Fig. 5: Illustration of a large momentum bandgap for propagating waves.
From: Expanding momentum bandgaps in photonic time crystals through resonances
a, Optical time-varying metasurface designed to exhibit a momentum bandgap for propagating waves. The purple arrow indicates a propagating eigenmode whose amplitude is growing in time. The geometry of the metasurface is the same as in Fig. 4a. b, Band structure of a time-varying metasurface with modulation frequency ωm3. c, Magnified band structure in the green highlighted region in b. d, The corresponding imaginary part of the frequency for fixed ℜ(ω) = ωm3/2. e, Imaginary part of the eigenfrequency ℑ(ω) at the centre of the bandgap and the relative amplification bandwidth \(\Delta {k}_{| | }^{{\rm{a}}}\) as a function of the damping factor γ for the bandgap shown in c and d. Note that the band structure shown in b accommodates the eigenmodes for both transverse-magnetic and -electric polarizations; however, in c and d we optimize the metasurface for transverse-electric waves.
