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

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.