Energy estimates for wave amplification in quasiperiodic Fibonacci time-modulated media

TL;DR

This paper investigates wave energy amplification in Fibonacci time-modulated media, providing energy estimates that predict parametric amplification regions and validate exponential energy growth through the analysis of fractal gap structures.

Contribution

It introduces a method to estimate wave energy growth in Fibonacci quasiperiodic media, revealing fractal gap structures and independent super gaps that predict amplification.

Findings

Exponential wave energy amplification occurs in specific fractal gaps.

Energy estimates accurately predict amplification regions.

Super gaps are independent of supercell duration.

Abstract

Fibonacci time quasicrystals can be approximated by temporal supercells to reveal a fractal collection of $k$ gaps, in which wave energy is amplified exponentially. These estimates are validated by the observation of "super" $k$ gaps that are independent of the duration of the temporal supercell. This approach predicts the regions of parametric amplification and provides accurate estimates of the energy growth rate.