constitute undesired resistive heating problem for photovoltaics. Tailoring the geometric skin depth of metals and employing the natural bulk absorbance characteristics of the semiconductors in those absorbers can enable the exchange of undesired resistive losses with the useful optical absorbance in the active semiconductors. Thus, Ohmic loss dominated metamaterial absorbers can be converted into photovoltaic near-perfect absorbers with the advantage of harvesting the full potential of light m…
Complete absorption of electromagnetic waves is paramount in today's applications, ranging from photovoltaics to cross-talk prevention into sensitive devices. In this context, we use a genetic algorithm (GA) strategy to optimize absorption properties of periodic arrays of truncated square-based pyramids made of alternating stacks of metal/dielectric layers. We target ultra-broadband quasi-perfect absorption of normally incident electromagnetic radiations in the visible and near-infrared ranges (wavelength comprised between 420 and 1600 nm). We compare the results one can obtain by considering …
Designing broadband metamaterial perfect absorbers is challenging due to the intrinsically narrow bandwidth of surface plasmon resonances. Here, the paper reports an ultra-broadband metamaterial absorber by using space filling Gosper curve. The optimized result shows an average absorptivity of 95.78% from 2.64 to 9.79 μm across the entire mid-infrared region. Meanwhile, the absorber shows insensitivity to the polarization angle and the incident angle of the incident light. The underlying physical principles, used in our broadband absorber, involve a fractal geometry with multiple scales and a …
We study a polarizer-analyzer mounting for the terahertz regime with perfectly conducting metallic polarizers made of a periodic subwavelength pattern. We analytically investigate the influence on the transmission response of the multiple reflections which occur between polarizer and analyzer with a renewed Jones formalism. We demonstrate that this interaction leads to a modified transmission response: the extended Malus' Law. In addition, we show that the transmission response can be controlled by the distance between polarizer and analyzer. For particular set-ups, the mounting exhibits extre…
The direct writing using a focused electron beam allows for fabricating truly three-dimensional structures of sub-wavelength dimensions in the visible spectral regime. The resulting sophisticated geometries are perfectly suited for studying light-matter interaction at the nanoscale. Their overall optical response will strongly depend not only on geometry but also on the optical properties of the deposited material. In case of the typically used metal-organic precursors, the deposits show a substructure of metallic nanocrystals embedded in a carbonaceous matrix. Since gold-containing precursor …
The method of coordinate transformation offers a way to realize perfect cloaks, but provides less ability to characterize the performance of a multilayered cloak in practice. Here, we propose an analytical model to predict the performance of a multilayered cylindrical cloak, based on which, the cloak in practice can be optimized to diminish the intrinsic scatterings caused by discretization and simplification. Extremely low scattering or "quasi-perfect invisibility" can be achieved with only a few layers of anisotropic metamaterials without following the transformation method. Meanwhile, the p…
We show that metamaterials can be used as a testing ground to investigate spontaneous symmetry breaking associated with non-Hermitian quantum systems. By exploring the interplay between near-field dipolar coupling and material absorption or gain, we demonstrate various spontaneous breaking processes of the $\mathcal{PT}$-symmetry for a series of effective Hamiltonians associated to the scattering matrix. By tuning the coupling parameter, coherent perfect absorption, laser action and gain-induced complete reflection ($π$ reflector) by using an ultra-thin metamaterial can be obtained. Moreover, …
The fabrication of functional metamaterials with extreme feature resolution finds a host of applications such as the broad area of surface/light interaction. Non-planar features of such structures can significantly enhance their performance and tunability, but their facile generation remains a challenge. Here, we show that carefully designed out-of-plane nanopillars made of metal-dielectric composites integrated in a metal-dielectric-nanocomposite configuration, can absorb broadband light very effectively. We further demonstrate that electrohydrodynamic printing in a rapid nanodripping mode, i…
The trapped rainbow effect has been mostly found on tapered anisotropic metamaterials (MMs) made of low loss noble metals, such as gold, silver, etc. In this work, we demonstrate that an anisotropic MM waveguide made of high loss metal tungsten can also support the trapped rainbow effect similar to the noble metal based structure. We show theoretically that an array of tungsten/germanium anisotropic nano-cones placed on top of a reflective substrate can absorb light at the wavelength range from 0.3 micrometer to 9 micrometer with an average absorption efficiency approaching 98%. It is found th…
