Ariel Epstein

Huygens’ metasurfaces via the equivalence principle: design and applications

We review the current trends in the design of Huygens’ metasurfaces (HMSs), which are planar arrays of balanced electric and magnetic polarizable particles (meta-atoms) of subwavelength size. We focus on schemes that follow the equivalence principle, as these can be rigorously incorporated into Maxwell’s equations, leading to design specifications in the form of (electric and magnetic) surface-impedance distributions. The advantages of this approach with respect to the more common phase-shift stipulation approach are highlighted and discussed. We present a (microscopic) methodology to associate a general meta-atom configuration with an equivalent surface impedance, and derive metasurface (macroscopic) design procedures for various beam forming applications. The methods and concepts developed in the paper provide the basic tools for understanding and designing scalar, passive, and lossless HMSs, and we indicate possible extensions applicable to more complex structures.

Passive Lossless Huygens Metasurfaces for Conversion of Arbitrary Source Field to Directive Radiation

We present a semianalytical formulation of the interaction between a given source field and a scalar Huygens metasurface (HMS), a recently introduced promising concept for wavefront manipulation based on a sheet of orthogonal electric and magnetic dipoles. Utilizing the equivalent surface impedance representation of these metasurfaces, we establish that an arbitrary source field can be converted into directive radiation via a passive lossless HMS if two physical conditions are met: local power conservation; and local impedance equalization. Expressing the fields via their plane-wave spectrum and harnessing the slowly-varying envelope approximation, we obtain semianalytical formulae for the scattered fields, and prescribe the surface reactance required for the metasurface implementation. The resulting design procedure indicates that the local impedance equalization induces a Fresnel-like reflection, while local power conservation forms a radiating virtual aperture which follows the total excitation field magnitude. The semianalytical predictions are verified by finite-element simulations of HMSs designed for different source configurations. Besides serving as a flexible design procedure for HMS radiators, the proposed formulation also provides a robust mechanism to incorporate a variety of source configurations into general HMS models, as well as physical insight on the conditions enabling purely reactive implementation of this novel type of metasurfaces.

Synthesis of Passive Lossless Metasurfaces Using Auxiliary Fields for Reflectionless Beam Splitting and Perfect Reflection

We introduce a paradigm for accurate design of metasurfaces for intricate beam manipulation, implementing functionalities previously considered impossible to achieve with passive lossless elements. The key concept involves self-generation of auxiliary evanescent fields which facilitate the required local power conservation, without interfering with the device performance in the far field. We demonstrate our scheme by presenting exact reactive solutions to the challenging problems of reflectionless beam splitting and perfect reflection, verified via full wave simulations.

Analytical estimation of emission zone mean position and width in organic light-emitting diodes from emission pattern image-source interference fringes

We present an analytical method for evaluating the first and second moments of the effective exciton spatial distribution in organic light-emitting diodes (OLED) from measured emission patterns. Specifically, the suggested algorithm estimates the emission zone mean position and width, respectively, from two distinct features of the pattern produced by interference between the emission sources and their images (induced by the reflective cathode): the angles in which interference extrema are observed, and the prominence of interference fringes. The relations between these parameters are derived rigorously for a general OLED structure, indicating that extrema angles are related to the mean position of the radiating excitons via Braggs condition, and the spatial broadening is related to the attenuation of the image-source interference prominence due to an averaging effect. The method is applied successfully both on simulated emission patterns and on experimental data, exhibiting a very good agreement with the results obtained by numerical techniques. We investigate the method performance in detail, showing that it is capable of producing accurate estimations for a wide range of source-cathode separation distances, provided that the measured spectral interval is large enough; guidelines for achieving reliable evaluations are deduced from these results as well. As opposed to numerical fitting tools employed to perform similar tasks to date, our approximate method explicitly utilizes physical intuition and requires far less computational effort (no fitting is involved). Hence, applications that do not require highly resolved estimations, e.g., preliminary design and production-line verification, can benefit substantially from the analytical algorithm, when applicable. This introduces a novel set of efficient tools for OLED engineering, highly important in the view of the crucial role the exciton distribution plays in determining the device performance.

