Nonparaxial scalar treatment of sinusoidal phase gratings

Abstract

Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.

Azopolymer‐based micro‐ and nanopatterning for photonic applications

“…In this respect, we would like to emphasize that these numbers are correct only for diffraction gratings that are treatable within the paraxial approximation of traditional Fourier optics. For gratings beyond this approximation, such as those having a period of few wavelengths or smaller and phase modulation amplitude close to π, the maximum values of the first‐order diffraction efficiency can be different . In fact, the first‐order diffraction efficiency of a reflective sinusoidal phase grating can reach even the level of 100%, for example, when the grating operates near the regime where the diffraction order becomes evanescent .…”

Light trapping in solar cells: numerical modeling with measured surface textures

“…According to nonparaxial scalar scattering theory [15,16], the diffracted radiance of wavelength λ in direction cosine space is given by…”

Recent developments in the analysis of surface scatter phenomena

“…20 allowed us to calculate diffraction grating efficiencies in Ref. 27, have led us to believe that the non-intuitive surface scatter effects reported by O'Donnell and Mendez, and illustrated in Figure 1, might be the result of inappropriately comparing different radiometric quantities.…”

“…27 These include: (i) the redistribution of energy from the evanescent orders to the propagating ones, (ii) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (iii) non-paraxial diffraction efficiencies (for TE polarization) predicted with an accuracy usually thought to require rigorous electromagnetic vector theory.…”