Light Scattering predictions.

1. Light Scattering predictions. G. Grehan L. Méès, S. Saengkaew, S. Meunier-Guttin-Cluzel Muscle, September 2004

2. Rainbow: Far field scattering • Fluorescence : Internal field Muscle, September 2004

3. Theories • Airy theory (1838): A scalar solution. Could be applied only close • of rainbow • Lorenz-Mie theory (1890-1908): 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 2004

4. Airy, Lorenz-Mie, Debye, Nussenzveig Global Lorenz-Mie, Debye Internal field Multiple scattering Muscle, September 2004

5. 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 2004

6. Rainbow far the rainbow angle according with Nussenzveig Muscle, September 2004

7. Comparison of Lorenz-Mie, Debye, Nussenzveig and Airy predictions for one particle Muscle, September 2004

8. Rainbow far the rainbow angle according with Nussenzveig Muscle, September 2004

9. Z is the argument of Airy function Y= -0.2523Z+1.2807 D<=15 Y= -0.1642Z+1.1722 15>D<=35 35>D<=75 Y= -0.0946Z+1.0982 75>D<=150 Y= -0.0593Z+1.0639 Muscle, September 2004

10. Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for one particle Muscle, September 2004

11. Comparison of Lorenz-Mie, Debye and Nussenzveig predictions for cloud of particle Muscle, September 2004

12. Effect of an imagining part of the refractive index Muscle, September 2004

13. Refractive index at center is nc Refractive index at surface is ns The law is : Muscle, September 2004

14. Muscle, September 2004

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16. 2D model • Two steps: • Excitation by the laser • Collection in a given solid angle of the fluorescence Muscle, September 2004

17. 2D 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 2004

18. 2D model : Detection map Muscle, September 2004

19. 2D model : Answer 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°. Muscle, September 2004

20. 2D 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 2004

21. 3D model : Excitation map Muscle, September 2004