Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

Details Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

2002-07-07

arxiv.org/abs/math-ph/0207011v1

Physics

Mathematical Physics

AMS-TeX, 14 pages

Scientific paper

Berry and Klein (J. Mod. Opt. (1997) 43 2139-2164) showed that the Talbot effects in classical optics are naturally explained by Gauss sums studied in number theory. Their result was based on Helmholtz equation. In this article, we explain the effect based on Fresnel integral also by Gauss sums. These two explanations are shown to agree with by the reciprocity law of Gauss sums. The relation between this agreement and the wave-particle complementarity is also discussed.

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