Fundamentals of Nonlinear Optics, Second Edition

501 Pages·2017·58.05 MB·English

by  Peter E. Powers, Joseph W. Haus

POWERS
PHYSICS / ENGINEERING
HAUS
Fundamentals of
Fundamentals of
Nonlinear Optics
Nonlinear Optics F
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second edition d
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second edition
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Praise for the 1st Edition e
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“well written and up to date…. The problem sets at the end of each chapter reinforce and enhance the
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material presented, and may give students confidence in handling real-world problems.” a
—Optics & Photonics News l
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“rigorous but simple description of a difficult field keeps the reader’s attention throughout…. serves
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perfectly for an introductory-level course.”
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—Physics Today
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This fully revised introduction enables the reader to understand and use the basic principles related to many o
phenomena in nonlinear optics and provides the mathematical tools necessary to solve application-relevant n
problems. The book is a pedagogical guide aimed at a diverse audience including engineers, physicists, and
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chemists who want a tiered approach to understanding nonlinear optics. The material is augmented by nu- i
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merous problems, with many requiring the reader to perform real-world calculations for a range of fields,
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from optical communications to remote sensing and quantum information. Analytical solutions of equa-
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tions are covered in detail and numerical approaches to solving problems are explained and demonstrated.
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The second edition expands the earlier treatment and includes:
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• A new chapter on quantum nonlinear optics.
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• Thorough treatment of parametric optical processes covering birefringence, tolerances and beam
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optimization to design and build high conversion efficiency devices.
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• Treatment of numerical methods to solving sets of complex nonlinear equations.
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• Many problems in each chapter to challenge reader comprehension.
• Extended treatment of four-wave mixing and solitons. Peter E. Powers
• Coverage of ultrafast pulse propagation including walk-off effects.
SECOND Joseph W. Haus
Peter E. Powers was professor of Physics and Electro-Optics,
EDITION
and the Brother Leonard A. Mann Chair in the Sciences
at the University of Dayton.
Joseph W. Haus is professor of Departments of Electro-Optics and
Photonics, Electrical and Computer Engineering and Physics
K26507
at the University of Dayton.
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
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Fundamentals of
Nonlinear Optics

Fundamentals of
Nonlinear Optics
Second Edition
Peter E. Powers
Joseph W. Haus
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2017 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
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Library of Congress Cataloging-in-Publication Data
Names: Powers, Peter E., author. | Haus, Joseph W., 1948- author.
Title: Fundamentals of nonlinear optics / Peter E. Powers, Joseph W. Haus.
Description: Second edition. | Boca Raton, FL : CRC Press, Taylor & Francis
Group, [2017] | Includes bibliographical references and index.
Identifiers: LCCN 2016044943| ISBN 9781498736831 (hardback ; alk. paper) |
ISBN 1498736831 (hardback ; alk. paper)
Subjects: LCSH: Nonlinear optics.
Classification: LCC QC446.2 .P69 2017 | DDC 535/.2--dc23
LC record available at https://lccn.loc.gov/2016044943
Visit the Taylor & Francis Web site at
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To
My nonlinear family: Deborah, William, Gregory, Regina, and Eric
—PEP
… and to mine:
Jean, Alison, Michelle, Paul, Karin, Thomas, and Monica
—JWH

