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Tsukerman I. Computational Methods for Nanoscale Computational Methods for Nanoscale Applications Nanostructure Science and Technology Series Editor: David J. Lockwood, FRSC National Research Council of Canada Ottawa, Ontario, Canada Current volumes in this series: Functional Nanostructures: Processing, Characterization and Applications Edited by Sudipta Seal Light Scattering and Nanoscale Surface Roughness Edited by Alexei A. Maradudin Nanotechnology for Electronic Materials and Devices Edited by Anatoli Korkin, Evgeni Gusev, and Jan K. Labanowski Nanotechnology in Catalysis, Volume 3 Edited by Bing Zhou, Scott Han, Robert Raja, and Gabor A. Somorjai Nanostructured Coatings Edited by Albano Cavaleiro and Jeff T. De Hosson Self-Organized Nanoscale Materials Edited by Motonari Adachi and David J. Lockwood Controlled Synthesis of Nanoparticles in Microheterogeneous Systems Vincenzo Turco Liveri Nanoscale Assembly Techniques Edited by Wilhelm T.S. Huck Ordered Porous Nanostructures and Applications Edited by Ralf B. Wehrspohn Surface Effects in Magnetic Nanoparticles Dino Fiorani Interfacial Nanochemistry: Molecular Science and Engineering at Liquid-Liquid Interfaces Edited by Hitoshi Watarai Nanoscale Structure and Assembly at Solid-Fluid Interfaces Edited by Xiang Yang Liu and James J. De Yoreo Introduction to Nanoscale Science and Technology Edited by Massimiliano Di Ventra, Stephane Evoy, and James R. Heflin Jr. Alternative Lithography: Unleashing the Potentials of Nanotechnology Edited by Clivia M. Sotomayor Torres Semiconductor Nanocrystals: From Basic Principles to Applications Edited by Alexander L. Efros, David J. Lockwood, and Leonid Tsybeskov Nanotechnology in Catalysis, Volumes 1 and 2 Edited by Bing Zhou, Sophie Hermans, and Gabor A. Somorjai (Continued after index) Igor Tsukerman Computational Methods for Nanoscale Applications Particles, Plasmons and Waves 123 Igor Tsukerman Department of Electrical and Computer Engineering The University of Akron Akron, OH 44325-3904 USA [email protected] Series Editor David J. Lockwood National Research Council of Canada Ottawa, Ontario Canada ISBN: 978-0-387-74777-4 e-ISBN: 978-0-387-74778-1 DOI: 10.1007/978-0-387-74778-1 Library of Congress Control Number: 2007935245 c 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Cover Illustration: Real part of the electric field phasor in the Fujisawa-Koshiba photonic waveguide bend. From “Electromagnetic Applications of a New Finite-Difference Calculus”, by Igor Tsukerman, IEEE Transactions on Magnetics, Vol. 41, No. 7, pp. 2206–2225, 2005. c 2005 IEEE (by permission). Printed on acid-free paper. 987654321 springer.com To the memory of my mother, to my father, and to the miracle of M. Preface The purpose of this note ... is to sort out my own thoughts ... and to solicit ideas from others. Lloyd N. Trefethen Three mysteries of Gaussian elimination Nobody reads prefaces. Therefore my preference would have been to write a short one that nobody will read rather than a long one that nobody will read. However, I ought to explain, as briefly as possible, the main motivation for writing the book and to thank – as fully and sincerely as possible – many people who have contributed to this writing in a variety of ways. My motivation has selfish and unselfish components. The unselfish part is to present the elements of computational methods and nanoscale simulation to researchers, scientists and engineers who are not necessarily experts in computer simulation. I am hopeful, though, that parts of the book will also be of interest to experts, as further discussed in the Introduction and Conclusion. The selfish part of my motivation is articulated in L. N. Trefethen’s quote above. Whether or not I have succeeded in “sorting out my own thoughts” is not quite clear at the moment, but I would definitely welcome “ideas from others,” as well as comments and constructive criticism. *** I owe an enormous debt of gratitude to my parents for their incredible kindness and selflessness, and to my wife for her equally incredible tolerance of my character quirks and for her unwavering support under all circumstances. My son (who is a business major at The Ohio State University) proofread parts of the book, replaced commas with semicolons, single quotes with double quotes, and fixed my other egregious abuses of the English language. VIII Preface Overall, my work on the book would have been an utterly pleasant ex- perience had it