Numerical modelling of time-dependent metamaterials with the FDTD method

Abstract: Metamaterials are artificial materials, usually composed of so-called meta-atoms, with electromagnetic properties which cannot be found in naturally occurring materials. In this work we study the properties of time-dependent metamaterials (meaning that their electromagnetic properties are varying with time), as well as their potential applications. Since the analytical results available are limited, we have developed and implemented a numerical technique based on the Finite-Differences Time-Domain (FDTD) method. The method and its implementation are discussed in detail. A state-of-the-art variation of the total-field / scattered-field technique is used to introduce plane waves into the computational domain, so that numerical artifacts are within the limits of computing precision. We use convolutional perfectly matched layers as absorbing boundary conditions and practically demonstrate that they are well-suited for applications involving time-dependent media. Transmission of plain monochromatic waves through a time-dependent slab with the dielectric permittivity and magnetic permeability changing linearly with time, which has been investigated analytically in an earlier work, is studied numerically. Propagation of pulses with a finite continuous spectrum through the same system is studied both analytically and numerically. In all cases, the analytical and numerical results are in good agreement, which demonstrates that the code developed produces physically valid results. The technique developed is a powerful tool for designing new devices based on time-dependent metamaterials. We discuss one example of such an application, namely modelling a tunable wavelength-division multiplexer, as well as the prospects of designing other optical devices.