Rigorous analysis of shadowing effects in blazed transmission gratings

Abstract

Blazed transmission gratings have become crucial components in many hybrid optical systems. Shadowing effects are known to occur at their passive blaze facets, which may impair the system's efficiency performance. For optical designs, it is desirable to have a simple but accurate description of this phenomenon. We show that the efficiency reduction in low diffraction orders is dominated by a linear dependence on the ratio of wavelength to grating period rather than a quadratic dependence as proposed in extended scalar theory. The strength of the electromagnetic shadowing will be determined using rigorous diffraction methods and discussed with respect to imaging optical components. Results are compared to existing ray-optical models.

High-performance axicon lenses based on high-contrast, multilayer gratings

“…However, when the grating periods are near the operation wavelength and the deflection angles are large (i.e., the "resonance domain"), the device efficiencies decrease due to shadowing effects incurred by the physical topology of these grating structures. [13][14][15] Alternative device designs utilizing very high aspect ratio structures have been proposed to improve the performance of glass multilayer blazed grating structures operating in the resonance domain. 16,17 While these devices support enhanced efficiency, they a Author to whom correspondence should be addressed: jonfan@stanford.edu require patterning using electron-beam lithography, together with complicated, multi-step fabrication techniques.…”

Period interaction on diffraction efficiency of blazed transmission gratings

“…In our method, field E r is treated completely different from that in the extended scalar theory in which it is thought to be the critical reason of the efficiency reduction because of a direct geometrical shadow or a dead zone at the passive facet, known as the shadowing effect [4]. We take E r as one of the two direct transmission fields in that in this intermediate structure it does possess indispensable contribution to the diffraction field, even part of the incident energy is lost via reflection on the passive facet.…”

“…Already along the transition from refractive to diffractive micro-optical components, this issue poses an enormous challenge for both the analysis and design. Diffraction efficiency is definitely a crucial parameter of blazed transmission gratings, which is related to comprehensive factors, such as grating material, the ratio of structure period to illumination wavelength (L/l), fabrication error of inclination angles and height, shadowing effects [4], etc. Fabrication error is inevitable in any fabrication process and thus ideal sawtooth relief is not available, which results in the enhancement of the period interaction deriving from the increased lights reflected by both of the blaze and passive facets of the neighboring structures.…”

Analysis of blazed diffractive optical elements formed with artificial dielectrics

“…First, it assumes that the unwrapped phase function is slowly varying at the wavelength scale. This implies that the model cannot take into account shadowing effects [19] that prevent the realization of 100% efficiencies. But for components with a characteristic size larger than Ϸ10, the model predictions remain accurate.…”