Circuit analysis of radiation reaction in metamaterials by retarded electromagnetic coupling

Because radiation is essential in high-frequency circuits, such as those used in metamaterials and plasmonics, the investigation of radiation loss is important. This study describes the characteristics of radiation loss, which is a radiation reaction in circuits with retarded electromagnetic couplings. The structure of wired metallic spheres is used to demonstrate metamaterial equivalent circuits, where charges and current exist on the spheres and wires, respectively. An inductance matrix and a potential coefficient matrix with retarded electromagnetic couplings are defined to address the radiation reaction. Subsequently, based on the topology of the wires and spheres, an equivalent circuit equation with retardation is formulated to discuss the losses in the resonant circuit caused by the inductive and capacitive elements. Thereafter, the relationship between the resonant frequency and radiation loss caused by the retarded couplings is demonstrated and the difference between the retarded couplings and couplings with transmission lines is clarified. Furthermore, we indicate that retarded coupling generates singularity on a dispersion curve for a one-dimensional array of resonant circuits. Thus, the circuit with retarded couplings generates novel characteristics of radiation reactions that are not represented by the circuit without retardation. This circuit analysis is expected to afford new aspects in studies on topics, such as metamaterials and plasmonics

On the passivity of the quasi-static partial element equivalent circuit method

International audienceThe partial element equivalent circuit (PEEC) electromagnetic method has attracted a lot of attention for its capability to give a circuit interpretation to Maxwell's equations. The PEEC equivalent circuits are usually connected with terminations such as drivers and receivers in a time‐domain circuit simulator. Passivity is a fundamental property for the time‐domain simulations of circuit models connected to terminations at their electrical ports. Stable, but nonpassive, models can produce unstable systems when connected to other stable, even passive, loads. The so‐called quasi‐static PEEC formulations leads to a descriptor state‐space circuital representation of the electromagnetic phenomena. Multiple state‐space representations are possible. In this paper, we study the passivity property of different quasi‐static PEEC representations in detail. A novel analytical additive decomposition is proposed concerning the admittance formulation, which allows extracting the polynomial part of the transfer function that represents the behavior at infinity in the Laplace domain. This decomposition is discussed from a mathematical and a physical point of view. Such a detailed study for the passivity of quasi‐static PEEC models and the novel analytical decomposition is not available in the literature. Numerical results support the theoretical analysis