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This is the first part in a series of two papers that concern with thequantitative analysis of the electromagnetic field enhancement and anomalousdiffraction by a periodic array of subwavelength slits. The scattering problemin the diffraction regime is investigated in this part, for which the size ofthe period is comparable to the incident wavelength. We distinguish scatteringresonances and real eigenvalues, and derive their asymptotic expansions whenthey are away from the Rayleigh cut-off frequencies. Furthermore, we presentquantitative analysis of the field enhancement at resonant frequencies, byquantifying both the enhancement order and the associated resonant modes. Thefield enhancement near the Rayleigh cut-off frequencies is also investigated.It is demonstrated that the field enhancement becomes weaker at the resonantfrequency if it is close to the Rayleigh cut-off frequencies. Finally, we alsocharacterize the embedded eigenvalues for the underlying periodic structure,and point out that transmission anomaly such as Fano resonant phenomenon doesnot occur for the narrow slit array.

Scattering by a periodic array of subwavelength slits I: field enhancement in the diffraction regime