Towards the Full Control of Elastic Waves propagation.pdf

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Phononic Crystals:

Towards the Full Control of Elastic Waves propagation

José Sánchez-DehesaWave Phenomena Group, Department of Electronic Engineering,

Polytechnic University of Valencia, SPAIN .

OUTLINE

1.

Introduction

2. Wave propagation through phononic crystals

3. Refractive devices based on phononic crystals: lenses

4.

Focusing of waves by negative refraction

5. Acoustic metamaterials: molding the propagation of sound

6. Inverse design of phononic devices

7. Conclusion



Phononic Crystals

periodic elastic media

with phononic band gaps: “vibration insulators”

2-D

periodic intwo directions

3-D

periodic inthree directions

1-D

periodic inone direction



Sonic Crystals

periodic media in which one material (at least!) is a fluid or gas

with sonic band gaps: “sonic insulators”

2-D

periodic intwo directions

3-D

periodic inthree directions

1-D

periodic inone direction

FluidFluid Fluid



3D Pho to nic C rysta l with De fe c ts

can trap vibration (sound) in cavities and waveguides (“wires”)

Defects in Phononic/Sonic CrystalsPeriodic elastic composites



2D Phononic/Sonic Crystals

MicroSource

Sample

R. Martinez-Sala et al . Nature (1995)



Phononic/Sonic Crystals: Practical realizations

1D2D3D

Science, 289, 1739 (2000) PRL, 80, 5325 (1998) PRL, 98, 134301 (2007)



1. Introduction

2. Wave propagation through phononic crystals

3.

Refractive devices based on phononic

crystals: lenses

4. Focusing of waves by negative refraction

5. Acoustic metamaterials: molding the waves

6. Inverse design of phononic devices

7. Conclusion



Sound waves in air

)(~),( t xk iet x p ω −⋅

k c

=ω

k

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SURPRISES OF PERIODICITY

Bloch wave

( ))(),( x pet x p k

t xk i

ω −⋅

= periodic “envelope”Plane wave

k c

≠ω )(k

ω



SOUND PROPAGATION TROUGH PHONONIC CRYSTALS

f=0.4

f=0.25

Complete bandgap

Partial bandgap

(pseudogap)

ω(k )



Sound attenuation by phononic crystals

PRL, 80, 5325 (1998)

Noise barriers based on

phononic crystals

Only 3 rows are enough to efficiently

reduce the traffic noise

!!



PHONONIC CRYSTALS :

PERIODIC COMPOSITES with SONIC/ELASTIC BANDGAPS

Possible applications

- filters

- vibration/sound insulation

- waveguides for vibrations/sound



0 5 10 15 20

-10

-5

0

5

10

15

20

25

Γ J

Γ X

Frequency (kHz)

A t t e n u a t i o n ( d B )

Hexagonal

ΓJ

ΓX

0 5 10 15 20

-15

-10

-5

0

5

10

15

20

25

30

35

ΓX

ΓJ

Frequency (kHz)

A t t e

n u a t i o n ( d B )

ΓX

ΓJ

honeycomb

Attenuation of surface elastic waves (earthquakes)

by phononic crystals

PRB, 59, 12169 (1999)



1. Introduction2. Wave propagation through phononic crystals

3.


crystals: lenses


5. Acoustic metamaterials: molding the waves

6.

Inverse design of phononic

devices

7. Conclusion



HOMOGENIZATION = LIMIT 0

Effective

medium

>> a

a

k ceff =ω

ω ⎟ ⎠ ⎞⎜

⎝ ⎛ =

→ k c

k eff

ω

0lim

k



0,0 0,1 0,2 0,3 0,4

250

300

350

0 1 2 3 4

Rod diameter (cm)

S o u n d v e l o c i t y ( m / s )

Filling fraction ( f )

Hexagonal lattice (a=6.35)

Sound

propagation

trough

lattices

of

solid

cylinders

in air

ceff

=cair

/ n ≈

cair

/√(1+ f)

PRL, 88, 023902 (2003)



Refractive devices based on PHONONIC CRYSTALS: lenses

Why optical lenses are possible?

a)

Light velocity is lower in solids

than in air: c solid < c air (nsolid

> nair

)

b) Dielectric materials exist thatare transparent to light :

nsolid

≈

nair

f

Why sonic lenses did not exist?

a)

Sound velocity is larger in solids

than in air:vsolid

< vair

(≈340 m/sec))

b) Solids materials are not transparentto sound:

Zsolid

>>

Zair



PHONONIC CRYSTALS make sonic lenses possible

Why?

a) Sound

propagtion

inside

the

PC is

lower

than

in air: vSC

< vair

b) They are almost transparent to sound (low reflectance at the

air/PC interface): ZSC

≈

Zair

S f



4550

5550

4540

60

0 50 100 150 200 250 3000

20

40

60

80

100

120

25262627272828292930303131323233333434353536363737383839394040414142424343444445454646474748484949505051515252535354545555565657575858595960606161

X Axis (cm)

Y A x i s ( c m )

61 dB

25 dB

4550

50

0 50 100 150 200 250 3000

20

40

60

80

100

120

Y A x i x ( c m )

25262627272828292930303131323233333434353536363737383839394040414142424343444445454646474748484949505051515252535354545555565657575858595960606161

X Axis (cm)

61 dB

25 dB

Acoustic lenses in the audible based on PHONONIC CRYSTALS

PRL, 88, 023902 (2003)



Phononic

crystals made of mixing two different elastic materials in air

Refractive device proposed:

A gradient index sonic lens

New J. Phys. 9, 323 (2007)




3.


crystals: focusing


5. Acoustic metamaterials: manipulation of waves

6.


devices

7. Conclusion



PHONONIC CRYSTALS also present “negative refraction”

S f

Positive refraction

S f

Negative refraction

≈

a >>

a



Imaging and focusing of water waves by negative refraction

Exp.

