The macroscopic mechanism of light traveling based on the general Snell's laws records the interactions between the gradient phases of meta-surfaces and the involved fields, but it can hardly adequately account for the detailed contributions of meta-atoms to the behaviors of light. Here, we demonstrate the light-microscopic observation of the interference from meta-atoms to characterize the meta-surface with the inhomogeneous spatial distribution of surface susceptibility. The meta-surface will generate multi-order diffractions with a main propagating channel and several other weaker channels, and the light emitted by the meta-atoms will also coherently cancel out the original incidence. Such an extinction theorem in the meta-surface regime can sufficiently predict the negative refraction with a phase gradient beyond the critical angle, instead of vanishing when following the route of general Snell's laws.
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