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Talbot Carpet for a Ronchi Grating

A Ronchi grating is a set of equally spaced parallel wires that creates a diffraction pattern known as a Talbot carpet. The pattern is repeated at multiples of a fixed distance (the Talbot distance).

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DETAILS

The wave in the carpet has the functional form
,
where is the separation between slits in the Ronchi grating. Here the series is approximated with terms and evaluated in steps of size .
References
[1] M. V. Berry, I. Marzoli, and W. Schleich, "Quantum Carpets, Carpets of Light," Physics World, 14(6), 2001 pp. 39–44.
[2] M. S. Kim, T. Scharf, C. Menzel, C. Rockstuhl, and H. P. Herzig, "Talbot Images of Wavelength-Scale Amplitude Gratings," Optics Express, 20(5), 2012 pp. 4903–4920.

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