CONTENTS
Preface to the First Edition xv
Preface to the Second Edition xvii
Authors xix
1 Introduction 1
1.1 Historical Background 1
1.2 Unifying Themes 5
1.3 Overview of Nonlinear Effects Covered in This Book 7
1.4 Labeling Conventions and Terminology 10
1.5 Units 11
Problems 11
References 12
Further Reading 14
2 Linear Optics 15
2.1 Introduction 15
2.1.1 Linearity 15
2.1.2 Maxwell’s Equations 16
2.1.3 Poynting’s Theorem 17
2.1.4 Intensity 19
2.1.5 Linear Polarization 20
2.1.6 Complex Representation of Polarization 21
2.1.7 Energy Exchange between a Field and Polarization 23
2.2 Tensor Properties of Materials 25
2.2.1 Tensors 26
2.3 Wave Equation 28
2.3.1 Constitutive Relationships for Complex Amplitudes 29
2.3.2 Wave Equation in Homogeneous Isotropic Materials 30
2.3.3 Dispersion 32
2.3.4 Wave Equation in Crystals 34
2.3.5 Fresnel’s Equation 37
2.3.6 o-Waves and e-Waves 37
2.3.7 Poynting Vector Walk-Off 39
2.4 Determining e-Waves and o-Waves in Crystals 41
2.4.1 Homogeneous Isotropic 41
2.4.2 Uniaxial Crystal 41
2.4.3 Biaxial Crystals 42
2.5 Index Ellipsoid 43
vii
2.6 Applications 45
2.6.1 Slowly Varying Envelope Approximation and Gaussian Beams 45
2.6.2 Gaussian Beam Propagation Using the q-Parameter 47
2.6.3 M2 Propagation Factor 51
2.6.4 Example of Formatting a Beam for SHG 52
Problems 55
References 63
Further Reading 63
3 Introduction to the Nonlinear Susceptibility 65
3.1 Introduction 65
3.1.1 Nonlinear Polarization 66
3.1.2 Parametric Processes 67
3.2 Classical Origin of the Nonlinearity 70
3.2.1 One-Dimensional Linear Harmonic Oscillator 70
3.2.2 One-Dimensional Anharmonic Oscillator 72
3.2.3 Third-Order Effects in Centrosymmetric Media 76
3.3 Details of the Nonlinear Susceptibility, χ(2) 78
3.3.1 Degeneracy and Subtleties of Squaring the Field 78
3.3.2 Tensor Properties of Susceptibility 79
3.3.3 Permuting the Electric Fields in the Nonlinear Polarization 80
3.3.4 Full Permutation Symmetry in Lossless Media 81
3.3.5 Kleinman’s Symmetry 81
3.3.6 Contracting the Indices in χ(2) 82
ijk
3.3.7 Effective Nonlinearity and d 86
eff
3.3.8 Example Calculation of d 91
eff
3.4 Connection between Crystal Symmetry and the d-Matrix 92
3.4.1 Centrosymmetric Crystals 94
3.4.2 Example Calculation of d-Matrix for 3m Crystals 95
3.5 Electro-Optic Effect 97
3.5.1 EO Effects and the r-Matrix 99
3.5.2 Example Calculation of EO Effect in KH DPO 101
2 4
3.5.3 EO Wave Plates 102
3.5.4 EO Sampling: Terahertz Detection 103
3.5.5 Connection between d and r 107
Problems 110
References 116
Further Reading 116
4 Three-Wave Processes in the Small-Signal Regime 119
4.1 Introduction to the Wave Equation for Three Fields 119
4.1.1 Wave Equation for a Three-Wave Process 120
4.1.2 Slowly Varying Envelope Approximation Extended 122
viii Contents
4.1.3 Introduction to Phase Matching 124
4.1.4 First Solution to the Coupled Amplitude Equations 125
4.1.5 k-Vector Picture 129
4.2 Birefringent Phase Matching 130
4.2.1 Birefringent Phase-Matching Types 130
4.2.2 Example: Phase-Matching Problem 133
4.2.3 Phase-Matching SHG 136
4.3 Tuning Curves and Phase-Matching Tolerances 137
4.3.1 Phase-Matching Bandwidth and Angular Acceptance 139
4.4 Taylor Series Expansion Techniques for Determining Bandwidth 141
4.4.1 Temperature Bandwidth 143
4.4.2 Phase-Matching Bandwidth and Acceptance Bandwidth 144
4.4.3 Angular Acceptance and Noncritical Phase Matching 146
4.5 Noncollinear Phase Matching 147
4.5.1 Off-Axis Propagation SVEA Equations 148
4.5.2 Noncollinear Application 150
Problems 152
Reference 160
Further Reading 160
5 Quasi-Phase Matching 161
5.1 Introduction to Quasi-Phase Matching 161
5.2 Linear and Nonlinear Material Considerations 161
5.3 QPM with Periodic Structures 164
5.4 QPM Calculation: An Example 167
5.5 Fourier Transform Treatment of QPM 168
5.6 Tolerances 172
5.7 Fabricating Quasi-Phase-Matched Structures 173
Problems 176
Reference 181
Further Reading 181
6 Three-Wave Mixing beyond the Small-Signal Limit 183
6.1 Introduction 183
6.2 DFG with a Single Strong Pump 183
6.2.1 Defining Equations for the Undepleted Pump Approximation 184
6.2.2 Solution for Difference-Frequency Output 185
6.2.3 Solution with Specific Boundary Conditions 186
6.3 DFG with Strong Pump and Loss 189
6.4 Solutions for All Three Coupled Amplitude Equations 193
6.4.1 Manley–Rowe Relations 193
6.4.2 Analytic Solution for Three Plane Waves 195
Contents ix