Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings

The diffraction characteristics of finite-number-of-periods (FNP) gratings are determined by using rigorous electromagnetic analysis based on the two-region formulation of the exact boundary element method. Gratings with 5, 9, 13, and 17 periods are analyzed and compared with infinite-number-of-periods (INP) gratings in terms of diffraction efficiencies and field patterns. Both dielectric transmission diffractive devices and metallic reflection diffractive devices are treated for TE and TM normally incident light. Furthermore, both 2-level and 8-level grating structures are treated. The diffraction properties of FNP gratings are shown to approach smoothly those of INP gratings as the number of periods increases.