title: Factorization of numbers with the temporal Talbot effect: optical implementation by a sequence of shaped ultrashort pulses.
abstract: We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.
authors.affiliation: Laboratoire de Collisions, Agrégats, Réactivité, IRSAMC (Université de Toulouse, UPS, CNRS) Toulouse, France.
authors.forename: Damien
authors.initials: D
authors.lastname: Bigourd
authors.forename: Béatrice
authors.initials: B
authors.lastname: Chatel
authors.forename: Wolfgang P
authors.initials: WP
authors.lastname: Schleich
authors.forename: Bertrand
authors.initials: B
authors.lastname: Girard