Electromagnetic Radiation from Organic Light-emitting Diodes

An analytical prototype model for the electromagnetic radiation emitted from a nanometric organic light-emitting diode device is presented and thoroughly investigated herein. The results are obtained via asymptotic evaluation of the resultant radiation integral in con- junction with coherence considerations, resulting in closed-form analytical expressions. For the sake of simplicity and clarity, we focus on a two-dimensional canonical conflguration excited by impulsive (line) sources. The resultant expressions can be most efiectively utilized by engineers for improved design, as they enable the calculation of the devices physical parameters, such as electrical to optical conversion e-ciency and emission angular distribution, as a function of de- vice structure. It should be pointed out that the incorporation of both rigorous electromagnetic analysis and coherence efiects is addressed in our report, to the best of our knowledge, for the flrst time. This results in a precise model capable of repeating and interpreting experimental and simulated data.

Rigorous analysis of image force barrier lowering in bounded geometries: application to semiconducting nanowires

Bounded geometries introduce a fundamental problem in calculating the image force barrier lowering of metal-wrapped semiconductor systems. In bounded geometries, the derivation of the barrier lowering requires calculating the reference energy of the system, when the charge is at the geometry center. In the following, we formulate and rigorously solve this problem; this allows combining the image force electrostatic potential with the band diagram of the bounded geometry. The suggested approach is applied to spheres as well as cylinders. Furthermore, although the expressions governing cylindrical systems are complex and can only be evaluated numerically, we present analytical approximations for the solution, which allow easy implementation in calculated band diagrams. The results are further used to calculate the image force barrier lowering of metal-wrapped cylindrical nanowires; calculations show that although the image force potential is stronger than that of planar systems, taking the complete band-structure into account results in a weaker effect of barrier lowering. Moreover, when considering small diameter nanowires, we find that the electrostatic effects of the image force exceed the barrier region, and influence the electronic properties of the nanowire core. This study is of interest to the nanowire community, and in particular for the analysis of nanowire I-V measurements where wrapped or omega-shaped metallic contacts are used.

On the relevance of two‐dimensional models for radiation of statistical sources in stratified media

We present analytical closed-form expressions for the radiation patterns of 2-D line sources and 3-D point dipoles embedded in a general multilayered configuration. While the former are simplified model sources, used as a preliminary analytical step to reduce derivation complexity, the latter have been shown experimentally to reproduce the electromagnetic behavior of many elementary statistical sources. By decomposing the sources to current elements generating pure transverse electric (TE) or transverse magnetic (TM) polarized radiation, we arrive at a unified format for the radiation pattern expression for all sources considered. Analyzing the common 1-D (characteristic) Greens function, we show that the normalized TE-polarized emission of model 2-D electric line sources reproduces exactly the measured TE-polarized radiation of statistical (3-D) dipoles with random in-plane orientation; the connection between the TM-polarized emission of the two species is discussed, and physical interpretation is provided via the unified expression. These results specify the precise relations between the 2-D and 3-D models, providing intuition as well as guidelines for proper usage of simplified 2-D results for analysis of realistic 3-D statistical configurations.

Ray-oriented design of Huygens metasurfaces for multiple source excitation

Huygens metasurfaces (HMS), combining subwavelength electric and magnetic polarizable particles, have demonstrated impressive wave manipulation capabilities, such as engineered refraction, focusing, and polarization control. Recently, a general methodology to design HMSs for converting given (arbitrary) source fields to directive radiation has been presented, facilitating antenna design (A. Epstein and G.V. Eleftheriades, IEEE Trans. Antennas Propag., 62, 5680–5695, 2014). However, this methodology guarantees proper performance only for the designated source excitation, whereas for many modern applications multifunctional devices, e.g. multidirectional antenna, are desirable.

Coupling localized sources to controlled polarized broadside radiation using Huygens metasurfaces

We present a path for integrating arbitrary 3D localized sources with Huygens metasurfaces (HMS) to form directive broadside radiators with desirable polarization. This step is essential for development of practical devices based on this novel class of metasurfaces, harnessing both electric and magnetic sheet impedances to manipulate fields with reduced reflections. Extending previous work, we utilize the plane-wave spectral representation of the vectorial fields to synthesize passive lossless HMSs by locally enforcing power conservation and impedance equalization; polarization control is achieved via unit cell rotation. Semianalytical design formulas are derived and applied to devise an HMS coupling a vertical magnetic dipole to directive circularly-polarized radiation.