Fiber Lasers: Fundamentals with MATLAB Modelling

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
1. Fundamentals of Fiber Lasers
	1.1 Introduction
	1.2 Interest of Lasers in Fiber Form
	1.3 Chronological Review of Fiber Lasers
		1.3.1 Erbium and the Ytterbium Co-doping
		1.3.2 Continuous-wave and Pulsed Fiber Lasers
		1.3.3 Single Longitudinal Mode Fiber Lasers
		1.3.4 Power scalability and High Power Fiber Lasers
		1.3.5 Other Types of Fiber Lasers
	1.4 Fiber Laser Applications
		1.4.1 Manufacturing
		1.4.2 Medical Applications
		1.4.3 Spectroscopy
		1.4.4 Various Scientific Applications
	1.5 Conclusion
	References
2. Optical Fibers
	2.1 Introduction
		2.1.1 Ray Optic Description
			2.1.1.1 Total Internal Reflection (TIR)
			2.1.1.2 Optical Fiber
			2.1.1.3 Meridional and Skewed Rays
			2.1.1.4 Propagating Modes of an Optical Fiber
			2.1.1.5 Single-mode and Multi-mode Fiber
			2.1.1.6 Step Index and Graded-index Fiber
	2.2 Wave Optic Description
		2.2.1 Number of Transverse Modes
		2.2.2 Linearly Polarized (LP) Modes
	2.3 Attenuation and Losses in Optical Fibers
		2.3.1 Attenuation Coefficient
		2.3.2 Material Absorption
		2.3.3 Rayleigh Scattering
		2.3.4 Bending Losses
	2.4 Dispersion in Single-Mode Fibers
		2.4.1 Modal Dispersion
		2.4.2 Group Velocity Dispersion
		2.4.3 Material Dispersion
		2.4.4 Waveguide Dispersion
		2.4.5 Polarization Mode Dispersion
	2.5 Non-linear Effects in Optical Fiber
		2.5.1 Stimulated Light Scattering
		2.5.2 Stimulated Brillouin Scattering
		2.5.3 Stimulated Raman Scattering
	2.6 Optical Fiber Materials
		2.6.1 Silica Glass
		2.6.2 Fluoride Glass and ZBLAN
		2.6.3 Other Types of Glass
	2.7 Optical Fiber Fabrication Techniques
		2.7.1 Vapour Phase Deposition Methods
			2.7.1.1 Outside Vapour Deposition (OVD)
			2.7.1.2 Modified Chemical Vapour Deposition (MCVD)
			2.7.1.3 Plasma-Activated Chemical Vapour Deposition (PCVD)
			2.7.1.4 Plasma-Enhanced Chemical Vapour Deposition (PCVD)
		2.7.2 Vapour Axial Deposition (VAD)
		2.7.3 Rare-Earth Doped Fiber Fabrication Techniques
			2.7.3.1 Solution Doping Method
		2.7.4 Fiber Drawing from a Preform
	2.8 Summary
	References
	Appendix 2.1 MATLAB® program for Propagation Constant b as a Function of Normalized Frequency V
	Appendix 2.2 Matlab Program for Bessel Function of the First Kind
	Appendix 2.3 Matlab Program for Bessel Function of the Second Kind (Neumann functions)
	Appendix 2.4 Matlab Program for Modified Bessel Function of the First Kind
	Appendix 2.4 Matlab Program for Modified Bessel Function of the Second Kind
3. Rare-Earth Ions and Fiber Laser Fundamentals
	3.1 Introduction
	3.2 General Properties and Electronic Structure of Rare-Earths
	3.3 Energy Levels of Rare-Earth Ions
		3.3.1 Atomic Interactions of the Free Ions and Crystal Field Influence
		3.3.2 Terms Symbols—Spin-orbit Coupling
			3.3.2.1 Total Orbital Quantum Number L
			3.3.2.2 Total Spin Quantum Number S
			3.3.2.3 Total Angular Momentum Quantum Number J
			3.3.2.4 Total Spin Multiplicity
		3.3.3 Atomic Interactions and Energy Levels Splitting
	3.4 Light Emission and Absorption by Lanthanides—Basis Aspects
		3.4.1 Selection Rules
		3.4.2 The \"Puzzle\" of 4f Electron Optical Spectra—Selection Rules
