DanielTorrent,YabinJinandBahramDjafari-RouhaniRamónyCajalFellow

UniversitatJaumeI,CastellóndelaPlana(Spain)

ControlofLambWavesbyPhononicCrystalPlates

1.  Introduction2.  RefractiveDevicesfortheA0Mode

3.  ApplicationtotheControloftheS0Mode

4.  FullControlofLambWaves

DanielTorrent

î Vibration of Phononic Crystal Plates

Propagation:xaxis

u!≈ux x!

u!≈uz z!

u!≈uy y"!

ω ≈

cph

12kA2

ω ≈ cpks

ω ≈ cSHks

SymmetricmodeS

ShearmodeSH

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Anti-symmetricmodeA(Flexuralmode)

DanielTorrent

î Vibration of Phononic Crystal Plates

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DanielTorrent

î Vibration of Phononic Crystal Plates

Torrent,Pennec,Djafari-Rouhani,PRB(2014)

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EffectiveMediumTheoryforFlexrualWaves(A0Mode)

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î Vibration of Phononic Crystal Plates

DanielTorrent

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•  LuneburgandMaxwelllensrequirelessdemandingindexvariations

•  Thesetwodevicescanbedoneeasily•  Highfillingfractionsarerequirednearthe

centerofthelens

Luneburg: Maxwell:

î Vibration of Phononic Crystal Plates

DanielTorrent

DanielTorrent

î Vibration of Phononic Crystal Plates

LuneburgLensforFlexuralWaves

Torrent,Pennec,Djafari-Rouhani,JAP(2014)

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DanielTorrent

î Vibration of Phononic Crystal Plates

MaxwellLensforFlexuralWaves

Torrent,Pennec,Djafari-Rouhani,JAP(2014)

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DanielTorrent

2

,

12

p S

pA

v k

v hk

ω

ω

=

= ( )*

22* 1

bp

b b

EDvvρρ

=−

nS =

vp1

vp2

,nA2 =

vp1

vp2

h1

h2

h 1= h2nS

nA = nS

0

0.05

0.1

0.15

0.2

0.25

ωa/2π

c t

Holes Triangular Ra = 0.3a

0

0.05

0.1

0.15

0.2

0.25

ωa/2π

c t

Lead Triangular Ra = 0.3a

Γ XJ

î Vibration of Phononic Crystal Plates

CanwealsocontroltheS0mode?

Region1 Region2

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DanielTorrent

RefractivedevicesforboththeS0andA0modes

Jin,Torrent,Pennec,Pan,Djafari-Rouhani,JAP(2015)19/03/18

î Vibration of Phononic Crystal Plates

DanielTorrent

î Vibration of Phononic Crystal Plates

CanwealsocontroltheSH0mode?

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1 2 3 4 5nS

2

4

6

8

10

12

nSH

DanielTorrent

î Vibration of Phononic Crystal Plates

A0 ,S0 ,SH0

h0 ,Ra ,Rb

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DanielTorrent

x /a

y/a

S 0 mod e

−30 0 30

−30

0

30

x /a

SH 0 mod e

−30 0 30

−30

0

30

x /a

A 0 mod e

−30 0 30

−30

0

30

x /a

y/a

S 0 M od e

−22 0 22

−22

0

22

x/a

SH 0 M od e

−22 0 22

−22

0

22

x /a

A 0 M od e

−22 0 22

−22

0

22

S0 Mode

-22 0 22 x/a

-22

0

22

y/a

0 1

SH0 Mode

-22 0 22 x/a

-22

0

22

0 1

A0 Mode

-22 0 22 x/a

-22

0

22

0 1

x /a

y/a

S 0 M od e

−22 0 22

−22

0

22

x/a

SH 0 M od e

−22 0 22

−22

0

22

x /a

A 0 M od e

−22 0 22

−22

0

22

î Vibration of Phononic Crystal Plates

GRINLens LuneburgLens

MaxwellLens LN+LN+MX

Jin,Torrent,Pennec,Pan,Djafari-Rouhani,Sci.Rep(2016)

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DanielTorrent

î Vibration of Phononic Crystal Plates

1.  HomogenizationtheoryforFlexuralWaves,PRB(09-2014)

2.  RefractivedevicesfortheA0mode,JAP(12-2014)

3.  RefractivedevicesfortheA0andtheS0modes,JAP(06-2015)

4.  HomogenizationtheoryforBulkElasticWaves,PRB(11-2015)

5.  RefractivedevicesfortheA0,S0andtheSH0modes,Sci.Rep.(04-2016)

6.  BeamsplittersfortheA0,S0andtheSH0modes,AIPAdvances(12-2016)

7.  Invisiblelensforflexuralwaves,JPhysD.(05-2017)

8.  Analysisoftherobustnessoftopologicaledgestates,Submitted(2018)

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DanielTorrent

î Vibration of Phononic Crystal Plates

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