`Corrected Declaration of Timothy J. Drabik, Ph.D. (Exhibit 1039)
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`
`UNITED STATES PATENT AND TRADEMARK OFFICE
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`
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`
`
`Ciena Corporation,
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`Coriant Operations, Inc.,
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`Coriant (USA) Inc., and
`
`Petitioner
`
`v.
`
`CAPELLA PHOTONICS, INC.
`
`Patent Owner
`
`
`
`Inter Partes Review Case No. IPR2015-01961
`Patent No. RE42,678
`
`
`
`
`
`CORRECTED DECLARATION OF TIMOTHY J. DRABIK, Ph.D.
`
`
`
`
`
`
`Mail Stop “PATENT BOARD”
`Patent Trial and Appeal Board
`U.S. Patent and Trademark Office
`P.O. Box 1450
`Alexandria, VA 22313-1450
`
`
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-1
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`
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
`TABLE OF CONTENTS
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`B.
`
`INTRODUCTION ........................................................................................... 1
`A.
`Background ........................................................................................... 1
`B.
`Qualifications ........................................................................................ 2
`1.
`Education .................................................................................... 2
`2.
`Career History ............................................................................ 3
`3.
`Publications ................................................................................ 5
`4.
`Other Relevant Qualifications .................................................... 6
`THE ‘678 PATENT ........................................................................................ 7
`II.
`III. LIST OF DOCUMENTS CONSIDERED IN FORMULATING MY
`OPINION ........................................................................................................ 7
`IV. TECHNICAL BACKGROUND ................................................................... 10
`A. Optical switching for telecommunications ......................................... 10
`1.
`Fiber cross-connects ................................................................. 10
`2. Wavelength switches ................................................................ 12
`Free-space optical systems ................................................................. 13
`1.
`Basic properties of lenses ......................................................... 14
`2.
`Gaussian light beams ................................................................ 16
`3.
`The “Fourier lens” .................................................................... 18
`4.
`Concave mirrors as focusing elements ..................................... 20
`5. Wavelength-dispersive elements .............................................. 20
`STATE OF THE ART AT THE TIME OF THE ALLEGED
`INVENTION ................................................................................................. 24
`A.
`Transparent optical switching prior to the alleged invention ............. 24
`B.
`Reconfigurable Optical Add-Drop Multiplexers ................................ 25
`C. Wavelength Selective Switches .......................................................... 26
`D. MEMS Mirrors ................................................................................... 28
`VI. PERSON OF ORDINARY SKILL IN THE ART ........................................ 31
`VII. OVERVIEW OF THE ‘678 PATENT .......................................................... 31
`A. Operation of the disclosed system of the ’678 Patent ........................ 32
`i
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`V.
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`I.
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-2
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`VIII. THE CLAIMS OF THE ‘678 PATENT ....................................................... 34
`IX. LEGAL STANDARDS ................................................................................. 35
`A. Anticipation ........................................................................................ 35
`B.
`Obviousness ........................................................................................ 36
`CLAIM CONSTRUCTION .......................................................................... 41
`X.
`XI. ANALYSIS OF INVALIDITY .................................................................... 43
`A.
`Summary of Analysis ......................................................................... 43
`B.
`Point 1: Claims 1, 9, 10, 13, 17, 19, 44, 53, 61, 64 and 65 Are
`Not Innovative in View of Bouevitch and Carr .................................. 44
`1.
`Operation of the disclosed system of Bouevitch ...................... 45
`2.
`Combination of Bouevitch with Carr ....................................... 48
`Point 2: Claims 1-4, 19-23, 27, 29, 44-46 and 61-63 Are Not
`Innovative in View of Bouevitch and Sparks ..................................... 77
`XII. CONCLUSION ........................................................................................... 129
`
`C.
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`
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`ii
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-3
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`I, Timothy J. Drabik, hereby declare as follows:
`
`I.
`
`INTRODUCTION
`A. Background
`1. My name is Timothy J. Drabik. I am a researcher and consultant
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`working in areas related to optics, telecommunications, display technologies, and
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`microelectronics. I undertake consulting through my company, Page Mill
`
`Technology Corporation, and also work to develop commercial technologies for
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`information display and optical telecommunications.
