Transmission properties of time-dependent one-dimensional metamaterials

TL;DR

This paper provides an exact solution and numerical analysis of wave transmission in one-dimensional time-modulated metamaterials, revealing how temporal modulation influences band structure and transmission properties.

Contribution

It introduces an exact solution approach for wave equations in time-modulated metamaterials and validates a capacitance matrix approximation for efficient analysis.

Findings

Capacitance matrix approximation is accurate and efficient.

Time modulation affects formation of band gaps and degenerate points.

Numerical simulations confirm theoretical transmission properties.

Abstract

We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically using Muller's method. We prove a formula in the form of an ODE using a capacitance matrix approximation. Comparison of the exact results with the approximations reveals that the method of capacitance matrix approximation is accurate and significantly more efficient. We prove various transmission properties in the aforementioned structure and illustrate them with numerical simulations. In particular, we investigate the effect of time-modulated material parameters on the formation of degenerate points, band gaps and k-gaps.