Advances in Acoustics Metamaterials and Acoustic Cloaks José Sánchez-Dehesa

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

Outline 1. Acoustic Metamaterials (MtM) with double negative parameters and ρ-near-zero 2. Acoustic cloaks based on Transformation Acoustics and Scattering Cancellation 3. Mechanical MtM: Controlling flexural waves propagating in thin plates 4. Mechanical MtM: Energy redirection by a metallic slit embedded in water 5. Summary

ARIADNA Mini-Workshop, Sept 24 1/24

OUTLINE

1. Acoustic Metamaterials with double negative parameter and ρ-near-zero (DNZ)

2. Acoustic cloaks based on Transformation Acoustics and Scattering Cancellation

3. Mechanical Metamaterials: Controlling flexural waves in thin metallic plates

4. Mecanical Metamaterials: Energy redirection by a metallic slit embedded in water.

5. Summary

02/24 ARIADNA Mini-Workshop, Sept 24 (2014)

d2

d1

Transversal section

Quasi-2D structure for double negative and ρ≈0 (DNZ ) behavior

Building unit

Scheme of the artificial structure

h

bbs ddd ρρρ 2

2

21 =+

=

Spiousas et al., APL (2011)

Quasi-2D structure for double negative and DNZ behavior

ω-L Phase diagram ω-Rb Phase diagram

L=3.5h; Ra=0.5Rb

As predicted by Li and Chan, PRE(2004)

ρm < 0

ρm < 0 Bm<0

Bm<0

( a ) a

Sample B a=21 mm Rb=7mm h=9mm L=2.5h

Sample A a=21 mm Rb=9.2mm h=9mm L=3.5h

Quasi-2D acoustic metamaterials: Practical realization

( a ) a

Sample B

Sample A

Quasi-2D acoustic metamaterials: Practical realization

Experimental characterization

Model

Double negative

Double negative

Bm<0

Bm<0

Bm<0

ρm < 0

ρm < 0

Gracia-Salgado et al., Phys. Rev. B 88, 224305 (2013)

ρ-near-zero (DNZ) metamaterials

0 ;00 <≈< mm Bρ ∞→=m

mm

Bcρ

0≈mn

Z 2b

2 =≈= bbmmm BBZ ρρ 1≈xikme

Transmission through narrow channels λ>>a

EM counterpart: Edwards et al., PRL 100, 033903 (2008) Liu et al., PRL 100, 023903 (2008)

OUTLINE

1. Acoustic Metamaterials with double negative parameter and ρ-near-zero (DNZ)

2. Acoustic cloaks based on Transformation Acoustics and Scattering Cancellation

3. Mechanical Metamaterials: Controlling flexural waves in thin metallic plates

4. Mecanical Metamaterials: Energy redirection by a metallic slit embedded in water.

5. Summary

08/24 ARIADNA Mini-Workshop, Sept 24 (2014)

Ground cloaks based on Transformation acoustics

3D Ground cloak with arbitrary surfaces: Kan, García-Chocano et al., (to be published)

Reduced cloak: ρǁ=1.2ρair, ρ┴=5.4ρair κs=1.2κair

Ideal cloak: ρǁ=0.47ρair, ρ┴=2.13ρair κs=0.47κair

FEM Simulations (ν=2.68kHz; t/λ=0.008)

d

t

D

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

15 cm

ARIADNA Mini-Workshop, Sept 24 (2014)

d2

d1

Transversal section

Empty elliptical pot (ν=2.68kHz)

Pot with object

Pot with object and cloak

Layers of perforated plates as ground cloaks Experimental setup

2D cloak based on scattering cancellation

• We propose to hide a rigid cylinder by means of a set of small rigid cylinders surrounding it.

• The cylinders have the same radius and their positions are obtained through an optimization procedure.

• The fitness function for this process is defined in terms of the scattering cross section σ

𝐹𝐹 = 1 −𝜎𝜎𝑐𝑐𝑐𝑐𝑐𝑐+𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝜎𝜎𝑐𝑐𝑐𝑐𝑐𝑐

Scattering cancellation 2D cloak

• Parameters: – R0 = 11.25cm – r = 7.5mm – 120 cylinders – Frequency of operation: 3kHz (λ

= R0). – Fitness function: F=0.977

• Theoretical simulation shows that the structure does not distort the impinging wave.

• In the experimental characterization the pressure field is measured in the area of 0.75×0.46 m2 behind the sample.