`
`2.
`
`I have been retained to act as an expert witness on behalf of Petitioner
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`in connection with the above captioned Petition for Inter Partes Review of U.S.
`
`Patent No. RE42,678 (“Petition”). I understand that this proceeding involves U.S.
`
`Patent No. RE42,678 (“the ‘678 Patent”), titled “Reconfigurable Optical Add-Drop
`
`Multiplexers with Servo-Control and Dynamic Spectral Management
`
`Capabilities.” The ‘678 Patent is provided as Exhibit 1001.
`
`3.
`
`I understand that Petitioner challenges the validity of Claims 1–4, 9,
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`10, 13, 17, 19–23, 27, 29, 44–46, 53 and 61–65 of the ‘678 Patent (the “challenged
`
`claims”).
`
`4.
`
`I have reviewed and am familiar with the ‘678 Patent as well as its
`
`prosecution history. The ‘678 prosecution history is provided as Exhibit 1002.
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`Additionally, I have reviewed materials identified in Section III.
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`
`
`1
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-4
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`As set forth below, I am familiar with the technology at issue as of
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`5.
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`both the August 23, 2001 filing date of the application which led to the ‘678
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`Patent, and the March 19, 2001 priority date corresponding to the filing of
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`Provisional Patent Application No. 60/277,217. I have been asked to provide my
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`technical review, analysis, insights, and opinions regarding the prior art references
`
`that form the basis for the Petition. In forming my opinions, I have relied on my
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`own experience and knowledge, my review of the ‘678 Patent and its file history,
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`and of the prior art references cited in the Petition.
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`6. My opinions expressed in this Declaration rely to a great extent on my
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`own personal knowledge and recollection. However, to the extent I considered
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`specific documents or data in formulating the opinions expressed in this
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`Declaration, such items are expressly referred to in this Declaration.
`
`7.
`
`I am being compensated for my time in connection with this IPR at
`
`my standard consulting rate, which is $500 per hour.
`
`B. Qualifications
`Education
`1.
`I received my Ph.D. in Electrical Engineering from the Georgia
`
`8.
`
`Institute of Technology in 1990, where I also received a M.S. degree in Electrical
`
`Engineering in 1982. I received Bachelor’s degrees in Electrical Engineering and
`
`
`
`2
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-5
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`in Mathematics from Rose-Hulman Institute of Technology in 1981; I also
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`received certification in technical translation of German to English.
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`Career History
`
`2.
`I have over thirty years of experience in the areas of optics and optical
`
`9.
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`engineering, optoelectronics, telecommunications, liquid crystal display
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`technology, signal and image processing for video applications, microelectronics
`
`and integrated circuit design, device packaging, digital systems, and high-
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`performance computing. I have worked both in the academic and industrial
`
`environments.
`
`10.
`
`I held Assistant Professor and Associate Professor appointments at
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`Georgia Tech through the 1990s in electrical and computer engineering, and
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`Visiting and Consulting Professorships at Stanford University from 1999 to 2009.
`
`I have taught courses in a broad range of areas, run a research laboratory, and
`
`graduated Ph.D. students. I have done research program development with
`
`government and industrial entities in the U.S., France, the UK, and other countries.
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`I also have worked for a number of companies. I have been employed directly by
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`AT&T Bell Labs, Displaytech, Inc., Sun Microsystems, and Spectralane, Inc.
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`Among my past consulting clients are the NASA Jet Propulsion Laboratory,
`
`Siemens Corporate Research, and early-stage investors performing due diligence
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`prior to making investment decisions.
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`
`
`3
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-6
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`11. At AT&T Bell Labs in the early 1980s, I worked in a department that
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`was developing technologies and services for fiber-to-the home systems. Voice,
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`data, and television content were provided. I designed hardware and also
`
`investigated options for video bandwidth compression and coding.
`
`12. As a graduate student, I developed technologies for controlling arrays
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`of optical switches integrated with silicon chips. One of these technologies
`
`combined ferroelectric liquid crystals (LCs) on silicon integrated circuit chips
`
`(LCOS), and formed the basis for the microdisplays I developed later.
