1st Edition

Laser Modeling A Numerical Approach with Algebra and Calculus

By Mark Steven Csele Copyright 2014
    274 Pages 157 B/W Illustrations
    by CRC Press

    274 Pages 157 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    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