Advances in Acoustics Metamaterials and Acoustic Cloaks

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

Quasi-2D structure for double negative and ρ 0 (DNZ ) behavior Scheme of the artificial structure Building unit Transversal section d 2 h d 1 d + d ρ = 2ρ s 1 2 ρb = d2 Spiousas et al., APL (2011) b

Quasi-2D structure for double negative and DNZ behavior ω-l Phase diagram ω-r b Phase diagram ρ m < 0 B m <0 B m <0 ρ m < 0 L=3.5h; R a =0.5R b As predicted by Li and Chan, PRE(2004)

Quasi-2D acoustic metamaterials: Practical realization a ( a ) Sample A a=21 mm R b =9.2mm h=9mm L=3.5h Sample B a=21 mm R b =7mm h=9mm L=2.5h

Quasi-2D acoustic metamaterials: Practical realization Experimental characterization ρ m < 0 a Double negative ( a ) B m <0 Model B m <0 Sample A ρ m < 0 B m <0 Sample B Double negative Gracia-Salgado et al., Phys. Rev. B 88, 224305 (2013)

ρ-near-zero (DNZ) metamaterials ρ m 0 0; B < < m 0 c m = Bm ρ m n m 0 Z m 2 = ρmbm ρbbb = Z 2 b ik m x e 1 Transmission through narrow channels λ>>a EM counterpart: Edwards et al., PRL 100, 033903 (2008) Liu et al., PRL 100, 023903 (2008)

Ground cloaks based on Transformation acoustics 3D Ground cloak with arbitrary surfaces: Kan, García-Chocano et al., (to be published) FEM Simulations (ν=2.68khz; t/λ=0.008) 15 cm D=1.6 mm; d=5mm; t=1 mm t d D ARIADNA Mini-Workshop, Sept 24 (2014) Ideal cloak: ρ ǁ =0.47ρ air, ρ =2.13ρ air κ s =0.47κ air Reduced cloak: ρ ǁ =1.2ρ air, ρ =5.4ρ air κ s =1.2κ air

Experimental setup Layers of perforated plates as ground cloaks Empty elliptical pot (ν=2.68khz) Pot with object Transversal section d 2 Pot with object and cloak d 1

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 σσ cccccc+cccccccccc σσ cccccc

Scattering cancellation 2D cloak Parameters: R 0 = 11.25cm r = 7.5mm 120 cylinders Frequency of operation: 3kHz (λ = R 0 ). Fitness function: F=0.977 R 0 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 m 2 behind the sample.

2D cloak based on scattering cancellation Experimental results: P Free space Real(P) γγ = 1 NN PP mmmmmm,jj jj PP mmmmmm,jj PP mmiiii,jj + PP mmiiii,jj 0.6 Averaged visibility (γ) 0.5 0.4 0.3 0.2 0.1 Free space Object Cloak Cylinder Cylinder with cloak 0.0 3.00 3.02 3.04 3.06 3.08 3.10 3.12 Frequency (khz) García-Chocano et al., APL 99, 074102 (2011)

3D Cloak based on scattering cancellation Parameters: 60 tori with minor radius 2.67mm. Sphere with radius R sph = 4cm. Frequency of operation: f 0 =8.62kHz (R sph = λ 0 ) Fitness function F=0.978 (optimum value). Range of operation (σ s+cloak/ σ sphere < 0.3): Bandwidth: 120Hz. Angle of incidence: ±2.25º. FF = 1 σσ sssssssssss+cccccccccc σσ sssssssssss 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 0.2m 2, 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:

Free space Bare sphere Sphere with cloak x z y Metamaterials 2013

Free space Bare sphere Sphere with cloak

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: where a ( a ) RADIAL PROFILE Modulus of the vertical displacement W(x, y) without (c1) and with (c2) the absorptive material in the region 0.5 r/r ap 0.75. ARIADNA Mini-Workshop, Sept 24 (2014) Climente et al., JAPL 114, 214903 (2013)

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 a ( a ) Luneburg Maxwell 90 o rotating Eaton Concentrator ARIADNA Mini-Workshop, Sept 24 (2014) Climente et al., APL 105, 064101 (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) ( ) dz x z x z C R z L 0 0, * ) (0, = = α α ( ) dz x z x z h C T h z L = = 0, * ), ( γ γ ( ) dx z z x B d x B C T d z h 2 0, ) 2, ( = =

Sound redirection by a metallic slit embedded in water Punto 4 (426kHz), d=1mm 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! ARIADNA Mini-Workshop, Sept 24 (2014 24/24