`
`13. At Georgia Tech and Stanford, I directed research activity in liquid
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`crystal microdisplay technology, diffractive optics, optoelectronic packaging and
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`hybrid integration, and high-speed interconnection of digital systems, and
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`graduated four Ph.D. students working in these areas. Specifically, I conducted
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`research with Displaytech, Inc., which led to the development of commercial
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`liquid-crystal-on-silicon microdisplays. I developed new manufacturing
`
`technology, designed the underlying pixel array and peripheral/driver circuitry for
`
`a dozen designs, and tested and evaluated displays. I also taught courses in digital
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`signal processing, Fourier optics and holography, optical information processing,
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`information theory, pattern recognition, semiconductor electronics, integrated
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`circuit design, linear system theory, operational mathematics, and other areas, at
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`the undergraduate and graduate levels.
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`
`
`4
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-7
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`14. As Director of Telecommunications with Displaytech, I developed
`
`liquid crystal devices and designed subsystems for transparent optical switching
`
`and signal restoration for single-mode, long haul optical transmission. This work
`
`entailed development of new optical switch architectures as well as investigation of
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`new liquid crystal component manufacturing technologies to meet the strenuous
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`reliability requirements of the optical telecommunication industry. In particular, I
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`worked in the 2000 time frame to develop optical add/drop multiplexor subsystems
`
`based on liquid crystal on silicon (LCOS) technology.
`
`Publications
`
`3.
`I have published more than 30 articles in scholarly journals, and am
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`15.
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`the first named inventor on four U.S. Patents. I have also delivered invited
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`addresses to the U.S.–Japan Joint Optoelectronics Project Expert Workshop
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`(Makuhari, Japan), the Scottish Optoelectronics Association and Institute of
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`Physics Meeting on Optical Interconnections for Information Processing
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`(Edinburgh, Scotland), the Annual Meeting of the Materials Research Society (San
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`Francisco, CA), and the IEEE/LEOS Workshop on Interconnections within High-
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`Speed Digital Systems (Santa Fe, NM). I have served the European Union as an
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`Expert Reviewer for EU research programs in microelectronics and optics, and the
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`National Science Foundation as a reviewer of research proposals.
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`
`
`5
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-8
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`4. Other Relevant Qualifications
`16. My consulting practice has involved the design of optoelectronic
`
`integrated systems on custom silicon platforms, development of new liquid crystal
`
`cell technology and manufacturing technology, investigation of advanced
`
`processor–memory architectures for high-performance parallel computing, and
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`development of long-haul optical fiber transmission subsystems. Specifically, for
`
`Spectralane, Inc., a Silicon Valley startup pursuing disruptive techniques for
`
`ameliorating nonlinear impairments in long-haul, wavelength-division-multiplexed
`
`fiber systems, I developed simulation and modeling tools to aid in subsystem
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`design, used those tools to develop effective subsystem architectures, and drafted
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`patents.
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`17. My practice also has involved preparing U.S. Patent applications,
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`providing patent infringement and validity studies and reports, and conducting
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`intellectual property due diligence investigations in connection with venture
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`financing. I have previously served as an expert in litigation matters relating to
`
`(among other areas) optical switching, optical fiber transmitter and receiver
`
`components, video processing technologies, the design, fabrication, and operation
`
`of liquid crystal displays, and optical disk drive technologies.
`
`18. My curriculum vitae, Exhibit 1017, includes a compilation of my
`
`publications and patents, lists litigation matters in which I have been engaged, and,
`
`
`
`6
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-9
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`in particular, includes those in which I have provided testimony over the previous
`
`four years.
`
`II. THE ‘678 PATENT
`19. The above-referenced IPR petition seeks review of U.S. Patent No.
`
`RE42,678 (“the ‘678 Patent”), Ex. 1001. U.S. Application No. 09/938,426, now
`
`U.S. Patent No. 6,625,346, was filed on August 23, 2001, and claims priority to
`
`U.S. Provisional Application No. 60/277,217, filed on March 19, 2001. U.S.
`
`Patent No. RE39,397, filed on December 31, 2004, is a reissue of U.S. Patent No.
