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Abstract A mathematical model has been developed to study far-field and near-field thermal emission from non-continuous periodic structures. Non-continuous periodic structures with appropriate geometries and materials can support electric or magnetic resonance, idealized for designing far-field perfect absorbers and near-field emitters/absorbers supporting long-distance photon tunneling. However, these structures do not have close format dyadic Green’s function to describe the thermal radiation from randomly fluctuating thermal current. Thus, simulating the near-field radiation spectrum between emitters and collectors patterned with these non-continuous periodic structures is challenging. Though finding eigenmodes of white-noise-like fluctuating thermal current satisfying this specific geometry, we extended the Wiener-Chaotic expansion type of near-field simulation to study far-field and near-field thermal emission from non-continuous periodic structures. After verifications with reference cases, the new mathematical method is applied to study photon tunneling between the emitter and the collector patterned with single-ring split ring resonance rings (SRR) supporting magnetic field resonance. It is observed from the new mathematical model that long photon tunneling can occur under such a configuration through magnetic field coupling between the emitter and collector at the magnetic resonance frequency of SRRs.