Polarization and spatial coherence of electromagnetic waves in disordered media

Transcription

1 Polarization and spatial coherence of electromagnetic waves in disordered media Kevin Vynck Laboratoire Photonique, Numérique et Nanosciences (LP2N) UMR 5298, CNRS IOGS Univ. Bordeaux Institut d'optique d'aquitaine, Talence (France)

2 LP2N (Bordeaux, France) Laboratoire Photonique, Numérique et Nanosciences Photons and nanosystems (Brahim Lounis) Matter waves (Philippe Bouyer) Artificial and quantum matter (Philippe Lalanne) Biophotonics (Laurent Cognet) Virtual reality (Jannick Rolland) Instrumentation (Giorgio Santarelli) Institut d'optique d'aquitaine

3 Acknowledgments Institut Langevin, ESPCI ParisTech (FR) Romain Pierrat Rémi Carminati + interesting discussions with Philippe Réfrégier, Aristide Dogariu & Ad Lagendijk

4 Contents Motivations Multiple scattering theory for polarized light Diffusion of polarization Spatial coherence of multiply-scattered light Conclusion

5 Scalar wave approximation E(r) Multiple scattering scrambles the direction, phase and polarization of propagating waves r0 Average over disorder... no preferential polarization state Vector wave equation Scalar wave equation Akkermans, Mesoscopic Physics of Electrons and Photons (2007) Sheng, Introduction to wave scattering, localization and mesoscopic phenomena (2010)

6 Light depolarization Polarization memory is kept on short trajectories Coherent backscattering van Albada, van der Mark & Lagendijk, PRL (1987) Rosenbluh et al., PRA (1987) Etemad, Thompson & Andrejco, PRL (1986) Time-resolved reflection Vreeker et al., Opt. Commun. (1989) Dogariu et al., Opt. Lett. (1997) Rojas-Cohoa et al., JOSA A (2004) (diffusing wave spect.) Theory Stephen & Cwilich, PRB 34, 7564 (1986); Akkermans, Wolf & Maynard, PRL 56, 1471 (1986);...

7 Polarization-related phenomena Specific morphology of disordered media retrieved by mesoscopic scale probe Local density of states fluctuations driven by near-field interaction Haefner, Sukhov & Dogariu, PRE 81, (2010) Carminati, PRA 81, (2010) No 3D Anderson localization for polarized light?! Skipetrov & Sokolov, arxiv: (2013) Cazé, Pierrat & Carminati, PRA 82, (2010) Sapienza et al., PRL 106, (2011)

8 Contents Motivations Multiple scattering theory for polarized light Diffusion of polarization Spatial coherence of multiply-scattered light Conclusion

9 Characterizing fluctuating fields Observation points Spatial field correlation matrix r Fluctuations due to disorder realizations (not to a fluctuating source) r' Dipole source r0 Polarization Correlation between orthogonal field components (i j) in one point (r=r') Spatial coherence Correlation between parallel field components (i=j) in two point (r r') Mandel & Wolf, Optical Coherence and Quantum Optics (1995) Brosseau, Fundamentals of polarized light: a statistical optics approach (1998)

10 Problem formulation Vector wave propagation equation with a source term White-noise Gaussian disorder with and Electric field in terms of Green function

11 Multiple scattering expansion Average Green function in the Born approximation and far field where Polarization dependence Scalar average Green function Bethe-Salpeter equation for polarized light Ladder & diffusion approximations and

12 Contents Motivations Multiple scattering theory for polarized light Diffusion of polarization Spatial coherence of multiply-scattered light Conclusion

13 Eigenmode decomposition Polarization (r = r'): Decomposition into polarization eigenchannels Eigenvalue Eigenvector Previous works by Stephen & Cwilich (PRB 1986) and MacKintosh & John (PRB 1988), but the calculations are incorrect in the diffusion approximation.

14 Polarization eigenchannels Eigensubspaces ij m kl m redistribution of the energy density from a given pair of input components (k, l) onto pairs of output components (i, j) Example (mode 2): <23 23> - 32> Mode 1: <11 11> + 22> + 33>; Mode 9: <11 11> + 22> - 33>;... Eigenvalues Dm speed of diffusion and attenuation that describe the propagation of the energy density in the individual polarization eigenchannels

15 Diffusion of the polarization Energy density in the mth polarization eigenchannel Diffusion constant Attenuation length At large distances from the source R, we recover the classical (scalar) mode.

16 Contents Motivations Multiple scattering theory for polarized light Diffusion of polarization Spatial coherence of multiply-scattered light Conclusion

17 Spatial field correlation matrix Spatial coherence (r r'): Bethe-Salpeter equation in reciprocal space ballistic (coherent) term Analytical expressions for the spatial coherence in real space (see paper)

18 Anisotropic field correlation Dependence on the orientation of the observation points The well-known result from scalar theory is recovered for the trace Shapiro, PRL 57, 168 (1986)

19 Contents Motivations Multiple scattering theory for polarized light Diffusion of polarization Spatial coherence of multiply-scattered light Conclusion

20 Summary Diffusion of polarization Spatial coherence of multiply-scattered light K. Vynck, R. Pierrat & R. Carminati, arxiv: Outcomes Calculation of fundamental properties of EM fields in disordered media Relevance of polarization when the problem involves mesoscopic scales Next steps Comparison with numerics on realistic systems (e.g. coupled dipole method) Extension to media with correlated disorder Speckle in the near-field of a disordered medium [Carminati, PRA 2010] Experiments on spatial coherence