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We put forward the concept of an optomagnonic crystal: a periodicallypatterned structure at the microscale based on a magnetic dielectric, which canco-localize magnon and photon modes. The co-localization in small volumes canresult in large values of the photon-magnon coupling at the single quantalevel, which opens perspectives for quantum information processing and quantumconversion schemes with these systems. We study theoretically a simple geometryconsisting of a one-dimensional array of holes with an abrupt defect,considering the ferrimagnet Yttrium Iron Garnet (YIG) as the basis material. Weshow that both magnon and photon modes can be localized at the defect, and usesymmetry arguments to select an optimal pair of modes in order to maximize thecoupling. We show that an optomagnonic coupling in the kHz range is achievablein this geometry, and discuss possible optimization routes in order to improveboth coupling strengths and optical losses.

Design of an optomagnonic crystal: towards optimal magnon-photon mode matching at the microscale