	3.5 Intensities of One-Photon Transitions—Judd-Ofelt Theory
	3.6 Light-Matter Interaction
		3.6.1 Blackbody Radiation
		3.6.2 Boltzmann\'s Statistics
		3.6.3 Radiation-Matter Interaction—Einstein Coefficients
			3.6.3.1 Absorption
			3.6.3.2 Spontaneous Emission
			3.6.3.3 Stimulated Emission
			3.6.3.4 Relations between Einstein Coefficients
		3.6.4 Transition Cross Section
		3.6.5 Ladenburg-Fuchtbauer Relation
		3.6.6 McCumber Theory of Emission Cross Sections
		3.6.7 Lifetimes
	3.7 Linewidth and Broadening
		3.7.1 Homogeneous Broadening
		3.7.2 Natural Broadening
		3.7.3 Collisional Broadening
		3.7.4 Inhomogeneous Broadening
	3.8 Ions-Ions Interaction
		3.8.1 Energy Transfer Mechanisms
		3.8.2 Cooperative Up-conversion
		3.8.3 Cross Relaxation
	3.9 General Considerations on Fiber Laser Operation
		3.9.1 Laser General Gain Coefficient
		3.9.2 Resonators: Linear and Ring cavity
			3.9.2.1 Fabry-Perot Cavity
			3.9.2.2 Ring Cavity
	References
4. Mathematical Methods for Fiber Lasers
	4.1 Introduction
	4.2 Rate Equations for the Gain Medium
		4.2.1 Two Energy Levels Systems
		4.2.2 Systems with More than 3 Energy Levels
	4.3 Coupled Propagation Equations
	4.4 Solutions Algorithms
	4.5 Shooting Methods
	4.6 Relaxation Methods
	4.7 Finite Difference Methods
	4.8 Conclusion
	References
5. Continuous-Wave Silica Fiber Lasers
	5.1 Introduction
	5.2 Architecture and Theory of Operation
		5.2.1 Amplifying Medium
			5.2.1.1 Erbium
			5.2.1.2 Ytterbium
			5.2.1.3 Erbium-Ytterbium Co-doping
			5.2.1.4 Other Rare-earth Ions
			Neodymium
			Thulium
			Praseodymium
		5.2.2 Optical Resonators and Feedback
			5.2.2.1 Fiber Bragg Grating
			5.2.2.2 Fabry-Perot Resonator
			5.2.2.3 Distributed Bragg Reflector Fiber Laser (DBR)
			5.2.2.4 Distributed Feedback
			5.2.2.5 Ring Cavities
		5.3 Continuous Wave Fiber Laser Modeling
			5.3.1 Formalism
			5.3.2 Linear Cavity Fiber Laser
			5.3.2.1 Backward Pumping
			5.3.2.2 Pump Absorption for Various Lengths and Explanation
			5.3.2.3 Internal Cavity Quantities Distribution
			5.3.2.4 Output Power Versus Fiber Length for Different Pump Powers
			5.3.2.5 Output Power Versus Coupling Coefficient for Different Pump Powers and Optimum Length
		5.3.3 Ring Cavity Fiber Laser
			5.3.3.1 Rate Equations and Transport Equations
			5.3.3.2 Numerical Solutions
		5.3.4 The Case of DFB Fiber Lasers
		5.3.5 DFB Fiber Laser Output Power Computation
			5.3.5.1 Pump Absorption
			5.3.5.2 Internal Intensity Distribution
			5.3.5.3 Population Density Distribution
			5.3.5.4 Gain Distribution
			5.3.5.5 Output Power
			5.3.5.6 DFB Fiber Laser Power Optimization
			5.3.5.7 Optimum Phase Shift and Coupling Coefficient
	5.4 Conclusion
	5.5 MatlabⓇ code
		5.5.1 Output Characteristics of Ring Cavity Fiber Laser Computed with Shooting Algorithm
		5.5.2 Function \"Propa\" Called in the Above Function
		5.5.3 Script to Compute Fabry-Perot Fiber Laser Characteristics in the Case of Forward Pumping
		5.5.4 Script to Compute the Characteristics of Fabry-Perot Fiber Laser in the Backward Pumping Scheme
		5.5.5 Pump Power Forward
		5.5.6 Pump Power Backward
		5.5.7 Laser Power Forward
		5.5.8 Laser Power Backward
