Non Linear Cavity

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Table of contents

Acknowledgments
Abstract
I. Theoretical Background
1. Introduction
1.1. The Maxwell Equations and the Wave Equations
1.2. Energy Considerations
1.3. Fourier Transforms
1.4. Dielectric Medium and the Wave Equation
1.4.1. Properties of Susceptibilities
2. Light Propagation
2.1. Linear Homogeneous Isotropic (LHI) Behavior
2.1.1. Gaussian Propagation Solution
2.1.2. High Order Propagation Mode Solutions
2.1.3. Astigmatism
2.1.4. ABCD Matrix
2.2. Linear Anisotropic Medium
2.2.1. Ordinary Beam
2.2.2. Extraordinary Beam
2.2.3. Dispersion Angle
2.3. Non Linear Medium
2.3.1. Propagation Equation
2.3.2. Second Harmonic Generation
2.3.3. Degenerate Parametric Amplification
3. Interface Conditions 25
3.1. Field Interface Conditions
3.1.1. Normal Fields
3.1.2. Tangential Fields
3.1.3. Poynting Vector
3.2. Fresnel Equations
3.2.1. TE Polarization or S-Polarization
3.2.2. TM Polarization or P-Polarization
4. Cavity
4.1. Beam Splitter Conventions
4.2. Cavity Transmission
4.3. Stability
4.4. Non Linear Cavity
5. Quantum Optics
5.1. Quantization of the Field
5.2. Quadratures and Homodyne Measurements
5.2.1. Quadratures
5.2.2. Optics Components
5.2.3. Homodyne
5.3. Different Light States and Wigner Function
5.3.1. Fock States
5.3.2. Coherent States
5.3.3. Squeezed States
5.4. Squeezing Creation and Interaction with Environment
5.4.1. Single pass squeezing generation in a non-linear crystal
5.4.2. Squeezing Interaction in a Lossy Channel
5.4.3. Squeezing generation in a non linear crystal in a cavity
II. Fibered Mini OPO
6. Introduction
6.1. Introduction
6.2. Squeezing Generation
6.3. Toward an all-fibered squeezer
7. Experimental Method
7.1. The OPO Cavity, Description of the Experiment
7.1.1. Coupling Mirror
7.1.2. Crystal and Crystal Mount
7.1.3. Fiber and Fiber Mount
7.1.4. Base
7.2. Other experimental consideration
7.2.1. Laser Source
7.2.2. Fibered Elements
7.2.3. Crystal Temperature Control
7.2.4. High Voltages Amplifiers:
7.2.5. Homodyne Detectors
7.2.6. Optical Suspension Table
7.3. Alignment of the Cavity
7.3.1. Schematic of the Set Up
7.3.2. Crystal Alignment with White Light Interferometry
7.3.3. Temperature Tuning
7.3.4. Homodyne Alignment:
7.3.5. Curved Mirror:
7.3.6. Alignment of the Green and Red:
7.4. System Limitations
7.4.1. Curvature Matching
7.4.2. Asphericity of the phase surfaces
7.4.3. Grey Tracking and Damaging:
7.5. Locking the System
7.5.1. PDH locking
7.5.2. Self Locking
7.5.3. Locking with a Micro-Controller
8. Results
8.1. Second Harmonic Generation and Amplification De-Amplification .
8.2. Squeezing
9. Conclusion
III. Square Monolithic Resonator
10.Introduction:
11.Resonator Coupling
11.1. Evanescent Prism Coupling
11.1.1. S-Polarization
11.1.2. P-Polarization
11.2. Resonator
11.3. Phase Control
11.4. TEM Modes
11.5. ABCD Matrix Considerations and Stability of the resonator
12.Experimental Methods
12.1. Creation of Resonators
12.1.1. Polishing
12.2. Prisms
12.3. Mechanical System
12.4. High Voltage
12.5. Alignment
12.5.1. How to Align Prisms and Resonators
12.5.2. How to Align the Beam with Contra-Propagating Beams
12.5.3. Temperature Tuning of the Crystal
12.5.4. Homodyne Alignment
12.5.5. Prism Switching and alignment for Squeezing
12.6. Lock and Self Locking
13.Results
13.1. Non Linearity
13.1.1. SHG and De-amplification
13.1.2. Squeezing
13.1.3. Conclusion
A. Fourier Transform of the Polarisation Field versus the Susceptibility
B. Index calculation for the green calcite coupler in p-polarization