Full 2π tunable phase modulation using avoided crossing of resonances

Active metasurfaces have been proposed as one attractive means of achieving high-resolution spatiotemporal control of optical wavefronts, having applications such as LIDAR and dynamic holography. However, achieving full, dynamic phase control has been elusive in metasurfaces. In this paper, we unveil an electrically tunable metasurface design strategy that operates near the avoided crossing of two resonances, one a spectrally narrow, over-coupled resonance and the other with a high resonance frequency tunability. This strategy displays an unprecedented upper limit of 4π range of dynamic phase modulation with no significant variations in optical amplitude, by enhancing the phase tunability through utilizing two coupled resonances. A proof-of-concept metasurface is justified analytically and verified numerically in an experimentally accessible platform using quasi-bound states in the continuum and graphene plasmon resonances, with results showing a 3π phase modulation capacity with a uniform reflection amplitude of ~0.65.