Integrated Optics, Second Edition (Topics in Applied Physics)

353 Pages·1979·15.448 MB·English

by  T. Tamir, T. Tamir, E. Garmire, J. M. Hammer, H. Kogelnik, F. Zernike

Topics in Applied Physics Volume 7
scipoT ni Applied Physics
Founded by Helmut K. V. Lotsch
Volume 57 Strong dna Ultrastrong Magnetic Fields
Applications Editor: F. Herlach
Volume 58 Hot-Electron Transport in Semiconductors
Editor: L. Reggiani
Volumes 1-56 are listed on the back inside cover
detargetnI scitpO
Edited by .T Tamir
With Contributions by
E. Garmire J.M. Hammer H. Kogelnik
.T Tamir .F Zernike
Second Corrected and Updated Edition
With 99 Figures
Springer-Verlag Berlin Heidelberg New York 1979
Professor RODOEHT RIMAT
Department of Electrical Engineering, Polytechnic Institute of New York
333 Jay Street, Brooklyn, NY 11201, USA
3rd Printing of the 2nd Edition 1985
2nd Corrected Printing of the 2nd Edition 1982
ISBN 3-540-09673-6 .2 Auflage Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-09673-6 dn2 edition Springer-Verlag New York Heidelberg nilreB
ISBN 3-540-07297-7 .1 Auflage Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-07297-7 ts1 edition Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically
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© Springer-Verlag Berlin Heidelberg 1975 and 1979
Printed in Germany
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Typesetting, printing and bookbinding: Briihlsche Universit/itsdruckerei, Giessen
2153/3 i 30-5432
Preface to the Second Edition
Integrated optics has proven to be a very dynamic and active area, with
new significant developments being made at a very fast pace. Because of
this rapid advance, the first edition of this book was projected to be
relevant for only 2-3 years. It has turned out, however, that the large
amount of basic material contained in the book has provided continued
interest, which now expresses itself as a demand for a second edition. To
accommodate this need, we have decided to issue the present updated
paperback edition, which also has a lower price so as to make it more
accessible to graduate students.
The paperback edition is essentially identical to the original hard-
cover book, except that a new chapter (Chap. 7) has been added. This
new chapter reviews briefly the recent advances in the area and provides
numerous new references. A few typographical errors in the original
edition were corrected.
Due to limitations of both time and space, Chapter 7 can do little
more than point the reader to the latest literature. However, we hope that
future volumes of Springer optics books will detail the continuing
progress of integrated optics.
Brooklyn, New York T. RIMAT
July 1979
Preface to the First Edition
The new area of integrated optics, which is now about six years old,
has been based primarily on the fact that light waves can propagate
through and be contained by very thin layers (films) of transparent
materials. By combining such layers together and shaping them into
appropriate configurations, integrated-optics technology has realized a
large variety of components which can perform a wide range of operations
on optical waves. Thus, light can be guided, modulated, deflected,
filtered, radiated into space or, by using laser action, it can also be
generated within a thin-film structure. These components are small
and compact and they are expected to promote a variety of goals, of
which the most promising is optical signal processing in optical com-
munications. For this, as well as for other related applications, the aim is
to develop integrated instrumentation and optical apparatus having
miniature dimensions, which are expected to be accompanied by
robust, durable and reliable construction, with low power requirements.
Other technological and scientific pursuits of integrated optics
include new devices made possible by the development of thin-film
structures having special properties, phenomena produced by the
concentration of high intensity fields in thin films and effects due to the
attendant enhancement of nonlinear and/or active properties of such
films. Motivated by so many goals, a host of new fabrication techniques
have been developed for both. amorphous and crystalline materials.
However, integrated optics has been stimulated most strongly by the
fact that, after centuries of interest in optical phenomena requiring
equipment of relatively large dimensions, the small scale and planar
features of thin film components offer intriguing and very promising
potentialities for both old and new areas of research and development.
Because it involves a variety of scientific and technological facets,
the advancement of integrated optics has needed contributions from
investigators having many different backgrounds. Thus, scientists with
interest in optics, microwave engineers, specialists in radiation and dif-
fraction, as well as physicists in the areas of semiconductors, crystals,
surface phenomena, materials science and other disciplines, have often
combined to explore and apply the optical wave phenomena occurring in
VIII ecaferP
thin films. To tie together these various areas, a fairly large number of
survey papers have been issued during recent years. However, these
surveys usually were either short simplified descriptions of integrated
optics and its goals, or they were addressed to a group specializing in
a narrow aspect of the broader area. The need has therefore existed
for a wider coverage of integrated optics in a manual that would provide
a comprehensive exposition of this new area to scientists and engineers
in all of the professional groups enumerated above.
The aim of this book is to satisfy this need by serving as a mono-
graph on the state of the present art in integrated optics. We have
therefore attempted here to highlight those topics that have received
