Muscle, September Light Scattering predictions. G. Grehan L. Méès, S. Saengkaew, S. Meunier-Guttin-Cluzel

Muscle, September Rainbow: Far field scattering Fluorescence : Internal field

Muscle, September Theories Airy theory (1838): A scalar solution. Could be applied only close of rainbow Lorenz-Mie theory ( ): rigorous solution of Maxwell equations. All the scattering effects are merged. Extension to multilayered spheres. Debye theory (1909): post processing of Lorenz-Mie. The different scattering effects could be separated. Nussenzveig theory (1969) : is “analytical integration” of Debye series, leading to a generalization of Airy. It is clean to have a larger domain of application than Airy

Muscle, September One particleA cloud (section) Rainbow Fluorescence Airy, Lorenz-Mie, Debye, Nussenzveig Global Lorenz-Mie, Debye Internal field Multiple scattering

Muscle, September List of program Internal field and homogeneous sphere : INTGLMT Internal fields+near field : NEARINT 1or 2 beam(s) impinging on a sphere, internal field : 3D2F (3 dimensions) 2D2F (2dimensions) DEBYE internal field : INTDEBYE Far field and homogeneous sphere : DIFFGLMT Far field and multilayered sphere : MCDIFF DEBYE Far field : DIFFDEBYE Far field for pulses : PULSEDIFF

Muscle, September Rainbow far the rainbow angle according with Nussenzveig

Muscle, September Comparison of Lorenz-Mie, Debye, Nussenzveig and Airy predictions for one particle

Muscle, September Rainbow far the rainbow angle according with Nussenzveig

Muscle, September D<=15 Y= Z Y= Z Y= Z Y= Z >D<=35 35>D<=75 75>D<=150 Z is the argument of Airy function

Muscle, September Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for one particle

Muscle, September Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for cloud of particle

Muscle, September Effect of an imagining part of the refractive index maximumRefractive index nk= nk= nk= nk=0.005 ///////

Muscle, September Refractive index at center is n c Refractive index at surface is n s The law is :

Muscle, September

Muscle, September b= b= b= b=

Muscle, September D model Two steps: Excitation by the laser Collection in a given solid angle of the fluorescence

Muscle, September D model : Excitation map Internal intensity (in log-scale) created by a beam with a beam waist diameter equal to 20 µm, and a wavelength equal to 0.6 µm. The particle is a water droplet with a diameter equal to 100 µm and a complex refractive index equal to 1.33 – 0.0 i. The parameter is the impact location of the beam: (a)  = 50 µm (on the edge of the droplet), (b)  = 30 µm and (c)  = 0 µm (on the symmetry axis of the droplet).

Muscle, September D model : Detection map

Muscle, September Map of fluorescence emission. The particle is a water droplet of 100 µm on which impinges a laser beam with a diameter equal to 20 µm, and for an impact location equal to 50 µm (Fig. 2a). The parameter is the location of the collecting lens: (a) 0°, (b) 90° and (c) 180°. 2D model : Answer

Muscle, September D model Diagram of fluorescence for a water droplet of 100 µm. The parameter is the impact location  which runs from 60 µm to –60 µm by steps of 10 µm. The left figure is in linear scale while rigth figure is in logarithm scale.

Muscle, September D model : Excitation map