`
`6,625,346. The ‘678 Patent, filed on June 15, 2010, is a reissue of U.S. Patent No.
`
`RE39,397. I understand that the ‘678 Patent is currently assigned to Capella
`
`Photonics, Inc. (“Capella”).
`
`20. The technology related to the claims of the ‘678 Patent has
`
`applications in fiber optic communications as, for example, switches, filters, and
`
`attenuators.
`
`21.
`
`Jeffrey P. Wilde and Joseph E. Davis are listed as the inventors for the
`
`‘678 Patent.
`
`III. LIST OF DOCUMENTS CONSIDERED IN FORMULATING MY
`OPINION
`
`22.
`
`In formulating my opinion, I have considered all of the following
`
`documents:
`
`Exhibit
`
`
`
`Description
`
`7
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-10
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`Ex. 1001 U.S. Patent No. RE42,678 to Chen et al.
`
`Ex. 1002 U.S. Patent No. 6,498,872 to Bouevitch et al.
`
`Ex. 1003 Prosecution History for U.S. Patent No. RE42,678.
`
`Ex. 1004 Joseph E. Ford et al., Wavelength Add-Drop Switching Using Tilting
`Micromirrors, 17(5) Journal of Lightwave Technology 904 (1999).
`
`Ex. 1005 U.S. Patent No. 6,442,307 to Carr et al.
`
`Ex. 1006 U.S. Patent No. 6,625,340 to Sparks et al.
`
`Ex. 1007 U.S. Patent Publication No. 2002/0081070 to Tew.
`
`Ex. 1008 U.S. Provisional Patent Application No. 60/250,520 to Tew.
`
`Ex. 1011 J. Alda, “Laser and Gaussian Beam Propagation and Transformation,”
`in Encyclopedia of Optical Engineering, R. G. Driggers, Ed. Marcel
`Dekker, 2003, pp. 999–1013. (“Alda”)
`Ex. 1012 Joint Claim Construction and Prehearing Statement, Capella
`Litigation, Case No. 3:14-cv-03348-EMC, Dkt. 151.
`Ex. 1013 Newton’s Telecom Dictionary (17th ed. 2001) (excerpted).
`
`Ex. 1014 Fiber Optics Standard Dictionary (3rd ed. 1997) (excerpted).
`
`Ex. 1015 Webster’s New World College Dictionary (3rd ed. 1997) (excerpted).
`
`Ex. 1018 U.S. Patent No. 6,253,001 to Hoen.
`
`Ex. 1019 U.S. Patent No. 6,567,574 to Ma et al.
`
`Ex. 1020 U.S. Patent No. 6,256,430 to Jin et al.
`
`Ex. 1021 U.S. Patent No. 6,631,222 to Wagener et al.
`
`Ex. 1022 U.S. Patent No. 5,414,540 to Patel et al.
`
`Ex. 1023 U.S. Patent Publication No. 2002/0097956.
`
`Ex. 1024 Shigeru Kawai, Handbook of Optical Interconnects (2005) (excerpted).
`
`
`
`8
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-11
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
`
`Ex. 1025 U.S. Patent No. 6,798,992 to Bishop et al.
`
`Ex. 1026 Joseph W. Goodman, Introduction to Fourier Optics, Second Edition,
`McGraw-Hill (1996).
`Ex. 1027 U.S. Patent No. 6,204,946 to Aksyuk et al.
`
`Ex. 1028 L.Y. Lin, “Free-Space Micromachined Optical Switches for Optical
`Networking, IEEE Journal of Selected Topics In Quantum
`Electronics,” Vol. 5, No. 1, pp. 4–9, Jan./Feb. 1999.
`
`Ex. 1029 S.-S. Lee, “Surface-Micromachined Free-Space Fiber Optic Switches
`With Integrated Microactuators for Optical Fiber Communications
`Systems,” in Tech. Dig. 1997 International Conference on Solid-State
`Sensors and Actuators, Chicago, June 16-19, 1997, pp. 85–88.
