In a recent paper [J. Opt. Soc. Am. A <b>16</b>, 1108 (1999)] Logofǎtu <i>et al</i>. demonstrated by experimental and numerical evidence that the 0th-order cross-polarization (<i>s</i> to <i>p</i> and <i>p</i> to <i>s</i>) reflection coefficients of isotropic, symmetrical, surface-relief gratings in conical mount are identical. Here an analytical proof is given to show that the observed identity is merely a manifestation of the electromagnetic reciprocity theorem for the 0th-order diffraction of symmetrical gratings. The above result is further generalized to bianisotropic gratings, to the 0th-order cross-polarization transmission coefficients, and to the <i>m</i>th-order reflection and transmission coefficients when the wave vector of the incident plane wave and the negative of the wave vector of the <i>m</i>th reflected order are symmetrical with respect to the plane perpendicular to the grating grooves.
© 2000 Optical Society of America
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(260.2130) Physical optics : Ellipsometry and polarimetry
Lifeng Li, "Symmetries of cross-polarization diffraction coefficients of gratings," J. Opt. Soc. Am. A 17, 881-887 (2000)