Fundamentals of Optical Waves and Lasers

184 Pages·2023·4.102 MB·English

by  Sanichiro Yoshida

Synthesis Lectures on
Wave Phenomena in the Physical Sciences
Sanichiro Yoshida
Fundamentals of
Optical Waves
and Lasers
Synthesis Lectures on Wave Phenomena
in the Physical Sciences
SeriesEditor
SanichiroYoshida,DeptofChem&Physics,SLU10878,SoutheasternLouisiana
University,Hammond,LA,USA
The aim of this series is to discuss the science of various waves. An emphasis is laid on
graspingthebigpictureofeachsubjectwithoutdealingformalism,andyetunderstanding
thepracticalaspectsofthesubject.Tothisend,mathematicalformulationsaresimplified
as much as possible and applications to cutting edge research are included.
Sanichiro Yoshida
Fundamentals of Optical
Waves and Lasers
SanichiroYoshida
DepartmentofChemistryandPhysics
SoutheasternLouisianaUniversity
Hammond,LA,USA
ISSN2690-2346 ISSN2690-2354 (electronic)
SynthesisLecturesonWavePhenomenainthePhysicalSciences
ISBN978-3-031-18187-0 ISBN978-3-031-18188-7 (eBook)
https://doi.org/10.1007/978-3-031-18188-7
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature
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Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whetherthewhole
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andretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownor
hereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublicationdoes
notimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective
lawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbookare
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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Thisbookisdedicatedtomywife,YukoYoshida,
andmyparents,SonokoandAkiraYoshida.
Preface
This book stems from my lecture notes and research logs. Over the last four decades,
I conducted research projects in many subfields of optics. I also taught various physics
coursesforrelatedsubjects.Duringthisperiod,Ihavefoundnumerousphysicalmeanings
in what I observe in my research and in the material I teach. Some of these observations
are what I had taken for granted for a long time. Finding the physical meaning of a
phenomenon is joy and, at the same time, leads to new ideas. I decided to summarize
these daily findings in a book.
The target audience of this book is undergraduate students majoring in physics or
physical sciences and graduate students in engineering. The primary aim of this book is
tohelpthereadergraspthebasicsofopticalwavesintuitivelybutbasedontheunderlying
physics. For more advanced information, the reader is encouraged to consult references
written at a more detailed level on the subjects.
We learn subjects most efficiently through research and teaching because we need to
analyze and digest the underlying concepts to conduct research or teach. I have tried
my best to provide comments and multiple interpretations on the topics covered by this
book. That is why sometimes the descriptions are long, and the derivation of the govern-
ing equations is detailed. If the reader does not need those comments or mathematical
procedures, I encourage them to skip these parts.
Discussions on the observations and findings with colleagues, teachers, and students
areessentialforthelearningprocess.Icannotthankenoughpeoplewhohelpedmeunder-
stand various concepts through discussions. I owe a great deal to my high school and
college teachers because my understanding always originates from what they taught me
decadesago.Iamgratefultomyparentsforprovidingmewiththeopportunitytoreceive
such an excellent education. William Coleman, my colleague and research partner, gave
mecritiques,whichIhighlyappreciate.IamthankfultoPaulPetraliaofSpringerNature
for his help during the writing process of this book. Finally, I thank my wife, Yuko
Yoshida, for her continuous support.
Hammond, LA, USA Sanichiro Yoshida
August 2022
vii
Contents
1 ReviewofWaveDynamics ............................................ 1
1.1 Oscillation and Wave ............................................. 1
1.1.1 Spring–Mass Systems ...................................... 1
1.1.2 Frequency Domain Expression .............................. 7
1.1.3 Oscillation to Wave ........................................ 10
1.1.4 Sound Wave .............................................. 14
1.2 Wave Equation and Solution ....................................... 19
1.2.1 Compressive Wave Equation and Solution .................... 19
1.2.2 Standing Wave and Traveling Wave .......................... 21
1.2.3 Three-Dimensional Compression Wave Equation ............... 25
1.2.4 Transverse Mechanical Wave ................................ 26
1.3 Resonance ....................................................... 28
1.3.1 Resonance in Harmonic Oscillations ......................... 28
1.3.2 Resonance in Wave Dynamics ............................... 29
1.4 Big Picture of Electromagnetic Wave ............................... 32
References ........................................................... 33
2 LightasEMWave .................................................... 35
