Resolution of the LDOS maps

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Table of contents

I Introduction and basic concepts 
General introduction
1 Light-matter interaction: a classical formalism
1.1 Electromagnetic radiation: the dyadic Green function
1.1.1 Green formalism
1.1.2 Eigenmode expansion of the dyadic Green function
1.2 Small particle in vacuum: the dynamic polarizability
1.2.1 Polarizability of a small spherical particle
1.2.2 Resonant scatterer polarizability
1.3 Light-matter interaction: weak and strong coupling regimes
1.3.1 Dressed polarizability in the presence of an environment
1.3.2 Coupling to one eigenmode: Weak and strong coupling regimes
1.3.3 General formulas in the weak-coupling regime
1.4 Conclusion
II Light localization in complex metallic nanostructures 
2 Characterization of a nanoantenna
2.1 Experimental setup and results
2.1.1 Fluorescent beads probe the LDOS
2.1.2 Experimental setup
2.1.3 Experimental results
2.2 Numerical model of the experiment
2.2.1 The Volume Integral Method
2.2.2 Model for the LDOS
2.2.3 Model for the fluorescence intensity
2.3 Numerical results
2.3.1 Numerical maps of the LDOS and fluorescence intensity
2.3.2 Resolution of the LDOS maps
2.4 Conclusion
3 Spatial distribution of the LDOS on disordered films
3.1 Simulation of the growth of the films
3.1.1 Numerical generation of disordered metallic films
3.1.2 Percolation threshold
3.1.3 Apparition of fractal clusters near the percolation threshold
3.2 Spatial distribution of the LDOS on disordered films
3.2.1 Statistical distribution of the LDOS
3.2.2 Distance dependence of the LDOS statistical distribution
3.2.3 LDOS maps and film topography
3.3 Radiative and non-radiative LDOS
3.3.1 Definition
3.3.2 Statistical distributions of the radiative and non-radiative LDOS
3.3.3 Distance dependence of the radiative and non-radiative LDOS distributions
3.4 Conclusion
4 The Cross Density Of States
4.1 The Cross Density Of States (CDOS)
4.1.1 Definition
4.1.2 CDOS and spatial coherence in systems at thermal equilibrium
4.1.3 Interpretation based on a mode expansion
4.2 Squeezing of optical modes on disordered metallic films
4.2.1 Numerical maps of the CDOS on disordered metallic films
4.2.2 Intrinsic coherence length
4.2.3 Finite-size effects
4.3 Conclusion
III Speckle, weak and strong coupling in scattering media 
5 R-T intensity correlation in speckle patterns
5.1 Intensity correlations in the mesoscopic regime
5.1.1 The mesoscopic regime
5.1.2 Dyson equation for the average field
5.1.3 Bethe-Salpether equation for the average intensity
5.1.4 Long range nature of the reflection-transmission intensity correlation .
5.2 Reflection-Transmission intensity correlations
5.2.1 Geometry of the system and assumptions
5.2.2 Ladder propagator for a slab in the diffusion approximation
5.2.3 Diffuse intensity inside the slab
5.2.4 Intensity correlation between reflection and transmission
5.2.5 Discussion
5.3 Conclusion
6 Nonuniversality of the C0 correlation
6.1 C0 equals the normalized fluctuations of the LDOS
6.1.1 The C0 correlation equals the fluctuations of the normalized LDOS
6.1.2 Physical origin of the C0 correlation
6.2 Long-tail behavior of the LDOS distribution
6.2.1 The “one-scatterer” model
6.2.2 Asymmetric shape of the LDOS distribution: Numerical results
6.3 C0 is sensitive to disorder correlations
6.3.1 The effective volume fraction: a “correlation parameter”
6.3.2 LDOS distribution and correlation parameter
6.3.3 C0 and correlation parameter
6.4 Conclusion and perspectives
7 Strong coupling to 2D Anderson localized modes
7.1 An optical cavity made of disorder: Anderson localization
7.1.1 LDOS spectrum of a weakly lossy cavity mode
7.1.2 Numerical characterization of a 2D Anderson localized mode
7.2 Strong coupling to a 2D Anderson localized mode
7.2.1 Strong coupling condition for a TE mode in 2D
7.2.2 Numerical observation of the strong coupling regime
7.3 Alternative formulation of the strong coupling criterion
7.4 Conclusion
General conclusion and perspectives
Appendices
A Lippmann-Schwinger equation 
B Regularized Green function and eigenmode expansion 
B.1 Regularized Green function
B.1.1 General case of an arbitrary volume δV
B.1.2 Case of a spherical volume δV
B.2 Eigenmode expansion of the regularized Green function
B.2.1 Case of a closed non-absorbing medium
B.2.2 Phenomenological approach of lossy environments
C Coupled Dipoles method 
D Simulation of the growth of disordered films 
D.1 Description of the algorithm
D.1.1 Vocabulary and notations
D.1.2 Interaction potential
D.1.3 Energy barrier for particle diffusion
D.1.4 Choice of a process
E Volume Integral method 
E.1 Weyl expansion of the Green function
E.1.1 Spatial Fourier transform
E.1.2 Weyl expansion
E.2 The Volume Integral method
E.2.1 The Lippmann-Schwinger equation
E.2.2 Analytical integration of the Green function over the unit cells
E.3 Energy balance
E.3.1 Power transferred to the environment
E.3.2 Absorption by the medium (non-radiative channels)
E.3.3 Radiation to the far field (radiative channels)
F T-T speckle intensity correlations in the diffusive regime 
F.1 Leading term for the long-range correlation
F.2 Useful integrals
Bibliography