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1、Ting-Chung Poon Taegeun KimENGINEERING OPTICS WITH AT LABENGINEERING OPTICS WITHMATLABT订s page 1s intentiooallv left blru1kTing-Chung PoonVirginia Tech, USATaegeun KimSejong University, South Korea,World ScientificNEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI. CHENNAIPublished byWorl
2、d Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HEBritish Library Cataloguing-in-Publication DataA catalogue record for this book is available from the B
3、ritish Library.ENGINEERING OPTICS WITH MATLABCopyright 2006 by World Scientific Publishing Co. 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 retr
4、ieval 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
5、 from the publisher.ISBN 981-256-872-7ISBN 981-256-873-5 (pbk)Printed in Singapore by World Scientific Printers (S) Pie LtdPrefaceThis 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 d
6、iffraction, and some fundamental background on Fourier optics. 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 au
7、thorsown 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 Fermats principle, while acousto-optics and electro-optics start from Maxwell equations. MATLA
8、B 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 IO-coupled differential equations in acousto
9、-optics. Finally, we cover acousto-optics with emphasis on modem applications such as spatial filtering and heterodyning.vThe 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 tha
10、t this book will stimulate the readersgeneral 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. T
11、he book may also be useful for scientists and engineers who wish to learn about theVIEngineering Optics with MATLABbasics of beam propagation in inhomogeneous media, acousto-optics and electro-optics.Ting-Chung Poon (TCP) would like to thank his wife Eliza and his children Christina and Justine for
12、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 opti
13、cs 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
14、 support and love.ContentsPreface.v1. Geometrical Optics1.1 Fermats Principle.21.2 Reflection and Refraction.31.3 Ray Propagation in an Inhomogeneous Medium:Ray Equation.61.4 Matrix Methods in Paraxial Optics.161.4.1 The Ray Transfer Matrix.171.4.2 Illustrative examples.251.4.3 Cardinal points of an
15、 optical system271.5 Reflection Matrix and Optical Resonators321.6 Ray Optics using MATLAB372. Wave Propagation and Wave Optics2.1 Maxwells Equations: A Review.462.2 Linear Wave Propagation.502.2.1 Traveling-wave solutions.502.2.2 Maxwells equations in phasor domain: Intrinsic impedance, the Poyntin
16、g vector, and polarization552.2.3 Electromagnetic waves at a boundary and Fresnels equations.602.3 Wave Optics.732.3.1 Fourier transform and convolution742.3.2 Spatial frequency transfer function and spatialimpulse response of propagation75VllVlllEngineering Optics with MATLAB2.3.3 Examples of Fresn
17、el diffraction792.3.4 Fraunhofer diffraction.802.3.5 Fourier transforming property of ideal lenses832.3.6 RResonators and Gaussian beams862.4 Gaussian Beam Optics and MATLAB Examples972.4.1 q-transformation of Gaussian beams992.4.2 MATLAB example: propagation of a Gaussian beam. 1023. Beam Propagati
18、on in Inhomogeneous Media3.1 Wave Propagation in a Linear Inhomogeneous Medium1113.2 Optical Propagation in Square-Law Media1123.3 The Paraxial Wave Equation.1193.4 The Split-Step Beam Propagation Method1213.5 MATLAB Examples Using the Split-Step BeamPropagation Method.1243.6 Beam Propagation in Non
19、linear Media: The Kerr Media1343.6.1 Spatial soliton.1363.6.2 Self-focusing and self-defocusing.1394. Acousto-Optics4.1 Qualitative Description and Heuristic Background1524.2 The Acousto-optic Effect: General Formalism1584.3 Raman-Nath Equations.1614.4 Contemporary Approach.1644.5 Raman-Nath Regime.
20、1654.6 Bragg Regime.1664.7 Numerical Examples.1724.8 Modern Applications of the Acousto-Optic Effect1784.8.1 Intensity modulation of a laser beam.1784.8.2 Light beam deflector and spectrum analyzer1814.8.3 Demodulation of frequency modulated (FM) signals1824.8.4 Bistable switching.1844.8.5 Acousto-o
21、ptic spatial filtering.1884.8.6 Acousto-optic heterodyning196ContentsIX5. Electro-Optics5.1 The Dielectric Tensor.2055.2 Plane-Wave Propagation in Uniaxial Crystals; Birefringence.2105.3 Applications of Birefringence: Wave Plates2175.4 The Index Ellipsoid.2195.5 Electro-Optic Effect in Uniaxial Crys
22、tals2235.6 Some Applications of the Electro-Optic Effect equations2275.6.1 Intensity modulation.2275.6.2 Phase modulation.236Index.241Chapter 1Geometrical OpticsWhen we consider optics, the first thing that comes to our minds is probably light. Light has a dual nature: light is particles (called pho
23、tons) and light is waves. When a particle moves, it processes momentum, p. And when a wave propagates, it oscillates with a wavelength,入Indeed, the momentum and the wavelength is given by the de Broglie relationh入pwhere h 6.62 x 10-34 Joule-second is Plancks constant. Hence from the relation, we can
24、 state that every particle is a wave as well.Each particle or photon is specified precisely by the frequency v and has an energy E given byE= hv.If the particle is traveling in free space or in vacuum, v = c从，where c is a constant approximately given by 3 x 108 m/ s. The speed of light in a transpar
25、ent linear, homogeneous and isotropic material, which we term v, is again a constant but less than c. This constant is a physical characteristic or signature of the material. The ratio clv is called the refractive index, n, of the material.In geometrical optics, we treat light as particles and the t
26、rajectory of these particles follows along paths thatwe call rays. We can describe an optical system consisting of elements such as mirrors and lenses by tracing the rays through the system.Geometrical optics is a special case of wave or physical optics, which will be mainly our focus through the re
