Transmission properties of time-dependent one-dimensional metamaterials

What is it about?

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.

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Photo by Jan Huber on Unsplash

Photo by Jan Huber on Unsplash

Why is it important?

Our paper provides the derivation of a capacitance matrix approximation formula for one-dimensional time-dependent problems. These problems are of particular interest as many analogies can be drawn to condensed matter physics and quantum mechanics. Thereby, our work proves important key results for these fields.