Simulations

Point source

PRE, 69, 030201 (2004)



Sound focusing by 3D phononic

crystal

0.8 mm diameter WC beads in water

fcc

(111)

Point source

PRL, 93, 024301 (2004)

Negative refraction

and focusing by a

3D phononic crystal

demonstrated!




3.


crystals: lenses


5. Acoustic metamaterials: manipulation of waves

6.


devices

7. Conclusion



Photonic/Sonic crystals Acoustic metamaterials

λ≈a λ>>a

band structure descriptionEffective medium description

Negative refraction

and other

band structure effects

Bragg scattering

Positive acoustic parameters Negative acoustic parameters

Positive refraction,

acoustic-like behavior

with unusual parameters by using

solid structures...

Negative group

velocity, negative

refraction,subwavelength

imaging...

HomogenizationResonances of

building blocks



Acoustical metamaterials

• Wave transport is controlled by only two parameters: ρ, K • Resonances can make one or both negative

•

If only one is negative→ forbidden propagation

• If both are negative→ propagation is allowed with negative

group velocity, negative refractive index



Negative mass materials (attenuation of low frequency sound!)

Metal spheres coated with Silicon

rubber embedded in a epoxy matrix

Science, 289, 1739 (2000) Negative mass obtained by a (dipolar) resonance



Negative effective modulus obtained by (monopolar) resonances

in 1D array of subwavelength

Helmholtz resonators in water

Nat. Materials, 5, 452 (2006)

Group transit delay time

Negative group delay

•Group velocity antiparallel

to phase velocity



Negative K and Negative ρ

PRL 99, 093904 (2007)

Bubble-contained water spheres

+

Gold spheres coated with rubber (in a epoxy matrix)

Monopolar resonances

Dipolar resonances

Pass band

with negative

group velocity

W i l ti i



Wave manipulation using

acoustic metamaterials

Acoustic cloaking:- Inspired in the similar phenomenon already demonstrated for EM

waves

-

Principle like mirage

Guide the sound as desired

W i l ti i



Wave manipulation using

acoustic metamaterials

2D Acoustic cloaking

New J. Phys. 9, 45 (2007)

Acoustic metamaterial:

This region is invisible to sound!



Collimation of sound assisted by ASW

Nat. Photonics (2007)

Surface acoustic waves are possible

in corrugated surfaces:

λ>10a




3.


crystals: lenses


5. Acoustic metamaterials: manipulation of mechanical waves

6.


devices

7. Conclusion



PHONONIC CRYSTALS show astonishing properties

that can be use to construct a new generation of devices

to control propagation of mechanical waves

But....

Optimization algorithms (Inverse design) can be

used to create new functionalities by using the

Phononic Crystals as starting structures




devices

Wave source(s) Material dist.(m) Observabledata d=[G(m)]sPerformanced=[G(m)]s



Scattering Acoustical Elements

(SAE)G(m) =

E1

(m1

,m2

,m3

) + E2

(m1

,m2

,m3

) + E3

(m1

,m2

,m3

)

Controlling the multiple scattering of waves!

The inverse problem is solved through optimization



Inverse Design-Tool

Direct Solver – Multiple Scattering Theory

• Semi analytical

• Fast

Optimization Method – Genetic Algorithm

• Great history

• Easy implementation



Inverse design of flat acoustic lens

Functionality: sound focusing at selected wavelengths

0,8

0,6

0,4

0,2

0,0

Y - A x i s ( m )

0,8

0,6

0,4

-0,6 -0,4 -0,2 0,0 0,2 0,4 0,6

X-Axis (m)

(b)

(a)

-9,0-8,0-7,0

-6,0-5,0-4,0-3,0-2,0-1,001,02,0

3,04,05,06,07,08,0

APL, 86, 054102 (2005)



Inverse design of a sonicInverse design of a sonic demultiplexordemultiplexor

Functionality: spatial separation of several wavelengths

-0.4 0.0 0.4 0.8 1.2

-0.4

0.0

0.4

0.4 0.8 1.2 0.4 0.8 1.2

Y - a x i s ( m )

X-axis (m) X-axis (m) X-axis (m)

1500 Hz1600 Hz1700 Hz

-0.4 0.0 0.4 0.8 1.2

-0.4

0.0

0.4

0.4 0.8 1.2 0.4 0.8 1.2

X-axis (m)

Y - a x i s ( m )

X-axis (m)

X-axis (m) APL, 88, 163506 (2006)

Prediction

Experiment

Inverse design of highly directional



Inverse design of highly directional

sound sources

Theoretical prediction Practical realization

APL, 90, 224107 (2007).

Onmidirectional

point source



PHONONIC CRYSTALS is going to be a hot topic in thenext few years

Many device applications are expected fromPHONONIC CRYSTALS in acoustics, elasticity and.....optics

Thanks for your attention!Thanks for your attention!

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Towards the Full Control of Elastic Waves propagation.pdf