Phononic Crystals: Fundamentals and Applications

247 Pages·2016·11.316 MB·English

by  Abdelkrim Khelif, Ali Adibi (eds.)

Abdelkrim Khelif · Ali Adibi Editors
Phononic
Crystals
Fundamentals and Applications
Phononic Crystals

Abdelkrim Khelif • Ali Adibi
Editors
Phononic Crystals
Fundamentals and Applications
123
Editors
AbdelkrimKhelif AliAdibi
InstitutFEMTO-ST SchoolofElectricalEngineering
CentreNationaldelaRechercheScientifique GeorgiaInstituteofTechnology
BesançonCedex,France Atlanta,GA,USA
ISBN978-1-4614-9392-1 ISBN978-1-4614-9393-8 (eBook)
DOI10.1007/978-1-4614-9393-8
LibraryofCongressControlNumber:2015943375
SpringerNewYorkHeidelbergDordrechtLondon
©SpringerScience+BusinessMediaNewYork2016
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Preface
Phononiccrystals(PnCs)arenovelsyntheticperiodicmaterialsforcontrollingand
manipulating the propagation of elastic (or acoustic) waves. The periodic nature
of PnCs gives them novel properties that cannot be found in bulk materials. For
example,PnCs can exhibitacoustic (or phononic)bandgaps,which are frequency
rangesinwhichthepropagationofacousticwavesinsidethePnCisprohibited.The
additionofdefectstoaperfectPnCwithaphononicbandgapallowsforthedesign
ofdeviceslikewaveguidesandcavitiestocontrolthepropagationofacousticwaves
insidethebandgapandtoenablenovelfunctionalitiesinaverycompactstructure.
Imminent impact of PnCs is expected in the near future in applications like
wirelesscommunications,sensing,acousticsignalprocessing,andultrasoundimag-
ing. Novel devices (such as acoustic filters, resonators, sources and lenses) with
outstanding performance measures are being enabled by the use of PnCs. In
addition, the use of these structures to form acoustic metamaterials can uncover
noveleffectslikenegativerefraction,acousticinvisibility,orsuperlensing.This,in
turn,canenableresearcherstodesignfunctionalstructureswithsuchperformance
thatcannotbeobtainedwithconventionalacousticmaterials.
While the researchin the field ofphononiccrystalsandacoustic metamaterials
is at the early stages, their optical counterparts (i.e., photonic crystals) have
alreadybeendemonstratedtopossessuniquepropertiesthatarenotachievedusing
conventional bulk materials. The properties of photonic crystals have been the
subjectof intensiveinvestigationsin the last decade,and severalsuccessfulbooks
havebeen publishedto addresstheir uniquepropertiesand applications.Knowing
thatthe researchin PnCs is in its infancy,and moreattentionis givento this field
lately,thefieldisexpectedtoexpandconsiderablyinthenextfewyears.
The purpose of this book is to present a detailed overview of the state of the
fieldfrommaterial,device,andapplicationperspectives,andprovidethenecessary
toolsforresearcherstoexplorethefield.Toachievethisgoal,thisbookcoversthe
simulation,fabrication,andcharacterizationmethodsusedtodesignandexperiment
withPnCstothelevelthatisaccessibleforboththeexperiencedandbeginnerinthe
field.Thebookalsoreportsthemostimportantadvancesinthefieldinthelastfew
years.
v
vi Preface
The idea forthisbookfirst cameup in summer2009,wherewe co-chairedthe
first International Workshop on Photonic Crystals (Nice, France, 2009), in which
allexpertsinthefieldwereinvited.Theneedforanall-encompassingreferencein
thefieldofphononiccrystalswasrecognizedinthemeeting.Afterthatmeeting,we
spentanextensiveamountoftimelookingintotheneedsofthecommunitytoform
thestructureofthechaptersinthebookandtoconvincetheexpertsinthefield(who
wereamongtheparticipantsintheworkshop)towritetheirrespectivechapters.
The authors of these chapters are among the world leaders in their respective
fields with yearsof experiencein performingcutting-edgeresearch and educating
young scientists and engineers. In addition to presenting the landscape of the
research in this field, we hope that this book can provide interested readers with
an in-depth knowledge of the field. The individual chapters are written in such a
waythattheycanbeusedasthetextmaterialforenhancinggraduate-levelcourses
inmechanicalorelectricalengineeringdisciplines.
At the end of this journey, we would like to thank all those who helped us in
formingthisbookthroughtheirdiscussions,contributionstothebook,andreviews
of the different sections. We also like to thank the many researchers (students,
postdocs, members of technical staff, and professors) whose contributions are
coveredinthisbook.OurspecialthanksgotoDr.AliA.Eftekharforhiskeyrolein
formingtheideaofthebook,hishelpindefiningdifferentchapters,andhisexcellent
feedbackatdifferentstagesofformingthebook.
BesançonCedex,France A.Khelif
Atlanta,GA,USA A.Adibi
March2015
Contents
1 Introduction to Acoustics of Phononic Crystals.