`Ex. 1030 H. Laor, “Construction and performance of a 576×576 single-stage
`OXC,” in Tech. Dig. LEOS ’99 (vol. 2), Nov. 8–11, 1999, pp. 481–482.
`
`Ex. 1031 R. Ryf, “1296-port MEMS Transparent Optical Crossconnect with 2.07
`Petabit/s Switch Capacity,” in Tech. Dig. OSA Conference on Optical
`Fiber Communication, March 2001, pp. PD28-1–PD28-3.
`Ex. 1032 A. Husain, “MEMS-Based Photonic Switching in Communications
`Networks,” in Tech. Dig. OSA Conference on Optical Fiber
`Communication, 2001, pp. WX1-1–WX1-3.
`Ex. 1033 U.S. Patent No. 5,661,591 to Lin et al.
`
`Ex. 1034 H. Laor et al., “Performance of a 576×576 Optical Cross Connect,”
`Proc. of the Nat’l Fiber Optic Engineers Conference, Sept. 26-30,
`1999.
`Ex. 1035 V. Dhillon. (2012, Sep. 18). Blazes and Grisms. Available:
`http://www.vikdhillon.staff.shef.ac.uk/teaching/phy217/instruments/ph
`y217_inst_blaze.html. (“Dhillon”)
`Ex. 1036 Fianium Ltd. WhiteLase SC480 New Product Data Sheet. Available:
`http://www.fianium.com/pdf/WhiteLase_SC480_BrightLase_v1.pdf.
`(“Fianium”)
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`
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`
`
`9
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-12
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`I have reviewed the substance of the Petition for inter partes review
`
`23.
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`submitted with this Declaration (and I agree with the technical analysis that
`
`underlies the positions set forth in the Petition).
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`IV. TECHNICAL BACKGROUND
`A. Optical switching for telecommunications
`Fiber cross-connects
`1.
`
`24. Optical fiber network systems most preferably have a flexible
`
`capability of provisioning so that bandwidth may be reconfigured to accommodate
`
`changes in demand or to recover from faults.
`
`25. At the coarsest level of network provisioning, links originating at
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`various geographic locations and entering a service facility may be selectively
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`interconnected with each other to allocate entire fiber paths to link locations. A
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`traditional way to implement this function is by means of a patch panel, an
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`example of which is pictured below, whereby fibers from various geographic
`
`locations may be connected by installing short patch cables manually.
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`
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`
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`10
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-13
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`If such changes are frequent, however, the cost and delay of “truck rolls” to bring
`
`technicians to service facilities may become onerous. Therefore, an automated
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`means for whole-fiber provisioning is desirable.
`
`26. The graphic below shows a possible arrangement for what is called a
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`space-division switch, or space switch, using arrays of computer-controlled
`
`mirrors, that implements the same function as a patch panel.1
`
`
`27. Such a switch may be referred to as an optical cross-connect (OXC).
`
`In operation, the optical signal from an input fiber is collimated by means of a lens
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`and continues in the form of a pencil-like beam to a dedicated mirror in a first
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`array. The mirror tilt is adjusted to point the reflected beam at the mirror
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`corresponding to the desired output fiber. The second mirror is adjusted to point
`
`
`1 It is desirable for a switch to be bidirectional, i.e., for signals to be routed reliably
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`from “outputs” to “inputs” as well as from “inputs” to “outputs.” This can
`
`generally be achieved with suitable engineering.
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`
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`11
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-14
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`its reflected beam so that it couples into the output fiber through its collimator.
`
`While two separate mirror arrays are shown in the graphic above, the same concept
`
`may be implemented with a single mirror array. Because the mirrors are under
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`computer control, no trucks need roll, and network operational costs can be
`
`reduced.
`
`2. Wavelength switches
`28. The granularity of such provisioning is coarse—a single fiber may
`
`carry multiple terabits per second (Tb/s) in each direction—and it is desirable to be
`
`able to allocate smaller chunks of bandwidth among fibers.
`
`29.
