review on acoustic metamaterials
TRANSCRIPT
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!