Antireflection or impedance matching is a topic that has been extensively researched by the optical and microwave communities over the past century and until today. However, due to the diverging wave impedances of TE (s) and TM (p) polarizations with increasing incident angle, it is impossible to achieve perfect matching simultaneously for both polarizations at an oblique incident angle with a single conventional matching layer. In this paper, we show that simultaneous perfecting matching of an arbitrary substrate at an arbitrary incident angle from air is possible with a single uniaxial metam…
Focusing of electromagnetic plane wave from a large size paraboloidal reflector, composed of layers of chiral and/or chiral nihility metamaterials, has been studied us- ing Maslov's method. First, the transmission and reflection of electromagnetic plane wave from two parallel layers of chiral and/or chiral nihility metamaterials are cal- culated using transfer matrix method. The effects of change of angle of incidence, chirality parameters and impedances of layers are noted and discussed. Special cases by taking very large and small values of permittivity of second layer, while assuming value …
We study a highly controllable perfect plasmonic absorber -- a thin metamaterial layer which possess balanced electric and magnetic responses in some frequency range. We show that this regime is compatible with both metal-backed variant of the structure or its semitransparent variant. This regime can be implemented in a prospective thin-film photovoltaic cell with negligible parasitic losses.
In order to reduce the difficulties in the experimental realizations of the cloak but still keep good performance of invisibility, we proposed a perfect cylindrical invisibility cloak with spatially invariant axial material parameters. The advantage of this kind of TE (or TM) cloak is that only rho and phi components of mu (or epsilon) are spatially variant, which makes it possible to realize perfect invisibility with two-dimensional (2D) magnetic (or electric) metamaterials. The effects of perturbations of the parameters on the performance of this cloak are quantitatively analyzed by scatteri…
The technologies of heating, photovoltaics, water photocatalysis and artificial photosynthesis depend on the absorption of light and novel approaches such as coherent absorption from a standing wave promise total dissipation of energy. Extending the control of absorption down to very low light levels and eventually to the single photon regime is of great interest yet remains largely unexplored. Here we demonstrate the coherent absorption of single photons in a deeply sub-wavelength 50% absorber. We show that while absorption of photons from a travelling wave is probabilistic, standing wave abs…
The ability to drive a system with an external input is a fundamental aspect of light-matter interaction. The coherent perfect absorption (CPA) phenomenon extends to the general multibeam interference phenomenology the well known critical coupling concepts. This interferometric control of absorption can be employed to reach full delivery of optical energy to nanoscale systems such as plasmonic nanoparticles, and multi-port interference can be used to enhance the absorption of a nanoscale device when it is embedded in a strongly scattering system, with potential applications to nanoscale sensin…
Traditionally, efforts to achieve perfect absorption have required the use of complicated metamaterial-based structures as well as relying on destructive interference to eliminate back reflections. Here, we have demonstrated both theoretically and experimentally that such perfect absorption can be achieved using a naturally occurring material, hexagonal boron nitride (hBN) due to its high optical anisotropy without the requirement of interference effects to absorb the incident field. This effect was observed for p-polarized light within the mid-infrared spectral range, and we provide the full …
In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile materials. Given a desired device function, the theory describes the electromagnetic properties that turn this function into fact. We consider media that facilitate space-time transformations and include negative refraction. Our theory unifies the concepts operating behind the scenes of perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect a…
We investigate numerically the use of a negative-permeability "perfect lens" for enhancing wireless power transfer between two current carrying coils. The negative permeability slab serves to focus the flux generated in the source coil to the receiver coil, thereby increasing the mutual inductive coupling between the coils. The numerical model is compared with an analytical theory that treats the coils as point dipoles separated by an infinite planar layer of magnetic material [Urzhumov et al., Phys. Rev. B, 19, 8312 (2011)]. In the limit of vanishingly small radius of the coils, and large wid…
