Table Of Content

SPIE PRESS | Field Guide FFiieelldd GGuuiiddee ttoo NNoonnlliinneeaarr OOppttiiccss Peter E. Powers FFGG2299 ccoovveerrss aanndd ttiittllee..iinndddd 11 66//55//1133 1100::2200 AAMM Nonlinear Optics Peter E. Powers SPIE Field Guides Volume FG29 John E. Greivenkamp, Series Editor Bellingham, Washington USA Library of Congress Cataloging-in-Publication Data Powers, Peter E. Field guide to nonlinear optics / Peter E. Powers. pages cm. – (The field guide series; FG29) Includes bibliographical references and index. ISBN 978-0-8194-9635-5–ISBN 978-0-8194-9636-2– ISBN978-0-8194-9637-9 1. Nonlinearoptics.I. Title. QC446.2.P688 2013 621.36094–dc23 2013014471 Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1.360.676.3290 Fax: +1.360.647.1445 Email: [email protected] www.spie.org Copyright©2013SocietyofPhoto-OpticalInstrumentation Engineers (SPIE) All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. Thecontentofthisbookreflectsthethoughtoftheauthor(s). Everyefforthasbeenmadetopublishreliableandaccurate information herein, but the publisher is not responsible for thevalidityoftheinformationorforanyoutcomesresulting fromreliancethereon. Printed in the United States of America. First printing Introduction to the Series WelcometotheSPIEFieldGuides—aseriesofpublications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, designconsiderations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, andprovides fullcoverageof that topicon that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as relatedmaterialoutsidethemainscopeofthevolume,key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. TheSPIEFieldGuidesareintendedtobelivingdocuments. Themodularpage-basedpresentationformatallowsthemto be updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at [email protected]. John E. Greivenkamp, Series Editor College of Optical Sciences The University of Arizona FieldGuidetoNonlinearOptics The Field Guide Series Keepinformation atyourfingertips withallofthetitles in the Field Guide Series: Adaptive Optics, Second Edition, Robert Tyson & Benjamin Frazier Atmospheric Optics, Larry Andrews Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich Diffractive Optics, Yakov Soskind Geometrical Optics, John Greivenkamp Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel ImageProcessing,KhanM.Iftekharuddin&AbdulAwwal Infrared Systems, Detectors, and FPAs, 2nd Edition, Arnold Daniels Interferometric Optical Testing, Eric Goodwin & Jim Wyant Laser Pulse Generation, Rüdiger Paschotta Lasers, Rüdiger Paschotta Lens Design, Julie Bentley & Craig Olson Microscopy, Tomasz Tkaczyk Nonlinear Optics, Peter Powers Optical Fabrication, Ray Williamson Optical Fiber Technology, Rüdiger Paschotta Optical Lithography, Chris Mack Optical Thin Films, Ronald Willey OptomechanicalDesign andAnalysis,KatieSchwertz& James Burge Physical Optics, Daniel Smith Polarization, Edward Collett Probability, Random Processes, and Random Data Analysis, Larry Andrews Radiometry, Barbara Grant Special Functions for Engineers, Larry Andrews Spectroscopy, David Ball Terahertz Sources, Detectors, and Optics, Créidhe O’Sullivan & J. Anthony Murphy Visual and Ophthalmic Optics, Jim Schwiegerling FieldGuidetoNonlinearOptics Field Guide to Nonlinear Optics This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, andtechniquesfornonlinearoptics.Topicscoveredinclude technologically important effects, recent developments in nonlinear optics, and linear optical properties central to nonlinearphenomena.Thefocusofeachsectionisbasedon my research, my interactions with colleagues in the field, and my experiences teaching nonlinear optics. Examples throughout this Field Guide illustrate funda- mental concepts while demonstrating the application