Time-dependent metasurfaces are playing an increasingly important role as a platform to change the frequency of optical signals. This is a result of the fact that the interaction length through a single surface is so small that it is nearly impossible to generate new spectral components using nonlinear effects. However, although the idea to generate new spectral components using time-dependent metasurfaces has been around for quite some time, this emerging research field is still lacking a coherent, self-consistent framework that explains how frequencies of optical pulses can be manipulated.
In this manuscript, we introduce such a general framework that allows for the understanding and designing of time-dependent metasurfaces that shift the frequencies of electromagnetic pulses. Based on an analytical model and FDTD numerical simulations, we obtain physical insight into the complex process that occurs when broadband electromagnetic pulses interact with time-varying metasurfaces. In particular, we find that there is an intriguing relation between the bandwidth of the incident pulse, the targeted frequency shift, and the number of Lorentzian resonators that need to be implemented. We also demonstrate that in certain parameter regimes, pulse distortion and deviating pulse amplitudes cannot be avoided.
We thus expose a fundamental limitation of time-dependent metasurfaces. These results are independent of the mechanism that generates the time-dependence and they do not dependent on the operating frequencies, nor the geometry, size or material of the unit cell. They are a direct result of the subtle interplay of Lorentzian resonances. In addition, we provide a widely usable design method for anyone who wants to use time-dependent metasurfaces to shift frequencies of electromagnetic pulses.
The manuscript was published in Physical Review B as a Rapid Communication and can be found here. Full Pdf.