`
` Wavelength-division multiplexing (WDM) is used to impress multiple
`
`Tb/s of information onto a single fiber. This is done by dividing the spectrum of
`
`light into wavelength channels, each of which is capable of carrying distinct
`
`information. Because power in different channels does not overlap in wavelength,
`
`a single channel or set of channels may be split off—demultiplexed— from a fiber
`
`by means of wavelength filtering. Many optical techniques for wavelength
`
`selectivity have been employed for wavelength multiplexing and demultiplexing.
`
`Gratings capable of dispersing light by wavelength have been used in this regard to
`
`create devices that can add (or drop) wavelengths or groups of wavelengths to (or
`
`from) a fiber. If individual wavelength channels can be reallocated among fibers,
`
`provisioning can be effected with a granularity of tens of Gb/s.
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`
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`12
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-15
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`30. Prior to the alleged invention, it was known to implement wavelength
`
`control in a space switch to effect wavelength provisioning in a remotely
`
`controllable fashion. This can be done by using space switches in conjunction with
`
`wavelength multiplexers and demultiplexers. In the exemplary system shown in
`
`the graphic below, for example, a demux element places each wavelength channel
`
`from a WDM input port onto a distinct optical path. Then, space switches are used
`
`to send each wavelength to a desired destination port. Multiple wavelengths
`
`intended for a destination port are combined by a mux element. Multiplexing and
`
`switching functions can be implemented in various ways.
`
`
`
`Free-space optical systems
`
`B.
`31. The art discussed in this Declaration employs optical architectures
`
`based at least in part on free-space propagation, i.e., optical propagation that is not
`
`
`
`13
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-16
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`confined to a fiber or other kind of waveguide. It is useful to understand the
`
`principles by which such systems function.
`
`Basic properties of lenses
`
`1.
`32. Focusing elements such as lenses and concave mirrors are long-
`
`known components of free-space optical systems. They groom light emerging
`
`from fibers, and they also operate on image fields bearing many independent
`
`channels of light.
`
`33. The illustration below highlights certain properties of ideal, thin
`
`lenses that are exploited in free-space systems. At left is a ray optics picture of
`
`propagating beams. An ideal lens is characterized by its focal distance f.
`
`
`
`Rays originating at a focal point (a distance f from the lens center along its axis)
`
`are transformed to horizontal rays on the other side of the lens. But also, rays
`
`originating at a common point anywhere in a focal plane all are transformed to
`
`parallel rays on the other side of the lens. The rays’ common direction may be
`
`found by tracing the ray passing through the lens center, which is not deflected.
`
`
`
`14
`
`Petitioner Ciena Corp. et al.
`Exhibit 1039-17
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`Note that there are no arrows in the ray diagrams to indicate propagation direction:
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`because of the principle of reciprocity, the ray diagrams may be interpreted either
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`for light traveling generally left-to-right or right-to-left. Thus, rays arriving in a
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`common direction also are transformed to pass through the focal plane at a
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`common point. These basic phenomena underlie the imaging properties of lenses.2
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`34. The image at right in the illustration above shows qualitatively how
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`beams having lateral extent are transformed by lenses. A collimated beam (one
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`having flat wavefronts) many wavelengths in diameter remains substantially
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`collimated until the lens transforms it into a converging beam that attains its
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`minimum spot size in the focal plane, which size may be of the order of a few
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`wavelengths. Reciprocally, a diverging beam emerging, e.g., from a cleaved,
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`single-mode fiber end in the focal plane, is collimated by the lens. Note that the
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`paths of the extended beams’ central axes are the same as in the simple ray picture
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`2 Single-lens imaging is often depicted as illustrated below, according to the
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`equation 1/S1 + 1/S2 = 1/f:
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`15
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-18
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`of lens behavior.3
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`2. Gaussian light beams
`35. Gaussian beams are solutions of a useful approximation to the
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`electromagnetic wave equation and are important in the field of optical switching.
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`A radially symmetric Gaussian beam g with waist radius w0 has a field profile at its
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`waist (narrowest point) of the form
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`𝑔(𝑥,𝑦)=𝑒−𝑟2/𝑤02= 𝑒−(𝑥2+𝑦2)/𝑤02
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`The waist radius w0 is the radius r at which the field amplitude takes on 1/e (i.e.,
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`about 37%) of its peak value. The plots below show such a radially symmetric
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`Gaussian profile:
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`The plot below shows a snapshot of the oscillatory field (red for positive, blue for
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`negative) in the vicinity of the waist of a radially symmetric Gaussian beam. The
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`3 The colors in the above diagram are provided for illustration only, and are not
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`meant to convey wavelength information. The focal distance of actual physical
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`lenses may vary non-negligibly with wavelength.