2.1 Maxwell’s Equations ............................................. 35
2.1.1 Gauss’s Law .............................................. 35
2.1.2 Electric Force ............................................. 37
2.1.3 Electric Potential Energy and Potential ....................... 38
2.1.4 Electric Dipole and Interaction with Light .................... 40
2.1.5 Ampère’s Law with Maxwell’s Term ......................... 41
2.1.6 Magnetic Force ............................................ 44
2.1.7 Magnetic Dipole ........................................... 46
2.1.8 Faraday’s Law and Maxwell’s Term as Lenz’s Law ............ 47
2.2 Wave Equation and Solutions ...................................... 50
2.2.1 Wave Dynamics of Electromagnetic Fields .................... 50
2.2.2 Pictorial Explanation of Electromagnetic Waves ............... 51
ix
x Contents
2.2.3 LC Oscillation as a Spring-like Mechanism ................... 53
2.2.4 Electric Energy Density .................................... 55
2.2.5 Magnetic Energy Density ................................... 58
2.2.6 Algebraic Explanation of Electromagnetic Waves .............. 60
2.2.7 Plane Wave Solutions ...................................... 61
2.2.8 Light Wave as a Flow of Electromagnetic Energy .............. 63
References ........................................................... 65
3 LightPropagationinMatter .......................................... 67
3.1 Maxwell Equations in Matter ...................................... 67
3.1.1 Electric Dipole and Polarization ............................. 67
3.1.2 Linear Medium ............................................ 70
3.2 Light–Matter Interaction .......................................... 71
3.2.1 Absorption of Light and Index of Refraction .................. 73
3.2.2 Amplitude of Light Wave ................................... 77
3.2.3 Phase of Light Wave ....................................... 78
3.2.4 Propagation of Poynting Vector .............................. 82
3.2.5 Polarization of Optical Waves ............................... 83
3.3 Light Propagation ................................................ 88
3.3.1 Paraxial Wave Approximation and Helmholz Equation .......... 88
3.3.2 Gaussian Optical Beam ..................................... 93
3.3.3 Ray Matrix ............................................... 95
3.3.4 Higher Order Hermit-Gaussian Modes ........................ 99
References ........................................................... 103
4 PropertiesofLight ................................................... 107
4.1 Reflection and Refraction ......................................... 107
4.1.1 Laws of Reflection and Refraction ........................... 107
4.1.2 Coefficients of Reflection and Refraction ..................... 109
4.1.3 External and Internal Reflection ............................. 115
4.2 Interference ..................................................... 118
4.2.1 Low Visibility in Interferometry ............................. 120
4.2.2 Interference of Multiple Light Rays and Speckles .............. 123
4.2.3 Unwanted Interference ..................................... 125
4.3 Dispersion ....................................................... 126
4.3.1 Group Velocity ............................................ 126
4.3.2 Normal and Anomalous Dispersion .......................... 126
4.4 Diffraction ...................................................... 128
4.4.1 Diffraction by a Single Slit .................................. 128
4.4.2 Diffraction by a Circular Aperture and Diffraction Limit ........ 130
4.4.3 Diffraction of a Laser Beam ................................. 131
References ........................................................... 132
Contents xi
5 Lasers ............................................................... 135
5.1 Laser in a Nutshell ............................................... 135
5.2 Atomic Physics .................................................. 135
5.2.1 Atomic Systems as a Resonator .............................. 135
5.2.2 Absorption and Emission ................................... 137
5.2.3 Optical Energy of Induced Transition ......................... 139
5.2.4 Optical Gain .............................................. 142
5.2.5 Population Inversion and Rate Equation ...................... 143
5.3 Optical Resonator ................................................ 144
5.3.1 Fabry-Perot Etalon ......................................... 145
5.3.2 Passive Resonator .......................................... 147
5.3.3 Active Resonator .......................................... 152
References ........................................................... 160
AppendixA:Maxwell’sTerm ............................................. 161
AppendixB: ManagementofOpticalPolarization .......................... 163
AppendixC:Interferometry .............................................. 167
AppendixD:SolvingHelmholtzEquation ................................. 171
Index ................................................................... 175