Measurement of the Transmission Matrix

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Table of contents

1 Theoretical Background
1.1 Scattering of Coherent Light by Disorder
1.2 Light Guidance in Ideal Passive Optical Fibers
1.2.1 The Guided Modes
1.2.2 Optical Fibers as Examples of Complex Media
1.2.3 Corrections for the Case of Graded-Index Optical Fibers
1.3 The Gain Medium and the Rate Equation of an Amplifier
1.3.1 The Two-Level Gain System and the Rate Equations
1.3.2 Spectral Dependence of the Gain and Line Broadening
1.4 Lasers
1.4.1 The Passive Fabry-Perot Cavity
1.4.2 The Cavity with Gain
1.4.3 Mode Competition within the Lasing Cavity
2 Wavefront Shaping in Non-Amplifying Complex Media and Multimode Fibers
2.1 Control of Light Propagation in Complex Media by Wavefront Shaping
2.1.1 Linearity of the Transmission and the Transmission Matrix
2.1.2 Measurement of the Transmission Matrix
2.1.3 Focusing Using the Transmission Matrix
2.2 Wavefront Shaping in Passive Optical Fibers
2.2.1 Multimode Fibers in Telecommunication
2.2.2 Multimode Fibers in Microscopy and Biomedical Applications
2.2.3 Approaches for Shaping the Input Wavefront and Coupling into the MM Fiber
2.3 Focusing Light through a Passive Multimode Fiber – Numerical Simulations
2.3.1 Focus Spot Size
2.3.2 Focus Spot Contrast and the Confinement Metric
2.4 Focusing Light through a Passive Multimode Fiber – Experimental Results
2.4.1 Motivation and Constraints
2.4.2 Ensuring Full Control in the Modal Space: The Reference Beam Problem
2.4.3 Benchmark Experiment with SLM image-conjugated to the Fiber Facet
2.4.4 Ensuring Full Control in tModal Space: The SLM Physical Positioning Problem
2.5 Summary and Discussion
3 Model and Numerical Simulations of a Multimode Fiber Amplifier with Configurable Pumping
3.1 Fiber Amplifiers – Background and Major Developments
3.1.1 General Background
3.1.2 Motivation for Multimode or Potentially-Multimode Fiber Amplifiers
3.1.3 Wavefront Shaping in Multimode Fiber Amplifiers – Literature Survey
3.2 Proposed Model for the Gain-Dependent TM of a Multimode Fiber Amplifier
3.2.1 Transmission Matrix for Realistic Passive Optical Fibers
3.2.2 Incorporation of Gain into the MMFA Model
3.2.3 Qualitative Analysis of Controllability Based on the Model
3.3 Numerical Simulations of a Multimode Fiber Amplifier
3.3.1 Specific Values for the Parameters Determining Amplifier Performance
3.3.2 Effect of MM pumping on the Signal – Statistics
3.3.3 Effect of MM pumping on the Signal – Optimization in the Modal Domain
3.3.4 Control of the Signal in the Spatial Domain by Optimization
3.3.5 Towards the Experimental System
3.4 Summary and Discussion
4 Experimental Results for Pump Shaping in Amplifier Configuration 
4.1 Set-up Configuration
4.1.1 Signal Branch
4.1.2 Pump Branch
4.1.3 Imaging of the Output
4.2 Yb-doped Fiber Characterization
4.2.1 Fiber Specifications
4.2.2 Signal Coupling and Propagation
4.2.3 Absorption and Saturation Measurements
4.2.4 Pump Coupling and Propagation
4.2.5 Design Considerations – Choice of Fiber Length
4.2.6 Benchmark for Effects of Gain – Passive Fiber ‘Benchmark’ Experiment
4.3 Results of Pump Wavefront Shaping Experiments
4.3.1 Gain Effects on the signal speckle – baseline vs. variations by pump shaping
4.3.2 Results of Pump Shaping – Maximizing Signal Decorrelation
4.4 Discussion and Summary
5 Wavefront Shaping of the Pump in a Lasing Cavity Configuration 
5.1 Background and Motivations
5.2 Experimental Setup and Some Elementary Results
5.2.1 Experimental Setup and Typed of Fiber-Based Cavities Implemented
5.2.2 Lasing in the fiber-only cavity
5.2.3 Lasing in the cavity based on external optics
5.2.4 Range of Lasing Wavelengths in Both Cavity Types
5.3 Theoretical Discussion of Lasing In Fiber-Based Cavities
5.4 Main Experimental Results
5.4.1 Evidence of Modal Discrimination through the Pump Shaping
5.4.2 Measurement of Slopes in a Cavity With Fully MM Guiding (no SM Filter)
5.4.3 Measurement of Slopes in a Cavity With a Spatial Filter– a Spliced SM Pigtail
5.5 Summary and Conclusions
General Conclusion and Prospects
Appendix A: Numerical Simulation Tool for the Computing the MMFA Transmission Matrix
Appendix B: Spatial Light Modulation Masks Corresponding to the Experimental Results in the Amplifier Configuration
Appendix C: Spatial Mode-Mixing in a Fiber-Based Cavity Defined By Free-Space