  This is the first part in a series of two papers that concern with the
quantitative analysis of the electromagnetic field enhancement and anomalous
diffraction by a periodic array of subwavelength slits. The scattering problem
in the diffraction regime is investigated in this part, for which the size of
the period is comparable to the incident wavelength. We distinguish scattering
resonances and real eigenvalues, and derive their asymptotic expansions when
they are away from the Rayleigh cut-off frequencies. Furthermore, we present
quantitative analysis of the field enhancement at resonant frequencies, by
quantifying both the enhancement order and the associated resonant modes. The
field enhancement near the Rayleigh cut-off frequencies is also investigated.
It is demonstrated that the field enhancement becomes weaker at the resonant
frequency if it is close to the Rayleigh cut-off frequencies. Finally, we also
characterize the embedded eigenvalues for the underlying periodic structure,
and point out that transmission anomaly such as Fano resonant phenomenon does
not occur for the narrow slit array.
