Non-reciprocal manipulation of subwavelength fields in locally-resonant metamaterial crystals

Locally-resonant metamaterial crystals are artificial materials built from small spatially-local resonant inclusions arranged periodically at subwavelength scale. Unlike conventional continuous metamaterials, for which spatial dispersion originates mostly (but not exclusively) from the non-locality of their inclusions, they exhibit large spatially non-local effects that emerge solely at the array level because of the periodic structuration of simple spatially-local scatterers, often allowing for an intrinsically subwavelength granularity. Here, we demonstrate the unique relevance of metamaterial crystals to induce non-reciprocal electromagnetic propagation at deep subwavelength scales. This is obtained by combining the breaking of time-reversal symmetry, using an externally biased magnetic material, with appropriate spatial-dispersion engineering, via subwavelength structural modification of the metamaterial crystal. Interestingly, the material unit cell can be scaled down without affecting this functionality, leading to the exciting possibility of largely enhanced wave-matter interaction at deep subwavelength scales. Altogether, our proposal provides an interesting route for transposing the rich physics of non-reciprocal systems down to the subwavelength scale.