Abstract
By using the recent theory of elemental scattering matrix, I study the critical-point behaviors of conically mounted and crossed gratings in Littrow mountings. As functions of the projected incident wave vector in the grating plane, the (
m
,
n
)th-order reflected principal diffraction efficiencies (the maximum and minimum diffraction efficiencies of a diffraction order for all possible incident polarizations) of a crossed grating have
C
2
symmetry with respect to the (
m
,
n
)th-order Littrow point, and for a conically mounted grating, the symmetry type is increased to
C
2
v
. In a Littrow mounting, each one of the two principal diffraction efficiencies, independent of the other, can only be at one of the three possible states: a local maximum, a local minimum, or a saddle point of an even (most likely the second) degree. If the grating is mirror-symmetric with respect to a plane parallel to the grating’s mean plane, the results hold for a transmitted diffraction order as well.
Funder
Chinese Academy of Sciences, Shanghai Branch
Subject
Computer Vision and Pattern Recognition,Atomic and Molecular Physics, and Optics,Electronic, Optical and Magnetic Materials