27、st of this Chapter. Indeed, by taking the limit in which the wavelength of light approaches zero in wave optics, we recover geometrical optics. In this limit, diffraction and the wave nature of light is absent.2Engineering Optics with MATLAB1.1 Fermats PrincipleGeometrical optics starts from Fermats
28、 Principle. In fact, Fermats Principle is a concise statement that contains all the physical laws, such as the law of reflection and the law of refraction, in geometrical optics. Fermats principle states that the path of a light ray follows is an extremum in comparison with the nearby paths. The ext
29、remum may be a minimum, a maximin, or stationary with respect to variations in the ray path. However, it is usually a minimum.lWe now give a mathematical description of Fermats principle. Let n(x, y, z) represent a position-dependent refractive index along a path C between end points A and B, as sho
30、wn in Fig. 1.1. We define the optical path length (0 PL) asOPL=n(x,y,z)ds,C(1.1-1)lwhere ds represents an infinitesimal arc length. According to Fermats principle, out the many paths that connect the two end points A and B, the light ray would follow that path for which the OP L between the two poin
31、ts is an extremum, i.e.,8(0PL) = 8n(x, y, z) ds = 0C(1.1-2)in which 8 represents a small variation. In other words, a ray of light will travel along a medium in such a way that the total OP L assumes an extremum. As an extremum means that the rate of change is zero, Eq.(1.1-2) explicitly means that矗
32、Jnds+嘉Jnds+立Jnds =0(1.1-3)Now since the ray propagates with the velocity v = c/n along the path,Cnds =ds = cdt,V(1.1-4)where dt is the differential time needed to travel the distance ds along3Geometrical Opticsthe path. We substitute Eq. (1.1-4) into Eq. (1.1-2) to get6fc n ds = c 6 fc dt = 0(1.1-5)
33、B9An(x,y,z)Fig. 1.1 A ray of light traversing a path C between end points A and BAs mentioned before, the extremum is usually a minimum, we can, therefore, restate Fermats principle as a principle of least time. In a homogeneous medium, i.e., in a medium with a constant refractive index, the ray pat
34、h is a straight line as the shortest OP L between the two end points is along a straight line which assumes the shortest time for the ray to travel.1.2 Reflection and RefractionWhen a ray of light is incident on the interface separating two different optical media characterized by n1 and n2, as show
35、n in Fig. 1.2, it is well known that part of the light is reflected back into the first medium, while the rest of the light is refracted as it enters the second medium. The directions taken by these rays are described by the laws of reflection and refraction, which can be derived from Fermats princi
36、ple.In what follows, we demonstrate the use of the principle of least time to derive the law of refraction. Consider a reflecting surface as shown in Fig. 1.3. Light from point A is reflected from the reflecting surface to point B, forming the angle of incidence仇and the angle ofreflection仇，measured
37、from the normal to the surface. The time required for the ray of light to travel the path AO + OB is given byt =(AO+ OB)/v, where v is the velocity of light in the medium4Engineering Optics with MATLABcontaining the points AOB. The medium is considered isotropic and homogeneous. From the geometry, w
38、e findt(z)=(hi+ (d - z)2尸屑z2尸）1V(1.2-1)Incident rayMedium 1 n1Medium2n2interfaceFig. 1.2 Reflected and refracted rays for light incident at the interface of two media.zd。Fig. 1.3 Incident (AO) and reflected (OB) rays.5Geometrical OpticsAccording to the least time principle, light will find a path th
39、at extremizes t(z) with respect to variations in z. We thus set dt(z)/dz = 0 to getd-zz困（d-平l2= h5十社l2(1.2-2)orso thatsin仇sin仇(1.2-3)仇仇，(1.2-4)which is the law of reflection. We can readily check that the second derivative of t(z) is positive so that the result obtained corresponds to the least time
40、 principle. In addition, Fermats principle also demands that the incident ray, the reflected ray and the normal all be in the same plane, called the plane of incidence.Similarly, we can use the least time principle to derived the law of refractionn1sin仇n2sin仇，(1.2-5)which is commonly known as Snells
41、 law of refraction. In Eq. (1.2-5)，仇 is the angle of incidence for the incident ray and心is the angle of transmission (or angle of refraction) for the refracted ray. Both angles are measured from the nom叫to the surface. Again, as in reflection, the incident ray, the refracted ray, and the normal all
42、lie in the same plane of incidence. Snells law shows that when a light ray passes obliquely from a medium of smaller refractive index n1 into one that has a largerrefractive index n2, or an optically denser medium, it is bent toward the normal. Conversely, if the ray of light travels into a medium w
43、ith a lower refractive index, it is bent away from the normal. For the latter case, it is possible to visualize a situation where the refracted ray is bent away from the normal by exactly 90. Under this situation, the angle of incidence is called the critical angle中c, given bysin仇兀I兀(1.2-6) When the
44、 incident angle is greater than the critical angle, the ray6Engineering Optics with MATLABoriginating in medium 1 is totally reflected back into medium 1. This phenomenon is called total internal reflection. The optical fiber uses this principle of total reflection to guide light, and the mirage on
45、a hot sun皿er day is a phenomenon due to the same principle.1.3 Ray Propagation in an Inhomogeneous Medium: Ray EquationIn the last Section, we have discussed refraction between two media with different refractive indices, possessing a discrete inhomogeniety in the simplest case. For a general inhomo
46、geneous medium, i.e., n(x, y, z), it is instructive to have an equation that can describe the trajectory of a ray. Such an equation is known as the ray equation. The ray equation is analogous to the equations of motion for particles and for rigid bodies in classical mechanics. The equations of motion can be derived from Newtonian mechanics based on Netwons laws. Alternatively, the equations of motion can be derived directly from Hamiltons principle of least action. Indeed Fermats