ENGINEERING OPTICS WITH MAT LAB*

1 Ting-Chung Poon Taegeun Kim ENGINEERING OPTICS WITH MAT LAB* ENGINEERING OPTICS WITH MATLAB* liiM Ting-Chung Poon Virginia Tech, USA Taegeun Kim Sejong University, South Korea !||jp World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ENGINEERING OPTICS WITH MATLAB Copyright 2006 by World Scientific Publishing Co.

2 Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-256-872-7 ISBN 981-256-873-5 (pbk) Printed in Singapore by World Scientific Printers (S) Pte Ltd Preface This book serves two purposes: The first is to introduce the readers to some traditional topics such as the matrix formalism of geometrical OPTICS , wave propagation and diffraction, and some fundamental background on Fourier OPTICS .

3 The second is to introduce the essentials of acousto- OPTICS and electro- OPTICS , and to provide the students with experience in modeling the theory and applications using MATLAB , a commonly used software tool. This book is based on the authors' own in-class lectures as well as research in the area. The key features of the book are as follows. Treatment of each topic begins from the first principles. For example, geometrical OPTICS starts from Fermat's principle, while acousto- OPTICS and electro- OPTICS start from Maxwell equations. MATLAB examples are presented throughout the book, including programs for such important topics as diffraction of Gaussian beams, split-step beam propagation method for beam propagation in inhomogeneous as well as Kerr media, and numerical calculation of up to 10-coupled differential equations in acousto- OPTICS .

4 Finally, we cover acousto- OPTICS with emphasis on modern applications such as spatial filtering and heterodyning. The book can be used for a general text book for OPTICS /Optical ENGINEERING classes as well as acousto- OPTICS and electro- OPTICS classes for advanced students. It is our hope that this book will stimulate the readers' general interest in OPTICS as well as provide them with an essential background in acousto- OPTICS and electro- OPTICS . The book is geared towards a senior/first-year graduate level audience in ENGINEERING and physics. This is suitable for a two-semester course. The book may also be useful for scientists and engineers who wish to learn about the V vi ENGINEERING OPTICS with MATLAB basics of beam propagation in inhomogeneous media, acousto- OPTICS and electro- OPTICS .

5 Ting-Chung Poon (TCP) would like to thank his wife Eliza and his children Christina and Justine for their encouragement, patience and love. In addition, TCP would like to thank Justine Poon for typing parts of the manuscript, Bill Davis for help with the proper use of the word processing software, Ahmad Safaai-Jazi and Partha Banerjee for help with better understanding of the physics of fiber OPTICS and nonlinear OPTICS , respectively, and last, but not least, Monish Chatterjee for reading the manuscript and providing comments and suggestions for improvements. Taegeun Kim would like to thank his wife Sang Min Lee and his parents Pyung Kwang Kim and Ae Sook Park for their encouragement, endless support and love.

6 Contents Preface v 1. Geometrical OPTICS Fermat's Principle 2 Reflection and Refraction 3 Ray propagation in an Inhomogeneous Medium: Ray Equation 6 Matrix methods in Paraxial OPTICS 16 The Ray Transfer Matrix 17 Illustrative examples 25 Cardinal points of an optical system 27 Reflection Matrix and

7 Optical Resonators 32 Ray OPTICS using MATLAB 37 2. Wave propagation and Wave OPTICS Maxwell's Equations: A Review 46 Linear Wave propagation 50 Traveling-wave solutions 50 Maxwell's equations in phasor domain.

8 Intrinsic impedance, the Poynting vector, and polarization 55 Electromagnetic waves at a boundary and Fresnel's equations 60 Wave OPTICS 73 Fourier transform and convolution 74 Spatial frequency transfer function and spatial impulse response of propagation 75

9 Vii viii ENGINEERING OPTICS with MATLAB Examples of Fresnel diffraction 79 Fraunhofer diffraction 80 Fourier transforming property of ideal lenses 83 Resonators and Gaussian beams 86 Gaussian beam OPTICS and MATLAB Examples 97 q-transformation of Gaussian beams 99 MATLAB example: propagation of a Gaussian beam .

10 102 3. beam propagation in Inhomogeneous Media Wave propagation in a Linear Inhomogeneous Medium Ill Optical propagation in Square-Law Media 112 The Paraxial Wave Equation 119 The Split-Step beam propagation Method 121 MATLAB Examples using the Split-Step beam propagation Method 124 beam propagation in Nonlinear