HomogenizationatLowFrequencies...................................... 1
JoséSánchez-DehesaandArkadiiKrokhin
2 FundamentalPropertiesofPhononicCrystal ............................ 23
YanPennecandBahramDjafari-Rouhani
3 TheThree-DimensionalPhononicCrystals............................... 51
BadreddineAssouar,RebeccaSainidou,andIoannisPsarobas
4 ComputationalProblemsandNumericalTechniques
fortheAnalysisofPhononicCrystals ..................................... 85
VincentLaudeandAbdelkrimKhelif
5 PhononicCrystalMembranes(SlabsorPlates).......................... 109
SaeedMohammadiandAliAdibi
6 SurfaceAcousticWavesinPhononicCrystals............................ 145
Tsung-TsongWu, Jin-ChenHsu, Jia-HongSun,
andSarahBenchabane
7 OpticalCharacterizationofPhononicCrystals
intheTimeDomain.......................................................... 191
OsamuMatsudaandOliverB.Wright
8 OpticalCharacterizationofPhononicCrystals
intheFrequencyDomain ................................................... 215
KimmoKokkonen
9 FutureProspectsofPhononicCrystalsandPhononic
Metamaterials................................................................ 239
SaeedMohammadi,AbdelkrimKhelif,andAliAdibi
vii
Chapter 1
Introduction to Acoustics of Phononic Crystals.
Homogenization at Low Frequencies
JoséSánchez-DehesaandArkadiiKrokhin
1.1 Introduction
Light and sound are the two most important carriers of information for live
organisms.Historicallythenatureandcharacteristicsofsoundhavebeenunderstood
earlier than that of light because the progress in classical mechanics usually
advanced the progress in electrodynamics. This is not the case for the recently
emergedareasofphotonicandphononiccrystals.Inthelastdecadeofthetwentieth
centurytherewasaburstinstudyofphotoniccrystals—periodicdielectricstructures
which may provide much higher efficiency than the traditional optical devices in
generation,waveguiding,focusing,splitting, slowing down, etc. of light. The first
theoreticalpublicationsbyYablonovich[1]predictingsuppressionofspontaneous
emissioninsemiconductorsstructureswhereelectronandphotonbandgapsoverlap,
and by John [2] predicting easier localization of light near photonic band gap
were followed by first experimental realization of 3D photonic crystal with fcc
lattice possessing a gap in the microwave region [3]. Regular and intensive study
ofsoundwavesinperiodicelasticmediahasretardedbyafewyears,ascompared
to similar study of electromagnetic waves. The first phononic band structures for
two-dimensional lattices of solid cylinders in solid background were calculated
practicallysimultaneouslybySigalasandEconomou[4]andKushwahaetal.[5].
J.Sánchez-Dehesa((cid:2))
GrupodeFenómenosOndulatorios,DepartamentodeIngenieríaElectrónica,
UniversitatPolitècnicadeValència,CaminodeVeras/n,Valencia46022,Spain
e-mail:[email protected]
A.Krokhin
DepartmentofPhysics,UniversityofNorthTexas,1155UnionCircle#311427,
Denton,TX 76203,USA
e-mail:[email protected]
©SpringerScience+BusinessMediaNewYork2016 1
A.Khelif,A.Adibi(eds.),PhononicCrystals,DOI10.1007/978-1-4614-9393-8_1
2 J.Sánchez-DehesaandA.Krokhin
Fig.1.1 ThispieceofmodernartbyE.Sempererepresentsatwo-dimensionalphononiccrystal
ofsteelrodswithadiameterof2.9cmarrangedinasquarelatticewithaperiod10cm
Firstexperimentalmeasurementofsoundattenuationduetoperiodicityhasbeen
performedunderambientconditionsusingasculpturebyE.Sempere,exhibitedin
openairinMadrid,seeFig.1.1.
The transmission coefficient for sound waves propagatingperpendicularto the
rods exhibited a minimum around frequency of 1.67 kHz [6]. This minimum
was originally attributed to a phononic band gap. However, soon the exact band
structurecalculations[7] have shownthatthe observedattenuationis dueto a dip
minimum in the phononic density of states but not to a complete band gap. The
origin of the minimum is related to wave diffraction in the lattice, i.e. the waves
interference is mostly distractive at the frequency (cid:2)D1.67 kHz, while the waves
donotcompensateeachothercompletely,givingrisetolow (butfinite)densityof
states. Thus,instead of a fullgapwhere the densityof states vanishesexactly,the
structureinFig.1.1possessesapseudogap.Thefullgapopensforthefillingfraction
ofthecylinders—therelativeareaoccupiedbymetalintheplaneofperiodicity—
exceedingf D0:3[7].ThefillingfractionofthephononiccrystalshowninFig.1.1
ismuchlower,f D0:066.
Thefirstphononiccrystalspossessingafullbandgapwerereportedin1998.The
periodic structures were a square lattice of cylindrical holes drilled in aluminum
alloy plate and filled with mercury [8] and a square (and triangular) lattice of
metallic rods in air [9]. In the former case the gap for longitudinal elastic waves