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Prime number decomposition using the Talbot effect
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DOI：10.1364/OE.26.015009.png)
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Abstract
En 中文
We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Keywords:
FACTORIZATION
CARPETS
INTEGERS
GRATINGS
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