not been interrupted by the sudden and heartbreaking death of my mother in the summer of 2006. I do wish to dedicate this book to her memory. Acknowledgment and Thanks Collaboration with Gary Friedman and his group, especially during my sabbatical in 2002–2003 at Drexel University, has influenced my research and the material of this book greatly. Gary’s energy, enthusiasm and innovative ideas are always very stimulating. During the same sabbatical year, I was fortunate to visit several research groups working on the simulation of colloids, polyelectrolytes, macro- and biomolecules. I am very grateful to all of them for their hospitality. I would particularly like to mention Christian Holm, Markus Deserno and Vladimir Lobaskin at the Max-Planck-Institut f¨ur Polymerforschung in Mainz, Ger- many; Rebecca Wade at the European Molecular Biology Laboratory in Hei- delberg, and Thomas Simonson at the Laboratoire de Biologie Structurale in Strasbourg, France. Alexei Sokolov’s advanced techniques and experiments in optical sensors and microscopy with molecular-scale resolution had a strong impact on my students’ and my work over the last several years. I thank Alexei for providing a great opportunity for collaborative work with his group at the Department of Polymer Science, the University of Akron. In the course of the last two decades, I have benefited enormously from my communication with Alain Bossavit (Electricit´´ e de France and Laboratoire de Genie Electrique de Paris), from his very deep knowledge of all aspects of computational electromagnetism, and from his very detailed and thoughtful analysis of any difficult subject that would come up. Isaak Mayergoyz of the University of Maryland at College Park has on many occasions shared his valuable insights with me. His knowledge of many areas of electromagnetism, physics and mathematics is very profound and often unmatched. My communication with Jon Webb (McGill University, Montr´eal) has al- ways been thought-provoking and informative. His astute observations and comments make complicated matters look clear and simple. I was very pleased that Professor Webb devoted part of his sabbatical leave to our joint research on Flexible Local Approximation MEthods (FLAME, Chapter 4). Yuri Kizimovich (Plassotech Corp., California) and I have worked jointly on a variety of projects over the last 25 years. His original thinking and elegant solutions of practical problems have always been a great asset. Yury’s help and long-term collaboration are greatly appreciated. Even though over 20 years have already passed since the untimely death of my thesis advisor, Yu.V. Rakitskii, his students still remember very warmly Preface IX his relentless strive for excellence and quixotic attitude to scientific research. Rakitskii’s main contribution was to numerical methods for stiff systems of dif- ferential equations. He was guided by the idea of incorporating, to the extent possible, analytical approximations into numerical methods. This approach is manifest in FLAME that I believe Rakitskii would have liked. My sincere thanks go to • Dmitry Golovaty (The University of Akron), for his help on many occasions and for interesting discussions. • Viacheslav Dombrovski, a scientist of incomparable erudition, for many pearls of wisdom. • Elena Ivanova and Sergey Voskoboynikov (Technical University of St. Petersburg, Russia), for their very, very diligent work on FLAME. • Benjamin Yellen (Duke University), for many discussions, innovative ideas, and for his great contribution to the NSF-NIRT project on magnetic as- sembly of particles. • Mark Stockman (Georgia State University), for sharing his very deep and broad knowledge and expertise in many areas of plasmonics and nano- photonics. • J. Douglas Lavers (the University of Toronto), for his help, cooperation and continuing support over many years. • Fritz Keilmann (the Max-Planck-Institut f¨ur Biochemie in Martinsried, Germany), for providing an excellent opportunity for collaboration on problems in infrared microscopy. • Boris Shoykhet (Rockwell Automation), an excellent engineer, mathemati- cian and finite element analyst, for many valuable discussions. • Nicolae-Alexandru Nicorovici (University of Technology, Sydney, Aus- tralia), for his deep and detailed comments on “cloaking,” metamaterials, and properties of photonic structures. • H. Neal Bertram (UCSD – the University of California, San Diego), for his support. I have
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