PASSIVE COMPONENTS FOR DENSE OPTICAL INTEGRATION

PASSIVE COMPONENTS FOR DENSE OPTICAL INTEGRATION

PASSIVE COMPONENTS FOR DENSE OPTICAL INTEGRA TION Christina Manolatou Massachusetts Institute oftechnology Hermann A. Haus Massachusetts Institute oftechnology SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging-in-Publication Data Manolatou, Christina. Passive components for dense opticai integration / Christina Manolatou, Hermann A. Haus. p. cm. Includes bibliographical references and index. ISBN 978-1-4613-5272-3 ISBN 978-1-4615-0855-7 (ebook) DOI 10.1007/978-1-4615-0855-7 1. Optoelectronic devices. 2. Integrated optics. 1. Haus, Hermann A. II. Title. TAI750.M355 2001 62I.381'045-dc21 2001050342 Copyright 2002 by Springer Science+Business Media New York Origina11y published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover lst edition 2002 AH rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. Printed an acid-free paper.

Contents Contents Preface v ix 1 Introduction 1 1.1 Motivation 1 1.2 Outline of the book 3 1.2.1 Theoretical background.3 1.2.2 The FDTD method 3 1.2.3 Resonant channel add/drop filters.4 1.2.4 Low-loss waveguide components.4 1.2.5 Fiber-P1C coupling 5 2 Theoretical Background 7 2.1 Modes in optical waveguides 7 2.1.1 Normal modes 7 2.1.2 Generalform ofguided fields 9 2.1.3 Orthogonality relations 10 v

PASSIVE COMPONENTS FOR DENSEOPTICALINTEGRATION 2.1.4 Completeness ofnormal modes 10 2.2 Excitation of modes by localized currents 11 2.3 Scattering matrix 14 2.4 Effective Index Method (ElM) 17 2.5 Resonators 20 2.5.1 Coupled resonators 21 2.5.2 Resonator-waveguide coupling 21 2.6 Gaussian Beams 28 2.6.1 Propagation ofgaussian beams 28 2.6.2 ABCDmatrices 30 2.6.3 Approximationofeffective index and mode profile using Gaussians.32 3 The Finite Difference Time Domain (FDTD) Method 35 3.1 The Yee algorithm.35 3.2 Finite Differencing 38 3.2.1 Three-dimensional algorithm.38 3.2.2 Two-dimensional algorithm 39 3.3 Boundary Conditions 41 3.4 Source Implementation.46 3.5 The use of Discrete Fourier Transform (DFT) in FDTD.48 3.6 Resonator calculations using FDTD 50 4 Resonant AddIDrop Filters 53 4.1 Introduction 53 4.2 Four-port system with single mode resonator 54 4.3 Symmetric standing-wave channel add/drop filters 60 4.3.1 General form ofa symmetric channel add/dropfilter 60 4.3.2 Symmetric add/drop filter with two identical standing-wave cavities 66 4.4 FDTD simulations 72 4.4.1 Polygon resonators 72 4.4.2 Single square resonator coupled with two waveguides 74 4.4.3 Channel add/drop filter using a pairofsquare resonators 76 4.5 High-order symmetric add/drop filters 80 vi

CONTENTS 4.6 Phase response and dispersion 91 5 High Density Integrated Optics 97 5.1 Introduction 97 5.2 Sharp 900 bends 98 5.3 3D simulations and measurements on HTC bends 111 5.4 T-splitters 117 5.5 Waveguide crossings 121 6 Fiber-PIC coupling 127 6.1 Introduction 127 6.2 Lateral mode conversion using cascade of square resonators 129 6.3 Mode conversion using dielectric planar lenses 136 6.4 3D mode-conversion scheme 142 7 Conclusions and Future Directions 151 7.1 Summary 151 7.2 Fiber-chip coupling 152 7.3 Polarization dependence 153 7.4 Numerical tools 155 References 157 Index 165 vii

Preface The steadily increasing bit-rates in modern optical communications call for hardware that processes optical signals optically (instead of converting them into electronic form and of processing them electronically). Integrated optics is the name that was applied in the early 70's to "hardware" intended for complex optical signal processing in the optical format. Integrated optics encountered fabrication challenges that could not be met decades ago. Also, the need for such hardware was not acute in the early days when optical fiber communications was in the early days when optical fiber communications was in the early laboratory stage. In the meantime, fabrication methods have improved and the tolerances required for the fabrication of integrated optical circuits are beginning to be met. An example of the sophisticated signal processing component, the array waveguide grating multiplexer-demultiplexer has been perfected to handle 40 channels simultaneously. The time has arrived for the development of other optical "hardware" integrated on the same substrate to perform optical signal processing functions. Integrated optical devices are generally much larger in their planar dimensions than an optical wavelength. Hence the density of integration achievable in the optics field will never reach the level achieved in electronic integrated circuits. However, ways of reducing the size of these devices are needed to achieve higher densities of integration. The Ph.D. thesis on which the monograph is based, is an attempt to reduce significantly the size of optical components, bends, T-junctions, resonators and filters. The current, intensive studies devoted to Photonic Band-Gap (PBG) devices have similar aim. The realm ofpbg structures is vast indeed and is likely that current studix

PASSIVE COMPONENTS FOR DENSE OPTICAL INTEGRATION ies will lead to classes of devices of new functionalities. However, the fabrication challenges are enormous. It is likely that simpler solutions to the optical integration problem, such as the ones discussed here, will be implemented sooner. This work presents a theoretical and numerical investigation of high index-contrast (HIC) passive components that can serve as building blocks at the end-points and nodes of WDM communications systems. The main characteristic of these structures is their miniature size (on the order of the optical wavelength), and their low radiation loss due to the strong light confinement in high index-contrast systems. Thus large scale, high density optical integration may be possible with the associated advantages of increased functionality, compactness and low-cost. Novel devices for filtering, optical interconnections and coupling to fibers are presented, specifically: a class of resonant add/drop filters that rely on symmetry and degeneracy of modes, low-loss right-angle bends, splitters, crossings based on transmission cavities, and fiber-chip couplers based on cascades of resonators or lensing mechanisms. Their operating principles are explained and an approximate analysis is obtained by analytical methods such as coupled-mode theory and gaussian/ray optics. For accurate analysis and optimized design, extensive numerical simulations are performed using the Finite Difference Time Domain method. The numerical results are in good agreement with the experimental data obtained for bends that were fabricated and tested at MIT. Issues that remain to be addressed for this technology to be viable and possible future directions are also discussed. We would like to thank professors E.P. Ippen, J. D. Joannopoulos and L.c. Kimerling for their contributions and the close collaboration with their research groups. Dr. Pierre Villeneuve and Dr. Shanhui Fan were extremely helpful in the early stages of this work. The idea of channel add/drop filters using coupled standing-wave cavities was first proposed by Dr. Shanhui Fan and the elmination of crosstalk in waveguide crossings by Dr. Steven Johnson, both in the context ofpbg cavities. The experimental work on HIC bends and splitters by Dr. Desmond Lim and Paul Maki is greatly appreciated. We also thank Dr. Kevin Lee for useful discussions on design and fabrication issues regarding the fiber-chip coupling problem, and Dr. Brent Little for his contributions and new ideas on - primarily ring - resonator design and applications. Many thanks to Jalal Khan for his excellent work on high-order filter design and other aspects of this work. Finally we would like to acknowledge the importance of our access to the Cray in the UC San Diego and U. of Texas supercomputer facilities, where almost all the numerical simulations of this work were performed. Christina Manolatou Hermann A. Haus x