Transmission of transient plane waves through perfect electrically conducting plates perforated by periodic arrays of subwavelength holes

Phenomena associated with the transmission of transient plane waves through plates perforated by subwavelength holes are studied. Specifically, the time domain transmitted field (TDTF) or transient response of a thin plate (sandwiched in between two dielectric slabs) that is perforated periodically by subwavelength holes and illuminated by a transient plane wave (TPW) is calculated by inverse Fourier transforming the product of the plate's frequency domain transmission coefficient (FDTC) and the TPWs Fourier transform. The incident TPW comprises smoothed and damped exponentials. The FDTC has pole and branch point (BP) singularities associated with resonant and Rayleigh-Wood anomalies. Special choice of branch cuts associated with the BPs allows choosing the poles on a single Riemann sheet. The TDTF is represented in terms of incident TPW and FDTC pole residues, and branch cut (BC) integrals. The latter are evaluated asymptotically for arbitrary small pole-branch point (BP) separations. The obtained expressions are simplified and interpreted for narrow- and wide-band incident fields, and key characteristics of the transient fields scattered from the above structure are identified. For narrowband fields, only the incident TPW pole contributions are significant and the resulting TDTF is an attenuated and delayed replica of the incident TPW. When the field frequency support is near a FDTC pole, significant positive delays are obtained. When the field frequency support is near a BP, small positive and noticeable negative delays are obtained for large and small pole-BP separation, respectively. For wide-band fields all contributions in the TDTF are significant. The incident TPW pole contributions are significant only for early time. The FDTC pole contributions are the counterparts of frequency domain leaky waves and only are significant for much later time. The BC contributions are the counterparts of frequency domain lateral wave and decay slowly, thereby resulting in a very long TDTF temporal tail. Their magnitudes are substantially larger for smaller pole-BP separations than for large ones. The investigated phenomena occur not only on hole-perforated plates but also on other types of periodic gratings. They can find use in constructing novel probes, antennas, and microwave and optical filters.