Abstract
We report on an experimental test of Babinet's principle in quantum reflection of an atom beam from diffraction gratings. The He beam is reflected and diffracted from a square-wave grating at near grazing-incidence conditions. According to Babinet's principle the diffraction peak intensities (except for the specular-reflected beam) are expected to be identical for any pair of gratings of complementary geometry. We observe conditions where Babinet's principle holds and also where it fails. Our data indicate breakdown conditions when either the incident or a diffracted beam propagates close to the grating surface. At these conditions, the incident or the diffracted He beam is strongly affected by the dispersive interaction between the atoms and the grating surface. Babinet's principle is also found to break down, when the complementary grating pair shows a large asymmetry in the strip widths. For very small strip widths, edge diffraction from half planes becomes dominant, whereas for the complementary wide strips the atom-surface interactions leads to a strong reduction of all non-specular diffraction peak intensities.
Highlights
Babinet’s principle is a basic theorem of classical optics, first formulated by the French scientist Jacques Babinet in 1837
The interaction affects an outbound diffraction beam appreciably, if the beam passes sufficiently close to the surface over an extended region in space, as is the case for a very small angle yn
The same holds true for the incident beam at sufficiently small yin, with the difference that any effect on the incident beam will as well affect each of the outbound diffraction beams
Summary
Babinet’s principle is a basic theorem of classical optics, first formulated by the French scientist Jacques Babinet in 1837. It states that two complementary geometric objects, such as, for instance, a slit and a strip of the same size and shape (see Fig. 1a), produce identical diffraction intensities, except for the part of direct geometrical illumination.[1] In the example of a slit in an opaque membrane and an opaque strip suspended in free space, it is obvious that the forward intensity must be far larger in the case of the strip than it is for the slit, because the slit limits the total transmitted flux. In sub-wavelength optics where Wood anomalies and related surface waves play important roles, Babinet’s principle holds between light transmission through hole arrays and reflection from complementary disk arrays.[5,6,7] it has found recent applications in the design of metasurfaces and metamaterials.[8,9]
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