Coherent light-matter interaction in ultrathin metamaterials has been demonstrated to dynamically modulate intensity, polarization and propagation direction of light. The gradient metasurface with a transverse phase variation usually exhibits an anomalous refracted beam of light dictated by so-called generalized Snell’s law. However, less attention has been paid to coherent control of the metasurface with multiple anomalous refracted beams. Here we propose an ultrathin gradient metasurface with single trapezoid-shaped slot antenna as its building block that allows one normal and two deflected transmitted beams. It is numerically demonstrated that such metasurface with multiple scattering modes can be coherently controlled to modulate output intensities by changing the relative phase difference between two counterpropagating coherent beams. Each mode can be coherently switched on/off and two deflected anomalous beams can be synchronously dictated by the phase difference. The coherent control effect in the trapezoid-shaped slit metasurface will offer a promising opportunity for multichannel signals modulation, multichannel sensing and wave front shaping.

The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.Comment: 2 page