of key equations. Equations are presented without proof or derivation;however,theinterestedreadermayrefertothe bibliography for a list of resources that go into greater detail.Inadditiontotheoverviewofnonlinearphenomena, this Field Guide includes an appendix of material properties for some commonly used nonlinear crystals. ThisFieldGuidefeaturesnotationscommonlyencountered in nonlinear optics literature. All equations are written in SI units for convenience when comparing calculations to laboratory measurements. The formalism of writing equa- tionsusingcomplexvariablenotationintroducesambiguity in defining the electric field’s complex amplitude. Though one convention is used throughout this text, conventions and conversions are presented as part of the first topic. Equationsinterms ofexperimentallymeasuredquantities such as power, intensity, and energy, have no ambiguity. Peter E. Powers University of Dayton March 2013 FieldGuidetoNonlinearOptics vii Table of Contents Glossary of Terms and Acronyms x Electromagnetic Waves and Crystal Optics 1 Conventions and Conversions 1 Maxwell’s Equations and the Wave Equation 2 Uniaxial Crystals 3 Biaxial Crystals 4 Nonlinear Susceptibility 5 Nonlinear Polarization for Parametric Interactions 5 Classical Expressions for Nonlinear Susceptibility 6 Nonlinear Susceptibilities 7 d Matrices 8 Working with d Matrices and SHG 9 Effective Nonlinearities 10 Tabulation of d Matrices 11 Electro-optic Effect 13 Electro-optic Effect 13 r Matrices 14 Electro-optic Waveplates 16 Q Switches 17 Amplitude and Phase Modulators 18 Electro-optic Sampling for Terahertz Detection 19 Photorefraction 20 x(2) Parametric Processes 21 x(2) Coupled Amplitude Equations 21 x(2) Processes with Focused Gaussian Beams 22 DFG and OPA 23 Sum-Frequency Generation 24 Second-Harmonic Generation 25 Three-Wave Mixing Processes with Depletion 26 Optical Parametric Generation 27 Optical Parametric Oscillator 28 Singly Resonant Optical Parametric Oscillator 29 FieldGuidetoNonlinearOptics viii Table of Contents Phase Matching 30 Birefringent Phase Matching 30 e- and o-Wave Phase Matching 31 DFGandSFGPhaseMatchingforUniaxialCrystals 32 SHG Phase Matching for Uniaxial Crystals 33 Biaxial Crystals in the XY Plane 34 Biaxial Crystals in the YZ Plane 35 Biaxial Crystals in the XZ Plane 36 Quasi-phase-matching 37 Birefringent versus Quasi-phase-matching 38 Noncollinear Phase Matching 39 Tuning Curves 40 Phase Matching Bandwidth 41 Bandwidths for DFG and SFG 41 Bandwidth Calculation Aids 42 SFG and DFG Bandwidth Formulae 43 SHG Bandwidth Formulae 46 Graphical Approach for Bandwidths 48 Noncollinear Bandwidth 49 x(2) Waveguides 50 x(2) Waveguide Interactions 50 x(2) Waveguide Devices 51 Waveguide Phase Matching 52 x(3)Parametric Processes 53 Four-Wave Mixing 53 Degenerate Four-Wave Mixing 54 Third-Harmonic Generation 55 x(3) Parametric Amplifier 56 Noncollinear Phase Matching for x(3) Processes 57 Nonlinear Refractive Index 58 Nonlinear Refractive Index 58 Nonlinear Absorption 59 Calculations of Nonlinear Index 60 Self-Phase Modulation 61 FieldGuidetoNonlinearOptics ix Table of Contents z Scan 62 Optical Bistability 63 Raman and Brillouin Processes 64 Spontaneous Raman Scattering 64 Stimulated Raman Scattering 65 Anti-Stokes Raman Scattering 66 Raman Microscopy 67 Photo-acoustic Interactions 68 Stimulated Brillouin Scattering 69 Ultrafast Nonlinear Effects 70 Saturable Absorption 70 Temporal Solitons 71 Spatial Solitons 72 High Harmonic Generation 73 Ultrashort-Pulse Measurement 74 Appendices 75 Gaussian Beams 75 Sellmeier Equations for Selected x(2) Crystals 76 Properties of Selected x(2) Crystals 78 References for Selected x(2) Crystals Tables 79 Equation Summary 81 Bibliography 90 Index 93 FieldGuidetoNonlinearOptics