UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)
UvA-DARE (Digital Academic Repository)
Universal wave phenomena in multiple scattering media
Ebrahimi Pour Faez, S.
Publication date
2011
Link to publication
Citation for published version (APA):
Ebrahimi Pour Faez, S. (2011). Universal wave phenomena in multiple scattering media.
General rights
It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
Contents
1 Introduction to waves in disordered media 1
1.1 Why should we study disorder? . . . 1
1.2 Waves and scattering . . . 2
1.3 Anderson localization phase transition . . . 3
1.3.1 Self-consistent theory . . . 4
1.3.2 Random matrices . . . 4
1.3.3 The critical state and its statistics . . . 5
1.3.4 Fragmented research on a universal phenomenon . . . 6
1.4 Overview of this dissertation . . . 7
2 Multiple-scattering theory 9 2.1 Building blocks . . . 9
2.1.1 Wave equations . . . 10
2.1.2 The t-matrix . . . 11
2.1.3 Average Green function in the multiple scattering regime . . . 13
2.1.4 Diffusion approximation . . . 14
2.2 Mesoscopic intensity correlations . . . 15
2.2.1 Average amplitude correlator . . . 16
2.2.2 Short-range intensity correlations . . . 18
2.2.3 Non-universal C0 correlations . . . 18
2.3 Nonlinear random media . . . 19
2.3.1 Second-harmonic t-matrix . . . 21
2.3.2 Diffusion approximation for the second-harmonic generation . . . 23
2.3.3 Derivation of the C0 vertex . . . 23
3 Random-matrix theory 25 3.1 A short history of RMT . . . 25 3.2 Wigner-Dyson ensembles. . . 26 3.2.1 Hamiltonians . . . 27 3.2.2 Scattering matrices . . . 28 3.3 Unconventional ensembles . . . 28 3.3.1 Banded matrices . . . 29 9
3.3.2 Complex-symmetric matrices . . . 31
3.4 Statistical probes in simulations and experiments . . . 31
3.4.1 Level-spacing distribution . . . 32
3.4.2 Open transmission channels . . . 33
3.4.3 Anderson localization in waveguide geometry . . . 34
3.4.4 Eigenfuntion statistics and Anderson localization . . . 36
3.5 Perturbation results for almost-diagonal Green matrices . . . 38
3.6 Concluding remarks . . . 41
4 Dipole chain 43 4.1 The model. . . 44
4.1.1 Dipole chain model . . . 45
4.1.2 Resonant point scatterer . . . 46
4.1.3 Dimensionless formulation . . . 46
4.1.4 Hypothetic models . . . 47
4.2 Analytical probes . . . 47
4.2.1 Perturbation results for the weak-coupling regime. . . 48
4.3 Numerical results . . . 49
4.3.1 Spectrum of the homogeneous chain . . . 49
4.3.2 The effect of disorder . . . 50
4.3.3 Scaling behavior of PDF . . . 52
4.3.4 Multifractal analysis . . . 56
4.3.5 The singularity spectrum . . . 57
4.4 Summary and conclusion . . . 58
5 Multifractal ultrasound waves 61 5.1 The experiment . . . 62
5.2 Scaling analysis . . . 62
5.3 Discussion . . . 64
5.3.1 Deviation from numerical results . . . 65
5.3.2 Final remarks . . . 65
6 Refractive index tuning 67 6.1 Theoretical principles . . . 68
6.2 Samples . . . 69
6.3 Setup and measurements. . . 70
6.4 Results and discussion . . . 71
6.4.1 Diffusion constant of porous plastic. . . 71
6.4.2 Comparison with the time-resolved method . . . 72
6.4.3 Tuning response of a photonic crystal . . . 73
6.5 A test for effective-medium theories . . . 74
6.6 Further applications . . . 76
6.7 Conclusions . . . 76
7 Diffuse nonlinear interference 77 7.1 Two classes of nonlinear random media . . . 78
7.2 Two-beam experiment . . . 79
7.2.2 Beyond the scalar approximation . . . 80
7.3 Experimental settings . . . 81
7.4 Results and discussion . . . 82
7.4.1 Dependence on scattering strength . . . 83
7.4.2 CX measurement in a single shot . . . 84
7.4.3 Applicability of the scalar model . . . 85
7.5 Final remarks . . . 87
Afterword 89
Summary 94
Samenvatting (Dutch summary) 97