greatest attention and to emphasize those applications and methods
that have proven themselves most trustworthy and practical. Because
the amount of material already available in this area is quite volu-
minous and its complete inclusion is beyond the scope of this mono-
graph, we did not aim to achieve the coverage required of a handbook.
Nevertheless, an attempt was made to include almost everything re-
ported in the area of integrated optics at least in the form of references.
Hence this monograph should serve adequately as a well informed
manual that provides a balanced and reasonably detailed coverage of
integrated optics and discusses in sufficient depth its most pertinent
theoretical and practical aspects.
As the present book represents the joint effort of five contributors,
each of whom is responsible for his own chapter, a certain lack of co-
hesiveness and some repetitions are practically unavoidable. We have
attempted to minimize such deficiencies and, whenever appropriate,
we have provided cross-references amongst the various chapters. If,
nevertheless, the attempt to achieve a well rounded monograph has not
been entirely successful, the authors rely on the readers to temper their
criticism with the understanding that the time scale for writing, editing
and publishing an up-to-date manual on a rapidly growing and very
active field is too brief for achieving a more carefully organized book.
The Editor wishes to thank the other contributors for many in-
teresting and productive discussions in connection with the preparation
of this book. In particular, the critical comments and the constructive
suggestions by Dr. J.M. REMMAH and Dr. H. KINLEGOK on the in-
troductory chapter are greatly appreciated.
Special thanks are due to Miss YRAM EEL HTIFFIRG for her careful
and very competent assistance with the editorial work.
Brooklyn, New York
April 1975 T. TAMIR
Contents
1. Introduction. By T. TAMIR (With 2 Figures)
1.1. Historical Perspectives . . . . . . . . . . . . . . . . 1
1.1.1. The First Six Years . . . . . . . . . . . . . . 2
1.1.2. The Last Six Years . . . . . . . . . . . . . . . 3
1.1.3. Immediate and Future Prospects . . . . . . . . 6
1.2. Organization of this Book . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . 11
2. Theory of Dielectric .sediugevaW By H. KOGELNIK (With 25 Figures)
2.1. Ray Optics of the Slab Waveguide . . . . . . . . . . . 15
2.1.1. Refraction and Reflection . . . . . . . . . . . 15
2.1.2. Guided Modes . . . . . . . . . . . . . . . . 19
2.1.3. The Goos-H~inchen Shift . . . . . . . . . . . . 25
2.1.4. Effective Guide Thickness . . . . . . . . . . . 27
2.2. Fundamentals of the Electromagnetic Theory of Dielectric
Waveguides . . . . . . . . . . . . . . . . . . . . 29
2.2.1. Maxwell's Equations . . . . . . . . . . . . . . 29
2.2.2. Modes of the Waveguide . . . . . . . . . . . . 31
2.2.3. The Wave Equations for Planar Guides ..... 32
2.2.4. Mode Properties Following from Symmetry .... 34
2.2.5. Orthogonality of the Modes . . . . . . . . . . . 35
2.2.6. Mode Expansion and Normalization . . . . . . . 37
2.2.7. The Variation Theorem for Dielectric Waveguides . 40
2.2.8. Power Flow and Stored Energy in a Dielectric
Waveguide . . . . . . . . . . . . . . . . . . 42
2.2.9. Variational Properties of the Propagation Constant 44
2.3. Modes of the Planar Slab Guide . . . . . . . . . . . . 45
2.3.1. TE-Modes . . . . . . . . . . . . . . . . . . 46
2.3.2. TM-Modes . . . . . . . . . . . . . . . . . . 50
2.4. Planar Guides with Graded Index Profiles . . . . . . . 53
2.4.1. The Parabolic Profile (Harmonic Oscillator) .... 54
2.4.2. The "l/cosh 2'' Profile . . . . . . . . . . . . . 55
2.4.3. The Exponential Profile . . . . . . . . . . . . 57
X Contents
2.4.4. Index Profiles with Strong Asymmetry . . . . . . 59
2.4.5. The WKB Method . . . . . . . . . . . . . . . 61
2.5. Strip Waveguides . . . . . . . . . . . . . . . . . . 62
2.6. Coupled-Mode Formalism and Periodic Waveguides . 66
2.6.1. Excitation of Waveguide Modes . . . . . . . . . 67
2.6.2. Waveguide Deformations . . . . . . . . . . . . 69
2.6.3. Coupled-Wave Solutions . . . . . . . . . . . . 71
2.6.4. Periodic Waveguides . . . . . . . . . . . . . . 73
2.6.5. TE-TM Mode Conversion . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . 79
3. Beam and Waveguide Couplers. By T. TAMIR (With 27 Figures)
3.1. Coupling of Beams to Planar Guides . . . . . . . . . . 84
3.1.1. Transverse Couplers . . . . . . . . . . . . . . 84
3.1.2. The Prism Coupler . . . . . . . . . . . . . . 86
Coupled-Mode Description . . . . . . . . . . . 86
Basic Characteristics . . . . . . . . . . . . . . 89
3.1.3. The Grating Coupler . . . . . . . . . . . . . . 90
3.1.4. Leaky-Wave Theory of Beam Couplers . . . . . . 93
Inhomogeneous Plane Waves . . . . . . . . . . 93
Leaky Waves along Layered Media . . . . . . . 96
Leaky Waves along Dielectric Gratings . . . . . . 98
Leaky Waves in Beam Couplers . . . . . . . . . 99
3.1.5. Design Considerations for Prism Couplers .... 101
Role of Beam Width . . . . . . . . . . . . . . 102
Effect of Beam Form . . . . . . . . . . . . . . 103
Deviations from the Phase-Matching Angle .... 107
Beam Shaping by Variable Air Gap . . . . . . . 107
Calculation of Leaky-Wave Characteristics .... 107
3.1.6. Design Considerations for Grating Couplers .... t 10
Single-Beam Couplers . . . . . . . . . . . . . 110
Effect of Grating Height . . . . . . . . . . . . 113
Effect of Higher-Order Modes . . . . . . . . . 115
Two-Beam Couplers . . . . . . . . . . . . . . 115
3.1.7. Other Beam Couplers . . . . . . . . . . . . . 118
The Thin-Film Tapered Guide . . . . . . . . . 118
The Holographic Coupler . . . . . . . . . . . . 119
3.2. Waveguide Couplers and Mode Converters . . . . . . . 120
3.2.1. Planar-to-Planar Guide Couplers . . . . . . . . 121
3.2.2. Planar-to-Linear Guide Couplers . . . . . . . . 123
3.2.3. Linear-to-Linear Waveguide Couplers . . . . . . 124