Spontaneous emission in the dipole approximation

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Table of contents

General introduction 
1 An introduction to fluorescence 
1.1 Spontaneous emission in the dipole approximation
1.1.1 Probability distribution of the excited-state lifetime
1.1.2 The dipole approximation
1.2 Emission rate of an electric dipole
1.2.1 Power emitted by an oscillating dipole
1.2.2 Decay rate of a two-level system
1.2.3 Intrinsic quantum yield
1.3 Energy transfer between two emitters
1.3.1 Energy transfer rate
1.3.2 Expression of the polarisability
1.3.3 Förster resonance energy transfer
1.4 Fluorescence microscopy
1.4.1 Angular spectrum representation of electromagnetic waves
1.4.2 Far-field microscopy
1.4.3 Near-field microscopy
1.5 Conclusion
I Micrometre-range plasmon-mediated energy transfer 
2 Plasmon-mediated energy transfer above a silver film 
2.1 Introduction
2.2 Properties of surface plasmons
2.2.1 Dispersion relations
2.2.2 Propagation length
2.3 Sample preparation and experimental setup
2.3.1 Selection of a donor-acceptor pair
2.3.2 Sample preparation
2.3.3 Optical setup
2.4 Evidences of the occurrence of energy transfer
2.4.1 Decay rate of the donor
2.4.2 Spectral measurements
2.5 Distance dependence of the energy transfer rate
2.5.1 Surface-plasmon propagation length
2.5.2 Energy transfer range
2.6 Efficiency of the energy transfer process
2.6.1 Modelling of the experiment
2.6.2 Distance between the mirror and the emitters
2.6.3 Energy transfer rate
2.6.4 Energy transfer efficiency and enhancement factor
2.7 Conclusion
3 Energy transfer mediated by single plasmons 
3.1 Introduction
3.2 Sample preparation and experimental setup
3.2.1 Donor-acceptor pair
3.2.2 Optical setup
3.2.3 Determination of the donor-to-acceptor distance
3.3 Generation of single surface plasmons
3.3.1 Demonstration of photon antibunching from single quantum dots
3.3.2 Statistical properties of the second-order correlation function
3.3.3 Quantitative characterisation of single-photon emission
3.3.4 Observation of single plasmons on silver nanowires
3.4 Study of decay histograms
3.4.1 Decay histogram of the quantum dot
3.4.2 Decay histogram of the acceptor bead under laser excitation
3.4.3 Evidence of the occurrence of energy transfer
3.5 Intensity fluctuations due to blinking
3.5.1 Blinking of the quantum dot
3.5.2 Characterisation of blinking by second-order correlations
3.5.3 Correlated blinking of the donor and the acceptor
3.6 Towards a demonstration of photon antibunching
3.6.1 Condition required to demonstrate photon antibunching
3.6.2 Comparison with the current experimental conditions
3.7 Conclusion
II Super-resolution imaging of the local density of states 
4 Spontaneous emission in the near field of silicon nanoantennas 
4.1 Introduction
4.2 Far-field analysis of resonant modes in silicon antennas
4.2.1 Dielectric antennas
4.2.2 Description of the sample and dark-field measurements
4.3 Experimental setup for near-field measurements
4.3.1 Description of the near-field fluorescence microscope
4.3.2 Fluorescent source
4.4 Near-field measurements
4.4.1 Methods
4.4.2 Spatial variations of the fluorescence decay rate
4.4.3 Observation of directional emission
4.5 Conclusion
5 Single-molecule super-resolution microscopy for lifetime imaging 
5.1 Introduction
5.2 Sample preparation and experimental setup
5.2.1 Sample preparation
5.2.2 Optical setup
5.2.3 Data acquisition
5.3 Drift correction
5.3.1 Correction in the sample plane
5.3.2 Defocus correction
5.4 Position and decay rate association
5.4.1 Position and decay rate estimations
5.4.2 Temporal and spatial correlations
5.4.3 Association conditions
5.5 Experimental results
5.5.1 Reconstruction of the decay rate map
5.5.2 Density of detected molecules
5.5.3 Decay rate enhancement
5.6 Conclusion
6 Fundamental limit on the precision of position and lifetime estimations
6.1 Introduction
6.2 Estimation theory
6.2.1 Estimators and sampling distributions
6.2.2 Cramér-Rao lower bound
6.2.3 Data modelling
6.3 Precision of position estimations
6.3.1 Point spread function
6.3.2 EM-CCD data model
6.3.3 Calculation of the information matrix
6.3.4 Experimental conditions
6.3.5 Numerical results
6.4 Precision of decay rate estimations
6.4.1 SPAD data model
6.4.2 Calculation of the information matrix
6.4.3 Experimental conditions
6.4.4 Numerical results
6.5 Towards an optimisation of the experimental setup
6.5.1 Beamsplitter transmission
6.5.2 Optimisation of the TCSPC setup
6.5.3 TCSPC models with several unknown parameters
6.6 Conclusion
General conclusion and perspectives 
Appendices 
A Dyadic Green function at an interface
A.1 Definition of the problem
A.2 Notations
A.3 Fresnel coefficients
A.4 Angular spectrum representation
A.5 Simplified expression
B Numerical evaluation of the LDOS
B.1 Power dissipated by a dipole
B.2 Poynting theorem
B.3 Case of a continuous source
B.4 Case of a Gaussian pulse
C Fisher information matrix for decay rate estimations
C.1 Definition of the problem
C.2 Discrete formulation
C.3 Limiting cases for the discrete formulation
C.4 Integral formulation
C.5 Limiting cases for the integral formulation