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Written by the department head of materials science and engineering at MIT, this concise and stringent introduction takes readers from the fundamental theory to in-depth knowledge.It sets out with a theoretical scheme for the design of desirable periodic structures, then presents the experimental techniques that allow for fabrication of the periodic structure and exemplary experimental data. Subsequently, theory and numerical data are used to demonstrate how these periodic structures control the photonic, acoustic, and mechanical properties of materials, concluding with examples from these three important fields of applications.The result is must-have knowledge for both beginners and veterans in the field.
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Martin Maldovan and Edwin L. Thomas Periodic Materials and Interference Lithography
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Martin Maldovan and Edwin L. Thomas
Periodic Materials and Interference Lithography for Photonics, Phononics and Mechanics
The Authors Dr. Martin Maldovan MIT Materials Science & Engineering 77 Massachusetts Avenue Cambridge, MA 02139 USA Prof. Edwin L. Thomas MIT Materials Science & Engineering 77 Massachusetts Avenue Cambridge, MA 02139 USA
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at . 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Typesetting Laserwords Private Limited, Chennai, India Printing Strauss GmbH, M¨orlenbach Binding Litges & Dopf GmbH, Heppenheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-31999-2
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Contents Preface XI Introduction
XIII
Theory 1 1 1.1 1.2 1.3 1.3.1 1.4 1.5 1.5.1 1.5.2 1.5.3
Structural Periodicity 3 Nonperiodic versus Periodic Structures 4 Two-dimensional Point Lattices 6 Three-dimensional Point Lattices 10 Primitive and Nonprimitive Unit Cells 14 Mathematical Description of Periodic Structures 16 Fourier Series 20 Fourier Series for Two-dimensional Periodic Functions 20 Fourier Series for Three-dimensional Periodic Functions 23 Arbitrary Unit Cells 25 Further Reading 26 Problems 26
2 2.1 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3 2.4
Periodic Functions and Structures 29 Introduction 30 Creating Simple Periodic Functions in Two Dimensions 31 The Square Lattice 31 The Triangular Lattice 38 Creating Simple Periodic Functions in