Laser Modeling: A Numerical Approach with Algebra and Calculus

✍ Scribed by Mark Steven Csele

• Publisher: CRC Press
• Year: 2014
• Tongue: English
• Leaves: 276
• Category: Library

✦ Synopsis

Offering a fresh take on laser engineering, Laser Modeling: A Numerical Approach with Algebra and Calculus presents algebraic models and traditional calculus-based methods in tandem to make concepts easier to digest and apply in the real world. Each technique is introduced alongside a practical, solved example based on a commercial laser. Assuming some knowledge of the nature of light, emission of radiation, and basic atomic physics, the text:

• Explains how to formulate an accurate gain threshold equation as well as determine small-signal gain
• Discusses gain saturation and introduces a novel pass-by-pass model for rapid implementation of "what if?" scenarios
• Outlines the calculus-based Rigrod approach in a simplified manner to aid in comprehension
• Considers thermal effects on solid-state lasers and other lasers with new and efficient quasi-three-level materials
• Demonstrates how the convolution method is used to predict the effect of temperature drift on a DPSS system
• Describes the technique and technology of Q-switching and provides a simple model for predicting output power
• Addresses non-linear optics and supplies a simple model for calculating optimal crystal length
• Examines common laser systems, answering basic design questions and summarizing parameters
• Includes downloadable Microsoft^® Excel^™ spreadsheets, allowing models to be customized for specific lasers

Don’t let the mathematical rigor of solutions get in the way of understanding the concepts. Laser Modeling: A Numerical Approach with Algebra and Calculus covers laser theory in an accessible way that can be applied immediately, and numerically, to real laser systems.

✦ Table of Contents

Basic Laser Processes
The Laser and Laser Light
Atomic Processes of the Laser
Example: Emission of Thermal Light
Three- and Four-Level Schemes
Example: Achieving Inversion in a Three-Level Laser
Rate Equations
Level Lifetime
Example: Lifetime of HeNe Energy Levels
Laser Gain
Example: Gain in a HeNe Amplifier
Losses in a Laser
Cavity Optics
Example: Stability of a HeNe Cavity
Optical Characteristics (Longitudinal and Transverse Modes)
Threshold Gain
Gain and Loss: Achieving Lasing
The Gain Threshold Equation
Example: Threshold Gain of a HeNe Laser
Example: Threshold Gain of a Non-Uniformly Pumped Ruby Laser
Example: Handling Distributed Losses
The Tale of Two Gains: g0 and gth
Application of gth: Determining g0
Example: Determining the Gain of a HeNe Laser
Example: Determining the Gain of a YAG Laser
An Atomic View of Gain: Cross-Section
Example: Calculating the Cross-Section of Transitions
Applications of the Gain Threshold Equation: Designing Laser Optics
Example: Calculating Minimum Reflectivity
Example: Calculating Cavity Optic Reflectivities
Example: Polarization in a HeNe Laser
A Theoretical Prediction of Pumping Threshold
Example: Minimum Pump Power of a YAG Laser
Example: Minimum Pump Power of a Diode Laser
Gain Saturation
Gain is Not Constant
A Third Gain Figure: Saturated Gain
Saturation Intensity
Example: Calculating the Saturation Power of a HeNe Transition
Saturated Gain and Intra-Cavity Power
Slope Efficiency
Predicting Output Power
Example: Predicting the Output Power of a HeNe Laser
Minimum Pump Power Revisited
Alternative Notations
A Model for Power Development in a Laser
Example: Modeling Power Buildup in a HeNe Laser
Improving the Model for use with High Gain Lasers
Example: Comparing Models for a Semiconductor Laser
Determining Cavity Decay Parameters
Example: Decay in a HeNe Laser
Analytical Solutions
The Rigrod Approach
Example: Predicting Output Power using the Rigrod Approach
Example: Application to a High Gain Laser
Ring Lasers
Example: A Ring Laser Example
Optimal Output Coupling
Example: Predicting Optimal Cavity Optics
Thermal Issues
Thermal Populations and Re-absorption Loss
Quasi-Three-Level Systems
Example: Estimating the Thermal Population of LLLs
Quantum Defect Heating
Example: Quantum Defect Calculations
Thermal Populations at Threshold
Example: Minimum Pump Power of a 946nm YAG Laser
Example: Computing Fractional Populations
Thermal Populations in an Operating Laser
Example: Pumping a 946nm Nd:YAG Laser
Thermal Effects on Laser Diodes
Modeling the Effects of Temperature on Laser Diodes (Wavelength)
Example: Predicting the Effect of Diode Wavelength Shift on Vanadate
Thermal Effects on Laser Diodes (Power and Threshold)
Example: Experimentally Determining Characteristic Temperature
Low Power DPSS Design
Scaling DPSS Lasers to High Powers
Generating Massive Inversions: Q-Switching
Inversion Buildup
Q-Switch Loss
Example: Minimum Loss of a Q-Switch
AOM Switches
Example: Bragg Angle in a Q-Switch
Example: AOM Deflection
EOM Switches
Example: Determining the Gain of a Laser using an EOM
Example: An Imperfectly-Aligned EOM
Passive Q-Switches
Example: A Passive Q-Switch
A Model for Pulse Power
Example: Output Power of a Q-Switched Laser
Multiple Pulse Output
Example: Predicting Q-Switch Settings for a Double-Pulse Laser
Modeling Flashlamp-Pumped Lasers
Example: Calculating the Time for Peak Inversion
Example: Calibrating the Model
Repetitively-Pulsed Q-Switched Lasers
Giant First Pulse
Ultrafast Lasers: Modelocking
Example: Modelocking Rate and Laser Size
Non-Linear Optics
Origins of Non-Linear Effects
Phase Matching
Non-Linear Materials
Practical Conversion Efficiency
Applications to Laser Design
Example: Intra- and Extra-Cavity Intensities
Application to DPSS Design
The Simple Approach
The Rigrod Approach
Example: A Small Green "Laser Pointer" DPSS
Common Lasers and Parameters
CW Gas Lasers
The Helium-Neon (HeNe) Gas Laser
Ion Gas Lasers
The Carbon-Dioxide Gas Laser
Pulsed Gas Lasers
TEA CO2 Lasers
Excimer Gas Lasers
Semiconductor (Diode) Lasers
Solid State Lasers
The Ruby Laser
Side-Pumped Nd:YAG Lasers
End-Pumped Nd:YAG Lasers
Other YAG Lasers
Other Solid-State Lasers

✦ Subjects

Физика;Матметоды и моделирование в физике;