Beam steering efficiency in resonant reflective metasurfaces

Beam steering is one of the prevailing functions performed by electromagnetic metasurfaces. Its efficiency depends on a large number of physical parameters associated with resonant elements comprising the metasurface and is thus notoriously difficult to optimize. Here we formulate a theoretical model for evaluating the diffraction efficiency of an array of lossy resonant elements whose spectral response is dominated by the coupling between a leaky eigenmode and a single incoming/outgoing channel. We use it to deduce a formula for the maximum attainable diffraction efficiency and the gradient parameter profile for which it is achieved. The optimization procedure is demonstrated on the example of an electrically tunable liquid-crystal terahertz beam steering metasurface. Finally, the proposed model is benchmarked against rigorous metasurface simulations.