Computational Methods for Nanoscale Applications

543 Pages·2007·7.23 MB·English

by  Igor Tsukerman

Computational Methods for Nanoscale Applications
Nanostructure Science and Technology
SeriesEditor: DavidJ.Lockwood,FRSC
NationalResearchCouncilofCanada
Ottawa,Ontario,Canada
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(Continuedafterindex)
Igor Tsukerman
Computational Methods
for Nanoscale Applications
Particles, Plasmons and Waves
123
IgorTsukerman
DepartmentofElectrical
andComputerEngineering
TheUniversityofAkron
Akron,OH44325-3904
USA
[email protected]
SeriesEditor
DavidJ.Lockwood
NationalResearchCouncilofCanada
Ottawa,Ontario
Canada
ISBN:978-0-387-74777-4 e-ISBN:978-0-387-74778-1
DOI:10.1007/978-0-387-74778-1
LibraryofCongressControlNumber:2007935245
(cid:1)c 2008SpringerScience+BusinessMedia,LLC
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Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
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Cover Illustration: Real part of the electric field phasor in the Fujisawa-Koshiba photonic waveguide
bend.
From“ElectromagneticApplicationsofaNewFinite-DifferenceCalculus”,byIgorTsukerman,IEEE
TransactionsonMagnetics,Vol.41,No.7,pp.2206–2225,2005.
(cid:1)c 2005IEEE(bypermission).
Printedonacid-freepaper.
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To the memory of my mother,
to my father,
and to the miracle of M.
Preface
The purpose of this note ... is to
sort out my own thoughts ...
and to solicit ideas from others.
Lloyd N. Trefethen
ThreemysteriesofGaussianelimination
Nobody reads prefaces. Therefore my preference would have been to write a
shortonethatnobodywillreadratherthanalongonethatnobodywillread.
However, I ought to explain, as briefly as possible, the main motivation for
writing the book and to thank – as fully and sincerely as possible – many
people who have contributed to this writing in a variety of ways.
My motivation has selfish and unselfish components. The unselfish part is
to present the elements of computational methods and nanoscale simulation
to researchers, scientists and engineers who are not necessarily experts in
computersimulation.Iamhopeful,though,thatpartsofthebookwillalsobe
ofinteresttoexperts,asfurtherdiscussedintheIntroductionandConclusion.
The selfish part of my motivation is articulated in L. N. Trefethen’s quote
above. Whether or not I have succeeded in “sorting out my own thoughts”
is not quite clear at the moment, but I would definitely welcome “ideas from
others,” as well as comments and constructive criticism.
* * *
I owe an enormous debt of gratitude to my parents for their incredible
kindnessandselflessness,andtomywifeforherequallyincredibletoleranceof
my character quirks and for her unwavering support under all circumstances.
My son (who is a business major at The Ohio State University) proofread
partsofthebook,replacedcommaswithsemicolons,singlequoteswithdouble
quotes, and fixed my other egregious abuses of the English language.
VIII Preface
Overall, my work on the book would have been an utterly pleasant ex-
perience had it not been interrupted by the sudden and heartbreaking death
of my mother in the summer of 2006. I do wish to dedicate this book to her
memory.
Acknowledgment and Thanks
Collaboration with Gary Friedman and his group, especially during my
sabbatical in 2002–2003 at Drexel University, has influenced my research and
the material of this book greatly. Gary’s energy, enthusiasm and innovative
ideas are always very stimulating.
During the same sabbatical year, I was fortunate to visit several research
groups working on the simulation of colloids, polyelectrolytes, macro- and
biomolecules. I am very grateful to all of them for their hospitality. I would
particularly like to mention Christian Holm, Markus Deserno and Vladimir
Lobaskin at the Max-Planck-Institut fu¨r Polymerforschung in Mainz, Ger-
many; Rebecca Wade at the European Molecular Biology Laboratory in Hei-
delberg, and Thomas Simonson at the Laboratoire de Biologie Structurale in
Strasbourg, France.
Alexei Sokolov’s advanced techniques and experiments in optical sensors
and microscopy with molecular-scale resolution had a strong impact on my
students’andmyworkoverthelastseveralyears.IthankAlexeiforproviding
a great opportunity for collaborative work with his group at the Department
of Polymer Science, the University of Akron.
Inthecourseofthelasttwodecades,Ihavebenefitedenormouslyfrommy
communicationwithAlainBossavit(E´lectricit´edeFranceandLaboratoirede
Genie Electrique de Paris), from his very deep knowledge of all aspects of
computational electromagnetism, and from his very detailed and thoughtful
analysis of any difficult subject that would come up.
Isaak Mayergoyz of the University of Maryland at College Park has on
many occasions shared his valuable insights with me. His knowledge of many
areas of electromagnetism, physics and mathematics is very profound and
often unmatched.
My communication with Jon Webb (McGill University, Montr´eal) has al-
ways been thought-provoking and informative. His astute observations and
commentsmakecomplicatedmatterslookclearandsimple.Iwasverypleased
thatProfessorWebbdevoted partofhissabbatical leavetoourjointresearch
on Flexible Local Approximation MEthods (FLAME, Chapter 4).
Yuri Kizimovich (Plassotech Corp., California) and I have worked jointly
onavarietyofprojectsoverthelast25years.Hisoriginalthinkingandelegant
solutions of practical problems have always been a great asset. Yury’s help
and long-term collaboration are greatly appreciated.
Even though over 20 years have already passed since the untimely death
