review on acoustic metamaterials

Review on acoustic metamaterials José Sánchez-Dehesa

Wave Phenomena Group , Universitat Politècnica de València, Camino de vera s.n., ES-46022 Valencia, Spain

Outline 1. Introduction 2. Acoustic metamaterials with negative mass density and density-near-zero 3. Acoustic metamaterials with negative bulk modulus 4. Acoustic metamaterials with double negative parameters 5. Acoustic metamaterials with inhomogeneous and anisotropic mass density 6. Mechanical metamaterials 7. Summary

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

03/31

ρeff (ω), Beff(ω)

Acoustic metamaterials / metafluids

Acoustic metamaterials are artificial structures made of subwavelength units such that their acoustic properties are NEW in comparison with that of the building units

λb>> a,d

d a

(ρb ,Bb) (ρin(ω) ,Bin(ω))

Homogenization

Acoustic metamaterials

ρeff

Beff

ρeff >0 Beff >0

ρeff <0 Beff >0

ρeff <0 Beff <0

(Monopolar +dipolar Resonances)

ρeff >0 Beff <0

(Monopolar resonances)

(Dipolar resonances) (No resonances)

Li and Chan, PRE (2004)

ρeff ≈0

(Monopolar resonances)

Acoustic metamaterials / Metafluids

Beff

ρeff >0; Beff >0 ρeff <0

(Dipolar resonances)

ρeff <0 Beff <0

(Monopolar + dipolar

Beff <0

(Monopolar resonances)

Torrent & JSD, PRL (2010)

N. Fang et al. Nat. Mat (2006) S.H. Lee et al. PRL (2010)

Z. Yang et al. PRL (2008) ρeff

Side holes

Membranes

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

06/31

Amplification of Acoustic Evanescent Waves using Metamaterial Slabs with ρ<0: Park et al., PRL (2011)

Membrane-Type Acoustic Metamaterial with ρ<0: Zhang et al., PRL (2008)

Dark acoustic metamaterials as super absorbers for low-frequency sound: Mei et al. Nat. Commun (2014)

SAMPLE MEASURED ABSORTION COEFFICIENT

Metamaterials consisting of arrays of membranes can stop sound at the resonant frequencies of the membranes. In order to broaden the effect Mei and coworkers have considered complex structures having hybrids resonaces:

Acoustic cloaking by a near-zero-index phononic crystal: Zheng et al. APL (2013)

0 ;00 <≈< mm Bρ ∞→=m

mm

Bcρ

0≈mn

Z 2b

2 =≈= bbmmm BBZ ρρ 1≈xikme

• Power splitters • Perfect transmission through waveguides with sharp corners

Applications of ρ≈0 metamaterials: Graciá-Salgado et al., PRB (2013)

Control of the radiation pattern

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

11/31

3. Acoustic Metamaterials with negative bulk modulus (1D)

N. Fang et al., Ultrasonic metamaterials with negative bulk modulus, Nat. Mat. 5, 452 (2006)

1D waterfilled waveguide

Effective modulus:

where Γ is the dissipation loss in the HR:

Γ =2π×400Hz

Acoustic Metamaterials with negative bulk modulus (1D)

•C. Ding et al., Acoustic metamaterial with negative modulus, J. Appl. Phys. 108, 074911 (2010)

•S.H. Lee et al., Acoustic metamaterial with negative modulus, J. Phys.: Cond. Matt., 21, 17504 (2009)

Split hollow sphere (SHS)

1D air waveguide where γ =2π×54Hz

Acoustic Metamaterials with negative Bulk modulus (2D) 2D Waveguide (h) + cylindrical holes (R, L)

holes with R=1 cm, L=9 cm, a=3cm 2D waveguide with h= 5 cm

hexagonal lattice with parameter a

a

Negative bulk modulus (quasi-2D): theory vs experiment

Γ+−

−= −−

ωωωω

iFBBm 2

02

201

01 1

F+<< 100 ωωω

Following Fokin et al., PRB, 76, 144302 (2007)

Parameters: ω0=2π×874Hz; Γ=2π×3.4Hz

García-Chocano et al., PRB, 85, 184102 (2012)

Applications of negative Bulk modulus: Stopping sound in ducts

For a sample made of 7 layers (D=21.9 cm)

1020

2010

21

12xikxik

xikxik

ePePePePR −−

−−

−−

=

Dikxik

xikxik

ee

ePPT 0

30

2020 Re

2

3 −−

− −=

Bm<0

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

16/31

4. Acoustic MtM with double negative parameters

Coupled Membranes with double negative parameters: Yang et al., PRL (2013)

Lee et al., PRL (2010)

Side holes Membranes

4. Acoustic MtM with double negative parameters

𝑛𝑛 = − 𝜌𝜌𝐵𝐵�

Acoustic waves propagate with the wave vector reversed to the energy flow, and the refractive index n becomes negative, given by:

Double negative metamaterial

Without the Xtal

With the Xtal With n<0

Theory

a diverging ultrasonic beam becomes a narrow focal spot.

