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FUNDAMENTALS OF SUM-FREQUENCY SPECTROSCOPY The first book on the topic, and written by the founder of the technique, this comprehensive resource provides a detailed overview of sum-frequency spectroscopy, its fundamental principles, and the wide range of applications for surfaces, interfaces, and bulk. Beginning with an overview of the historical context, and introductions to the basic theory of nonlinear optics and surface sum-frequency generation, topics covered include discussion of different experimental arrangements adopted by researchers, notes on proper data analysis, an up-to-date survey commenting on the wide range of successful applications of the tool, and a valuable insight into current unsolved problems and potential areas to be explored in the future. With the addition of chapter appendices that offer the opportunity for more in-depth theoretical discussion, this is an essential resource that integrates all aspects of the subject and is ideal for anyone using, or interested in using, sum-frequency spectroscopy. Y.R. SHEN is responsible for the development of second harmonic and sum-frequency generation spectroscopy into viable tools for surface and interface studies. He has been on the faculty of the physics department of the University of California at Berkeley since 1964 and has received many awards, including the Charles Hard Townes Award from the OSA, the Arthur L. Schawlow Prize and the Frank Isakson Prize from the APS, and the Max Planck Research Award. He is also a distinguished professor at Fudan University in Shanghai and an elected member of the US National Academy of Sciences, the American Academy of Arts and Sciences, the Chinese Academy of Sciences, and Academia Sinica. CAMBRIDGE MOLECULAR SCIENCE As we move further into the twenty-first century, chemistry is positioning itself as the central science. Its subject matter, atoms and the bonds between them, is now central to so many of the life sciences on the one hand, as biological chemistry brings the subject to the atomic level, and to condensed matter and molecular physics on the other. Developments in quantum chemistry and in statistical mechanics have also created a fruitful overlap with mathematics and theoretical physics. Consequently, boundaries between chemistry and other traditional sciences are fading and the term Molecular Science now describes this vibrant area of research. Molecular science has made giant strides in recent years. Bolstered both by instrumental and theoretical developments, it covers the temporal scale down to femtoseconds, a time scale sufficient to define atomic dynamics with precision, and the spatial scale down to a small fraction of an Angstrom. This has led to a very sophisticated level of understanding of the properties of small molecule systems, but there has also been a remarkable series of developments in more complex systems. These include: protein engineering; surfaces and interfaces; polymers; colloids; and biophysical chemistry. This series provides a vehicle for the publication of advanced textbooks and monographs introducing and reviewing these exciting developments. Series editors Professor Richard Saykally University of California at Berkeley Professor Ahmed Zewail California Institute of Technology Professor David King University of Cambridge FUNDAMENTALS OF SUM- FREQUENCY SPECTROSCOPY Y. R. Shen University of California at Berkeley University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107098848 © Y.R. Shen 2016 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2016 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication Data Names: Shen, Y. R., author. Title: Fundamentals of sum-frequency spectroscopy / Y.R. Shen, University of California, Berkeley. Other titles: Cambridge molecular science series. Description: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, [2016] | ©2015 | Series: Cambridge molecular science | Includes bibliographical references and index. Identifiers: LCCN 2015048473| ISBN 9781107098848 (Hardback ; alk. paper) | ISBN 1107098848 (Hardback ; alk. paper) Subjects: LCSH: Laser spectroscopy. | Nonlinear optics. | Nonlinear optical spectroscopy. | Second harmonic generation. | Surface chemistry. Classification: LCC QC454.L3 S53 2016 | DDC 535.8/4–dc23 LC record available at http://lccn.loc.gov/2015048473 ISBN 978-1-107-09884-8 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Hsiaolin Kai, Pearl, and Alex Contents Preface 1 Historical perspective 1.1. Early development of second-harmonic generation as a surface probe 1.2. Early development of sum-frequency spectroscopy for surface studies 1.3. Maturing of SHG and SFG for surface studies 1.4. Prospects 2 Basics of nonlinear optics 2.1. Maxwell’s equations in a medium 2.2. Linear and second-order nonlinear responses 2.3. Multipole expansion of nonlinear polarization 2.4. Structural symmetry of nonlinear susceptibilities 2.5. Nonlinear susceptibilities versus nonlinear polarizabilities 2.6. Microscopic expression of nonlinear polarizabilities 2.7. Summary Appendix: Multipole expansion of nonlinear polarization and definition of electric-dipole and electric-quadrupole nonlinear susceptibilities 3 Basic theory for surface sum-frequency generation 3.1. General description 3.2. Sum-frequency generation from an interfacial system with two semi- infinite bulk media 3.3. Sum-frequency radiation from a polarization sheet 3.4. Bulk contribution to sum-frequency generation 3.5. Sum-frequency generation from both surface and bulk 3.6. Surface and bulk nonlinear susceptibilities 3.7. Surface versus bulk contribution 3.8. Sum-frequency generation for material characterization 3.9. Summary Appendices