Theorem of resonance of Small Volume High Contrast multilayered materials

TL;DR

This paper presents two theorems that mathematically relate the resonance response of small, multilayered composite materials to their susceptibility and geometry, aiding in material characterization via spectroscopy.

Contribution

The paper introduces new theorems providing explicit formulas for the resonance of multilayered small-volume materials based on susceptibility and geometry.

Findings

Formulas for resonance of double-layered materials

Formulas for resonance of multilayered small volumes

Potential for material property detection using spectroscopy

Abstract

The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In this paper two theorems are presented, providing formulas of scattering resonance of double-layered and multilayered small volumes in terms of the coefficient of susceptibility, being high, and the geometric characteristics. Spectroscopy measurements of the composite medium can exploit the formula to detect its dimension and susceptibility index.