Yang et al., PRL (2004)

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

19/31

0.0 0.2 0.4 0.6 0.8 1.00.4

0.5

0.6

0.7

0.8

0.9

1.0

c ii/c b

Filling Fraction

cxx=cyy (Hex.) cxx ( b=a; Φ=450 ) cyy ( b=a; Φ=450 ) cxx ( b=2a; Φ=75º ) cyy ( b=2a; Φ=75º )

5. Acoustic MtM with inhomogeneous and anisotropic mass density

Components of the tensor of the effective speed of sound (Rigid cylinders)

12 −= ijij Bc ρρ/2 Bc =

Anisotropic: Isotropic:

a

b

φ x

y

Non-isotropic lattices:

MtM with (cylindrical) anysotropic mass density ρ(r, θ)>0

b

bbr

cc

c

hh

hh

cc

=

≤

+

+

=

θ

2

1

1

2 11

2

bb

br

c

hh

hh

cc

cc

≤

+

+

=

=

1

2

2

1 11

2θ

2 2 2 1 1 1 h1 h2

1

2

2

1

hh

=ρρBradley, JASA (1994)

Phys. Rev. Lett., 105, 174301 (2010)

Appl. Phys. Lett., 98, 244102 (2011)

Acoustic magnifying hyperlens based on anisotropic metamaterials: Li et al., Nat. Mater. (2009)

Hyperlens imaging at 6.6 kHz.

Gradient Index (GRIN) acoustic lenses for airborne sound in 2D

Hexagonal array of Al cylinders in air (a = 2cm)

Focusing at 4.5 kHz

Theory

Exp.

SOUND AMPLIFICATION (3.5 kHz-4.5 kHz)

Focusing at 3.5 kHz

Climente et al., APL (2010)

GRIN acoustic lenses for underwater operation

GRIN lens made of metal cylinders embedded in water

T. Martin et al., APL (2010)

(P/P0)2

Model

Exp.

Focusing at 20 kHz (λ≈4a)

Broadband Omnidirectional absorber: Acoustic black hole

Omnidirectional acoustic absorber (disipative core + GRIN shell)

Theory

Exp. Absorption

Experimental setup

Climente et al. APL 100, 144103 (2012)

Cloaks based on transformation methods

For airborne sound: Cummer & Schurig, NJP 9, 45 (2007) 2D H. Chen and C.T. Chan, APL (2007) 3D S.A. Cummer et al, PRL (2008) 3D

b

b

br

BRr

rR

RRrB

rRrr

Rrrr

1

2

2

12

2

1

)(

)(

)(

−

−=

−=

−=

ρρ

ρρ

ϑ

2D cloaks for underwater operation [Zhang, Xia & Fang, PRL (2011)]

Ground cloaks based on anisotropic MtM

D/d=0.32; t/d=0.25; t/λ=0.01 (3kHz)

9/33

D=1.6mm; d=5mm; t=1mm

Popa, Zigoneanu & Cummer, PRL, 106, 253901 (2011) 2D ground cloak:

3D ground cloak: Zigoneanu. Popa & Cummer, Nat. mat., 3901 (2014) D=1.7mm; d=5mm; t=1.6mm

D/dx=0.34; t/dx=0.32; t/λ=0.01 (3kHz)

Review on Acoustic Metamaterials

OUTLINE

1. Introduction

2. Acoustic metamaterials with negative mass density and density near zero

3. Acoustic metamaterials with negative bulk modulus

4. Acoustic metamaterials with double negative parameters

5. Acoustic metamaterials with inhomogeneous and anisotropic mass density

6. Mechanical metamaterials

7. Summary

28/31

• Controlling flexural waves: Elastic cloaking in thin plates

Stenger et al., PRL108, 014301 (2012).

7. Mechanical Metamaterials

Normal displacement W(x, y; t)

An elasto-mechanical “unfeelability” cloak: Bückman et al, Nat. Comunn (2014)

Elasto-mechanical measurements

Reference

Obstacle

Cloak

22×22×0.17 mm

4. Summary

A review has been presented on Acoustic Metamaterials

These artificial structures have properties that are unusual in natural material

Their extraordinary properties can be employed to develop amazing acoustic devices: Acoustic cloaks, acoustic hyperlenses, Gradient index lenses, acoustic black holes, negative refraction, etc.

Mechanical metamaterials are the next problem to tackle. They are very

promising to get new devices in the elasticity domain.

Thanks for your attention!