Asymptotic quantum inelastic generalized Lorenz–Mie theory G. Gouesbet * Laboratoire d’Electromagne ´tisme et Syste `mes Particulaires (LESP), Unite ´ Mixte de Recherche (UMR) 6614, du Centre National de la Recherche Scientifique (CNRS), Complexe de Recherche Interprofessionnel en Ae ´rothermochimie (CORIA), Institut National des Sciences Applique ´es de Rouen (INSA-Rouen), France Universite ´ de Rouen, BP 12, 76 801 Saint Etienne du Rouvray, Cedex, France Received 26 February 2007; received in revised form 16 May 2007; accepted 4 June 2007 Abstract The (electromagnetic) generalized Lorenz–Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz–Mie theory which deals with the simpler case of a plane wave illumina- tion. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz–Mie theory and (ii) elastic cross-sec- tions in an associated quantum generalized Lorenz–Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz–Mie theory, which is presented in this paper. Ó 2007 Elsevier B.V. All rights reserved. 1. Introduction The Lorenz–Mie Theory (LMT) describes the interac- tion between an electromagnetic plane wave and a homoge- neous, non-magnetic sphere, with a linear materisal [1–3] The Generalized Lorenz–Mie Theory (GLMT) deals with a more general problem when, instead of a plane wave illu- mination, we consider an arbitrary shaped beam illumina- tion. For a fairly recent review on GLMT and applications, see Ref. [4]. In recent papers [5,6], we demonstrated that a transpar- ent macroscopic sphere (i.e. dealing with an elastic prob- lem) is cross-sectionally equivalent to a superposition of two quantum-like radial potentials. The expression ‘‘quan- tum-like’’ has a restrictive meaning. It means that, actually, the equivalence is expressed in terms of scattering phase shifts, but explicit expressions of the equivalent potentials are not yet available. It is then desirable to examine whether a similar equiv- alence can be found for inelastic scattering. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz–Mie, which is the aim of this paper. The word ‘‘asymptotic’’ means that we are interested with scattered properties far away from the potential, more specifically with cross-sections. The asymptotic quantum inelastic gen- eralized Lorenz–Mie therefore examines cross-sections (scattering, absorption, extinction) for the case of a quan- tum radial potential interacting with quantum Eigen-arbi- trary shaped beams, as defined in Section 2. To avoid any misunderstanding, I insist that this theory pertains to quantum mechanics, not to electromagnetism. This work is a contribution to a research program aiming to the study and to the exploitation of analogies and differences between electromagnetic and quantum scatterings. The context of this work may also be broadened as fol- lows. Quantum mechanical scattering is commonly described under the assumption that the incident beam is a monochromatic plane wave. Experimentally, this is almost always the case due to the smallness of the targets (in particular in particle physics). But, under certain 0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.06.006 * Tel.: +33 2 35 52 83 92; fax: +33 2 35 52 83 90. E-mail address: gerard.gouesbet@coria.fr www.elsevier.com/locate/optcom Optics Communications 278 (2007) 215–220