		5.5.9 Population Density Function
		5.5.10 Uniform Grating
		5.5.11 π-phase Shifted Fiber Bragg Grating
		5.5.12 Shooting Algorithm for Simple DFB Fiber Laser Without CUP
		5.5.13 Shooting Algorithm for DFB Fiber Laser With CUP
		5.5.14 DFB Simulation
		5.5.15 DFB Simulation2
		5.5.16 Rate Equations Single Solver
		5.5.17 Rate Equation Pair Solver
	References
6. Q-switched Fiber Laser
	6.1 Introduction: Working Principle
	6.2 Fundamental Mathematical Description
	6.3 Switching Methods
	6.4 Active Q-switched Fiber Lasers
		6.4.1 Mechanical Devices
		6.4.2 Electro-optic Modulator
		6.4.3 Acousto-optic Modulator
	6.5 Passive Q-switched Fiber Lasers
	6.6 Theoretical Analysis of Active Q-switched Fiber Laser
		6.6.1 Gain Medium Modelling with Rate Equations
		6.6.2 Solution Algorithm
		6.6.3 Parameters Used in the Simulation
	6.7 Characteristics of the Active Q-switched Fiber Laser
		6.7.1 Influence of the Length of the Doped Fiber
		6.7.2 Influence of the Pump Power
		6.7.3 Influence of Concentration
		6.7.4 Influence of AOM Rise Time
		6.7.5 Influence of the Core Diameter
		6.7.6 Influence of the AOM Repetition Rate
	6.8 Modelling of Passive Q-switched Fiber Laser
		6.8.1 Type of Saturable Absorbers
		6.8.2 Rate Equations of Passive Q-switched Fiber Laser
	6.9 Q-switched Fiber Laser: State of the Art
	6.10 Matlab Code
		6.10.1 Active Q-switch Fiber Laser Function
		6.10.2 Distribution Function
		6.10.3 Multiple Pulse Active Q-switched Function
		6.10.4 Long Cavity Active Q-switched Function
		6.10.5 Laser Output Function
		6.10.6 Propa Function
		6.10.7 Boundary Function
		6.10.8 Boundary2 Function
		6.10.9 Passive Q-switched Fiber Laser
		6.10.10 Script to Plot the Dynamics of the Output Characteristics of Passive Q-switched Fiber Laser
	References
7. Narrow Linewidth Fiber Lasers
	7.1 Introduction
	7.2 Fundamental Concepts of Narrow Linewidth Fiber Lasers
	7.3 Narrow Linewidth Fiber Lasers
	7.4 Linear Cavity Single Longitudinal Mode Fiber Lasers
		7.4.1 Tunable Short Cavity Lasers
		7.4.2 Efficiency Enhancement Yb3+ Co-Doping
	7.5 Ring Cavities Single Longitudinal Mode Fiber Lasers
	References
8. High-Power Fiber Lasers
	8.1 Introduction
	8.2 High-Power Fiber Lasers Design
		8.2.1 Cavity Configurations
	8.3 Increasing Output Power: Cladding Pumping
		8.3.1 Brightness Enhancement in Cladding Pumped Fiber Lasers
		8.3.2 Cladding-Pumping Scheme
		8.3.3 Pump Combination Schemes
	8.4 Rare-Earth Ions for High-Power Fiber Lasers
	8.5 High-Power Fiber Laser Efficiency
	8.6 Beam Quality Analysis
	8.7 Doped and Undoped Fibers
		8.7.1 Rare-Earth Doped Fibers
		8.7.2 Undoped Fibers for High-Power Applications
	8.8 Detrimental Effect Affecting High-Power Operation
	8.9 Stimulated Brillouin and Stimulated Raman Scattering
		8.9.1 Stimulated Raman Scattering
		8.9.2 Stimulated Brillouin Scattering
	8.10 Self-Phase Modulation and Four-Wave Mixing
	8.11 Influence of Optical Damage
	8.12 Influence of Photodarkening
	8.13 Influence of TMI
	8.14 Working Regimes of High-Power Fiber Lasers
		8.14.1 Single-Fiber, Single-Mode CW Output Power
		8.14.2 Pulsed Fiber Laser Parameter Space
	8.15 Other Fiber Lasers
	8.16 Conclusion
	References
Index