Laser Modeling : A Numerical Approach with Algebra and Calculus book cover
1st Edition

Laser Modeling
A Numerical Approach with Algebra and Calculus

ISBN 9781466582507
Published April 8, 2014 by CRC Press
274 Pages 157 B/W Illustrations

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Book Description

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

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Mark Steven Csele is a full-time professor at Niagara College, Welland, Ontario, Canada. A physicist and professional engineer, he has taught for over 20 years at levels ranging from two-year technician to four-year undergraduate. Currently, he teaches photonics at Niagara College, which features an array of dedicated laboratories hosting a variety of laser systems. He has authored a previous book on fundamental laser concepts as well as several articles in magazines and trade encyclopedias.


"One of Marc Csele's key strengths is his clear and illustrative style; he grounds the material in everyday words and examples. …the choice and order of the chapters brings the reader along gradually from basic knowledge to practical application in a logical and comfortable way."
––Marc Nantel, Niagara College, Niagara Falls, Ontario, Canada

"This is a textbook, written so as to be accessible to undergraduate students. The aim is to introduce the reader to laser science, parallel with the presentation of basic mathematical models used for the description of lasers of various types, and of basic physical properties of those lasers. Accordingly, the mathematical models are classified as algebra-based and calculus-based ones. Particular chapters are dealing with fundamental topics, such as the lasing threshold, gain saturation, thermal effects, Q-switching, and some basic effects of nonlinear optics. Many particular examples are included, which may be used as teaching material. The book also contains a lot of practical material about basic types of existing lasers, such as gas lasers, semiconductor lasers, and solid-state ones."
––Boris A. Malomed (Tel Aviv), from Zentralblatt MATH 1320 – 1