ofmythesisadvisor,Yu.V.Rakitskii,hisstudentsstillrememberverywarmly
Preface IX
his relentless strive for excellence and quixotic attitude to scientific research.
Rakitskii’smaincontributionwastonumericalmethodsforstiffsystemsofdif-
ferential equations. He was guided by the idea of incorporating, to the extent
possible,analyticalapproximations intonumericalmethods.Thisapproachis
manifest in FLAME that I believe Rakitskii would have liked.
My sincere thanks go to
• DmitryGolovaty(TheUniversityofAkron),forhishelponmanyoccasions
and for interesting discussions.
• Viacheslav Dombrovski, a scientist of incomparable erudition, for many
pearls of wisdom.
• Elena Ivanova and Sergey Voskoboynikov (Technical University of St.
Petersburg, Russia), for their very, very diligent work on FLAME.
• BenjaminYellen(DukeUniversity),formanydiscussions,innovativeideas,
and for his great contribution to the NSF-NIRT project on magnetic as-
sembly of particles.
• Mark Stockman (Georgia State University), for sharing his very deep and
broad knowledge and expertise in many areas of plasmonics and nano-
photonics.
• J. Douglas Lavers (the University of Toronto), for his help, cooperation
and continuing support over many years.
• Fritz Keilmann (the Max-Planck-Institut fu¨r Biochemie in Martinsried,
Germany), for providing an excellent opportunity for collaboration on
problems in infrared microscopy.
• BorisShoykhet(RockwellAutomation),anexcellentengineer,mathemati-
cian and finite element analyst, for many valuable discussions.
• Nicolae-Alexandru Nicorovici (University of Technology, Sydney, Aus-
tralia), for his deep and detailed comments on “cloaking,” metamaterials,
and properties of photonic structures.
• H.NealBertram(UCSD–theUniversityofCalifornia,SanDiego),forhis
support. I have always admired Neal’s remarkable optimism and enthusi-
asm that make communication with him so stimulating.
• Adalbert Konrad (the University of Toronto) and Nathan Ida (the Uni-
versity of Akron) for their help and support.
• Pierre Asselin (Seagate, Pittsburgh) for very interesting insights, particu-
larlyinconnectionwitha priori errorestimatesinfiniteelementanalysis.
• Sheldon Schultz (UCSD) and David Smith (UCSD and Duke) for famil-
iarizing me with plasmonic effects a decade ago.
I appreciate the help, support and opportunities provided by the Interna-
tional Compumag Society through a series of the International Compumag
Conferences and through personal communication with its Board and mem-
bers: Jan K Sykulski, Arnulf Kost, Kay Hameyer, Franc¸ois Henrotte, Oszk´ar
B´ıro´, J.-P. Bastos, R.C. Mesquita, and others.
A substantial portion of the book forms a basis of the graduate course
“Simulation of Nanoscale Systems” that I developed and taught at the
X Preface
University of Akron, Ohio. I thank my colleagues at the Department of Elec-
trical&ComputerEngineeringandtwoDepartmentChairs,AlexisDeAbreu
Garcia and Nathan Ida, for their support and encouragement.
My Ph.D. students have contributed immensely to the research, and their
work is frequently referred to throughout the book. Alexander Plaks worked
on adaptive multigrid methods and generalized finite element methods for
electromagneticapplications.LeonidProektwasinstrumentalinthedevelop-
ment of generalized FEM, especially for the vectorial case, and of absorbing
boundary conditions. Jianhua Dai has worked on generalized finite-difference
methods. Frantisek Cˇajko developed schemes with flexible local approxima-
tion and carried out, with a great deal of intelligence and ingenuity, a variety
of simulations in nano-photonics and nano-optics.
I gratefully acknowledge financial support by the National Science Foun-
dation and the NSF-NIRT program, Rockwell Automation, 3ga Corporation
and Baker Hughes Corporation.
NECEurope(SanktAugustin,Germany)providednotonlyfinancialsup-
port but also an excellent opportunity to work with Achim Basermann, an
expert in high performance computing, on parallel implementation of the
Generalized FEM. I thank Guy Lonsdale, Achim Basermann and Fabienne
Cortial-Goutaudier for hosting me at the NEC on several occasions.
A number of workshops and tutorials at the University of Minnesota in
Minneapolis1 have been exceptionally interesting and educational for me. I
sincerelythanktheorganizers:DouglasArnold,DebraLewis,CheriShakiban,
Boris Shklovskii, Alexander Grosberg and others.
IamverygratefultoSergePrudhomme,thereviewerofthisbook,formany
insightfulcomments,numerouscorrectionsandsuggestions,andespeciallyfor
his careful and meticulous analysis of the chapters on finite difference and
finite element methods.2 The reviewer did not wish to remain anonymous,
which greatly facilitated our communication and helped to improve the text.
Further comments, suggestions and critique from the readers is very welcome
and can be communicated to me directly or through the publisher.
Finally,IthankSpringer’seditorsfortheirhelp,cooperationandpatience.
1 Electrostatic Interactions and Biophysics, April–May 2004, Theoretical Physics
Institute.
Future Challenges in Multiscale Modeling and Simulation, November 2004;
New Paradigms in Computation, March 2005; Effective Theories for Materials
and Macromolecules, June 2005; New Directions Short Course: Quantum Com-
putation, August 2005; Negative Index Materials, October 2006; Classical and
Quantum Approaches in Molecular Modeling, July 2007 – all at the Institute for
Mathematics and Its Applications, http://www.ima.umn.edu/
2 Serge Prudhomme is with the Institute for Computational Engineering and Sci-
ences (ICES), formerly known as TICAM, at the University of Texas at Austin.