Transient internal and scattered fields from a multi-layered sphere illuminated by a pulsed laser. L. Méès * , K.F. Ren, G. Gouesbet and G. Gréhan . LESP, UMR 6614 / CORIA. CNRS, INSA et Université de Rouen BP 12 76801 Saint Etienne du Rouvray Abstract : This paper is devoted to the interaction between pulsed lasers and multi-layered spheres. Internal and scattered fields are described in a rigorous electromagnetic approach, when a 50 fs pulse illuminates a 80 µm diameter particle. Whispering gallery modes generation inside a core-mantled sphere and effects of a refractive index gradient on scattered fields are in particular exhibited. 1.Introduction Since many years, a strong effort has been devoted to the description of interaction between laser beams and a family of particles with regular shapes (homogeneous sphere, multi-layered sphere, infinite cylinder with circular or elliptical cross section and ellipsoid), leading to a set of theories assembled under the name of generalized Lorenz-Mie theories (GLMTs). Generalized Lorenz-Mie theories present a particular interest for particle size parameter in the range 1 to 1000, where asymptotic approaches (geometrical optics, Rayleigh scattering) cannot be used (at least not always). These theories have been used, in particular, in the field of optical particle characterization, to design measuring instruments and to analyze their responses. Rather than quoting a literature which is now too large, we kindly request the reader to direct himself to a review paper [1], with more than 350 references. Another way of extending the Lorenz-Mie theory is to consider the temporal description of an electromagnetic interaction when the illuminating beam is a pulsed laser instead of a continuous wave. Such works are motivated by recent progresses in pulsed beam generation which open the way to many applications [2]. A few recent papers are devoted to the description of scattered fields [3-4] and internal fields [5] from a homogeneous sphere illuminated by an ultra-short pulse, providing a temporal separation of optical modes, due to the short length of the pulse (about 30 µm for a 100 fs pulse) when compared with the particle diameter (100 µm). In this paper, we describe the interaction between a multi-layered sphere and a pulsed laser. This configuration is of importance for metrology of refractive index (or temperature) gradients, or to take into account the case of a sphere with a concentric inclusion. The theoretical aspects are recalled in section 2. Section 3 is devoted to numerical predictions of internal fields in a two layered sphere illuminated by a pulse laser, while section 4 describes the temporal behavior of scattered intensity in the far field for a multi-layered sphere with the number of layers as the main parameter. 2. Theoretical background. A generic formulation extending GLMTs to pulsed illumination is given in ref. [6]. The electromagnetic incident field at a point r in space is written as ) ( ) 2 )exp( ( ) , ( 0 0 τ τ πν τ g i r X X r X s i i = (1) in which X designates either the electric field E or the magnetic field H, subscript i designates field components in a coordinate system matching the geometry of the scatterer. is called the spatial support of the pulse, ) (r X s i 0 ν is the carrier frequency and the real function ) (τ g is the pulse envelope. The variable τ in eq. (1) is a shifted time * corresponding author : mees@coria.fr / tel : 33 (0)2 32 95 37 49 / fax : 33 (0)2 32 95 37 94.