R0

2D cloak based on scattering cancellation

• Experimental results:

García-Chocano et al., APL 99, 074102 (2011)

3.00 3.02 3.04 3.06 3.08 3.10 3.120.0

0.1

0.2

0.3

0.4

0.5

0.6

Free space Object Cloak

Aver

aged

visi

bility

(γ)

Frequency (kHz)

𝛾𝛾 =1𝑁𝑁�

𝑃𝑃𝑚𝑚𝑐𝑐𝑚𝑚,𝑗𝑗 − 𝑃𝑃𝑚𝑚𝑖𝑖𝑖𝑖,𝑗𝑗

𝑃𝑃𝑚𝑚𝑐𝑐𝑚𝑚,𝑗𝑗 + 𝑃𝑃𝑚𝑚𝑖𝑖𝑖𝑖,𝑗𝑗𝑗𝑗

|P| Real(P) Free space

Cylinder

Cylinder with cloak

3D Cloak based on scattering cancellation • Parameters:

– 60 tori with minor radius 2.67mm. – Sphere with radius Rsph= 4cm. – Frequency of operation: f0=8.62kHz (Rsph= λ0)

• Fitness function F=0.978 (optimum value). • Range of operation (σs+cloak/ σsphere < 0.3):

– Bandwidth: 120Hz. – Angle of incidence: ±2.25º.

𝐹𝐹 = 1 −

𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠+𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝜎𝜎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

Sanchis et al., PRL. 110, 124301 (2013)

14/24

3D cloak: Experimental setup

• Acoustic field is recorded on three perpendicular planes • Each plane covers an area 0.2×0.2m2, with 5mm of resolution. • At each point a chirp in the range 7.5-9.5kHz was emitted,

received and processed.

Inside the anechoic room:

x y z

Free space Bare sphere

Sphere with cloak

Metamaterials 2013

Free space

Sphere with cloak

Bare sphere

OUTLINE

1. Acoustic Metamaterials with double negative parameter and ρ-near-zero (DNZ)

2. Acoustic cloaks based on Transformation Acoustics and Scattering Cancellation

3. Mechanical Metamaterials: Controlling flexural waves in thin metallic plates

4. Mecanical Metamaterials: Energy redirection by a metallic slit embedded in water.

5. Summary

18/24 ARIADNA Mini-Workshop, Sept 24 (2014)

( a ) a

ARIADNA Mini-Workshop, Sept 24 (2014)

Omnidirectional Insulating Device for Flexural Waves in thin plates Flexural waves are modeled by the Kirchoff-Love approximation. The vertical displacement W(x, y) is described by the equation:

Modulus of the vertical displacement W(x, y) without (c1) and with (c2) the absorptive material in the region 0.5≤ r/Rap≤ 0.75.

where RADIAL PROFILE

Climente et al., JAPL 114, 214903 (2013)

( a ) a

ARIADNA Mini-Workshop, Sept 24 (2014)

Gradient index lenses for flexural waves based on thickness variations

The local refractive index of the plate n(r, θ ) is associated to the plate thickness h(r, θ) by the expression

Luneburg Maxwell 90o rotating Eaton Concentrator

Climente et al., APL 105, 064101 (2014)

OUTLINE

1. Acoustic Metamaterials with double negative parameter and ρ-near-zero (DNZ)

2. Acoustic cloaks based on Transformation Acoustics and Scattering Cancellation

3. Mechanical Metamaterials: Controlling flexural waves in thin metallic plates

4. Mecanical Metamaterials: Energy redirection by a metallic slit embedded in water.

5. Summary

21/24 ARIADNA Mini-Workshop, Sept 24 (2014)

Sound redirection by a metallic slit embedded in water

L=12 cm; ℓ=8 cm; h= 1 - 10 mm: d=0.1-10 mm

ARIADNA Mini-Workshop, Sept , 24 (2014)

( ) dzx

zxzCRz

L

00

,*),0(=

∫ ∂∂

=αα

( ) dzx

zxzhCThz

L

=∫ ∂

∂=

0||,*),( γγ

( ) dxz

zxBdxBCTdz

h

20

,)2,(=

⊥ ∫ ∂∂

=

Punto 4 (426kHz), d=1mm

Sound redirection by a metallic slit embedded in water

ARIADNA Mini-Workshop, Sept 24 (2014)

5. Summary

We have reviewed recent results obtained by the Wave Phenomena Group at the Technical University of Valencia. They involved new artificial materials and devices on: 1) Acoustic MtM with double negative parameters and DNZ 2) 2D and 3D acoustic cloaks 3) Mechanical devices for energy redirection in plates

Thanks for your attention! 24/24 ARIADNA Mini-Workshop, Sept 24 (2014