Theoretical investigations of spatially multimode high-gain SU(1,1) interferometers / von Dennis Scharwald ; Erstgutachter: Prof. Dr. Torsten Meier, Zweitgutachter: Prof. Dr. Jan Sperling. Paderborn, 2026
Inhalt
- Abstract
- Zusammenfassung
- Table of Contents
- Chapter 1: Introduction
- Chapter 2: Fundamentals
- Chapter 3: Phase Sensitivity of High-Gain SU(1,1) Interferometers
- 3.1. SU(1,1) Interferometers and the Phase Sensitivity
- 3.2. Describing PDC in Cascaded Systems with Integro-Differential Equations
- 3.3. Diffraction-Compensated SU(1,1) Interferometers
- 3.4. Definition of the Experimental Gain
- 3.5. Results
- 3.5.1. Analytical Groundwork for a Finite-Width Pump
- 3.5.2. Analytical Expressions for a Plane-Wave Pump
- 3.5.3. Intensity Profiles and Covariance Functions for a Finite-Width Pump
- 3.5.4. Phase Sensitivity
- 3.6. Conclusion
- Chapter 4: Simultaneous Measurement of Multimode Squeezing
- 4.1. Squeezing
- 4.2. Schmidt Mode Structure of PDC Systems
- 4.2.1. Single Crystal
- 4.2.2. High-Gain SU(1,1) Interferometers
- 4.2.2.1. Balanced Fully Compensated SU(1,1) Interferometer
- 4.2.2.2. Unbalanced SU(1,1) Interferometer
- 4.2.3. Physical Interpretation and Uniqueness of the Schmidt Modes
- 4.3. Multimode Squeezing Measurements
- 4.3.1. Development of the Processing Method
- 4.3.1.1. Exact Reconstruction of the Squeezing
- 4.3.1.2. High-Gain Approximation
- 4.3.1.3. Theoretical Application
- 4.3.2. Experimental Application
- 4.4. Conclusion
- Chapter 5: PDC with Laguerre-Gaussian Pump Beams
- 5.1. Orbital Angular Momentum and Laguerre-Gaussian Beams
- 5.2. Schmidt-Mode Theory with Laguerre-Gaussian Pump Beams
- 5.2.1. The Two-Photon Amplitude for Laguerre-Gaussian Pump Beams
- 5.2.2. Separation of the Signal and Idler Variables
- 5.2.3. Input-Output Relations for Schmidt Mode Theory
- 5.3. Schmidt-Mode Structure
- 5.4. Angular Displacement Measurements
- 5.5. Conclusion
- Chapter 6: Concluding Remarks
- Appendix A: Auxiliary Results, Calculations and Proofs
- A.1. Integro-Differential Equations for the Transfer Functions
- A.2. Refraction Considerations
- A.3. Phase-Supersensitivity Region Width Δ for Compensated SU(1,1) Interferometers
- A.4. Integro-Differential Equations for the Full Three-Dimensional System
- A.5. Low-Gain Expansions of the Integro-Differential Equations
- A.6. Uniqueness of the Schmidt Modes in the General Case
- Appendix B: Phase-Matching Functions for the Diffraction-Compensated Configuration
- References
- List of Scientific Contributions