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`16
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-19
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`plot would look the same along a y–z section. It is apparent that the wavefront is
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`flat only at the waist, and exhibits converging or diverging behavior elsewhere.
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`x
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`z
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`The divergence angle of the beam as it propagates past its waist depends on the
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`optical wavelength and on the waist radius:
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`So, for a given wavelength, the divergence angle is practically inversely
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`proportional to the waist radius.
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`36. Lenses alter optical beams by imposing spatially varying delays on the
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`wavefronts incident upon them. The graphic below shows a diverging Gaussian
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`beam being substantially collimated by a converging lens:
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`17
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-20
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`The thick part of the lens at its axis delays light more than the thinner parts away
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`from the axis, and reduces the curvature of the phase fronts of the beam. A beam
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`diverging less as it approached the lens from the left would emerge from the lens
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`as a converging beam.
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`37. Radially symmetric Gaussian beams are not the most general type of
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`Gaussian beam. Gaussian beams can have elliptical cross section, and beam waists
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`in orthogonal directions may occur at different positions along the propagation
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`direction. A general treatment of Gaussian beams is found in Alda. Ex. 1011.
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`3.
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`The “Fourier lens”
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`38. The designation “Fourier lens” or “Fourier transform lens” is
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`commonly used in the art to refer to lenses that convey multiple information beams
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`within a system and are used to perform certain tasks. This designation arises from
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`a connection between lens phenomenology and the theory of Fourier signal
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`analysis.4
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`4 This correspondence is elucidated in Ex. 1026.
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`18
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-21
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`39. A useful consequence of this connection is routinely expressed as the
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`rule that lenses “transform angles to displacements and displacements to angles.”
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`This behavior can be observed in the above ray-optics illustration of light
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`propagating between the focal planes of a lens. The graphic below depicts the
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`“angles to displacements” principle more generally, in three dimensions:
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`y
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`x
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`y
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`x
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`z
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`Beams (depicted as rays for clarity) can be incident on the lens at any angle to its
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`axis (the z-axis in the graphic) and in any direction in the x–y plane.5 In the focal
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`plane behind the lens, a beam is seen to be displaced in the x–y plane in the same
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`direction as its angular tilt before traversing the lens, and by an amount
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`5 Rays lying strictly in the x–z or y–z planes are shown for the sake of clarity.
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`19
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-22
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`corresponding to the magnitude of the tilt. Consequently, a beam can be directed
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`to pierce the rear focal plane of the lens at any point, by controlling its angular
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`attitude in two directions.
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`Concave mirrors as focusing elements
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`4.
`40. Concave mirrors as well as positive lenses may be employed as
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`focusing elements (and Fourier transforming elements) in free-space optical
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`systems. The illustration below shows both a converging lens and a focusing
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`mirror having a common focal length f. Similarly to the lens, the mirror causes
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`parallel incident rays to converge to a common point on a focal plane; the fact that
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`incident and reflected light beams propagate on the same side of the mirror can be
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`an advantage in system design.
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`5. Wavelength-dispersive elements
`41. As noted above, it was known to employ dispersive elements such as
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`gratings in free-space systems to separate individual wavelength channels from a
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`WDM signal, so that they could be treated independently. The graphic below
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`shows both a prism and a grating that perform this function:
`20
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`Petitioner Ciena Corp. et al.
`Exhibit 1039-23
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`Inter Partes Review of USPN RE42,678
`Corrected Declaration of Timothy J. Drabik, Ph.D.
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`The prism deflects light because the thin end imposes a smaller delay on a light
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`wave passing through it than the thick end. But also, in terms of oscillation periods
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`of the optical field, a given time delay represents more cycles of short-wavelength
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`(e.g., blue) light than of long-wavelength (red) light. Thus, a prism deflects sho