Factorization of products of discontinuous functions applied to Fourier-Bessel basis.
The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.
Popov
Evgeny
E
Institut Fresnel, Case 161, Unité Mixte de Recherche (UMR 6133), Faculté des Sciences et Techniques de St.-Jérôme, 13397 Marseille Cedex 20, France. e.popov@fresnel.fr
Nevière
Michel
M
Bonod
Nicolas
N