Fundamental Bounds to Time-Harmonic Quadratic Metrics in Electromagnetism: Overview and Implementation

TL;DR

This paper develops a convex optimization framework to establish fundamental bounds on quadratic electromagnetic metrics, utilizing dual and method-of-moments formulations, and demonstrates the approach with examples supported by MATLAB codes.

Contribution

It introduces a novel convex optimization methodology for deriving bounds on electromagnetic metrics, including substructure bounds, with practical implementation tools.

Findings

Bounds formulated via convex optimization and dual methods.

Pareto-optimal trade-offs between metrics identified.

Open-source MATLAB package provided for implementation.

Abstract

Fundamental bounds on quadratic electromagnetic metrics are formulated and solved via convex optimization. Both dual formulation and method-of-moments formulation of the electric field integral equation are used as key ingredients. The trade-off between metrics is formulated as a multi-objective optimization resulting in Pareto-optimal sets. Substructure fundamental bounds are also introduced and formulated as additional affine constraints. The general methodology is demonstrated on a few examples of minimal complexity and all examples are supported with freely available MATLAB codes contained in the developed package on fundamental bounds.