This paper theoretically studies how the optics of multiple grooves in a metal change as the number of grooves gradually increased from a single groove to infinitely many arranged in a periodic array. In the case of a single groove, the out-of-plane scattering (OUP) cross section at resonance can significantly exceed the groove width. On the other hand, a periodic array of identical grooves behaves radically different and is a near-perfect absorber at the same wavelength. When illuminating multiple grooves with a plane wave, the OUP cross section is found to scale roughly linearly with the number of grooves and is comparable with the physical array width even for widths of many wavelengths. The normalized OUP cross section per groove even exceeds that of a single groove, which is explained as a consequence of surface plasmon
polaritons generated at one groove being scattered out of the plane by other grooves. In the case of illuminating instead with a Gaussian beam and observing the limit as the incident beam narrows and is confined within the multiple-groove array, it is found that the total reflectance becomes very low and that there is practically no OUP. The well-known result for periodic arrays is thus recovered. All calculations were carried out using Green’s function surface integral equation methods taking advantage of the periodic nature of the structures. Both rectangular and tapered grooves are considered.
- Surface plasmons
- Diffraction and gratings
- scattering theory
- metal optics