towards the full control of elastic waves propagation.pdf
TRANSCRIPT
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 1/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 2/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 3/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 4/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 5/41
2D Phononic/Sonic Crystals
MicroSource
Sample
R. Martinez-Sala et al . Nature (1995)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 6/41
Phononic/Sonic Crystals: Practical realizations
1D2D3D
Science, 289, 1739 (2000) PRL, 80, 5325 (1998) PRL, 98, 134301 (2007)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 7/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 8/41
Sound waves in air
)(~),( t xk iet x p ω −⋅
k c
=ω
k
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
SURPRISES OF PERIODICITY
Bloch wave
( ))(),( x pet x p k
t xk i
ω −⋅
= periodic “envelope”Plane wave
k c
≠ω )(k
ω
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 9/41
SOUND PROPAGATION TROUGH PHONONIC CRYSTALS
f=0.4
f=0.25
Complete bandgap
Partial bandgap
(pseudogap)
ω(k )
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 10/41
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
!!
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 11/41
PHONONIC CRYSTALS :
PERIODIC COMPOSITES with SONIC/ELASTIC BANDGAPS
Possible applications
- filters
- vibration/sound insulation
- waveguides for vibrations/sound
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 12/41
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)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 13/41
1. Introduction2. 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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 14/41
HOMOGENIZATION = LIMIT 0
Effective
medium
>> a
a
k ceff =ω
ω ⎟ ⎠ ⎞⎜
⎝ ⎛ =
→ k c
k eff
ω
0lim
k
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 15/41
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)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 16/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 17/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 18/41
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)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 19/41
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)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 20/41
1. Introduction2. Wave propagation through phononic crystals
3.
Refractive devices based on phononic
crystals: focusing
4. Focusing of waves by negative refraction
5. Acoustic metamaterials: manipulation of waves
6.
Inverse design of phononic
devices
7. Conclusion
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 21/41
PHONONIC CRYSTALS also present “negative refraction”
S f
Positive refraction
S f
Negative refraction
≈
a >>
a
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 22/41
Imaging and focusing of water waves by negative refraction
Exp.
Simulations
Point source
PRE, 69, 030201 (2004)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 23/41
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!
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 24/41
1. Introduction2. Wave propagation through phononic crystals
3.
Refractive devices based on phononic
crystals: lenses
4. Focusing of waves by negative refraction
5. Acoustic metamaterials: manipulation of waves
6.
Inverse design of phononic
devices
7. Conclusion
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 25/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 26/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 27/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 28/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 29/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 30/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 31/41
Wave manipulation using
acoustic metamaterials
2D Acoustic cloaking
New J. Phys. 9, 45 (2007)
Acoustic metamaterial:
This region is invisible to sound!
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 32/41
Collimation of sound assisted by ASW
Nat. Photonics (2007)
Surface acoustic waves are possible
in corrugated surfaces:
λ>10a
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 33/41
1. Introduction2. Wave propagation through phononic crystals
3.
Refractive devices based on phononic
crystals: lenses
4. Focusing of waves by negative refraction
5. Acoustic metamaterials: manipulation of mechanical waves
6.
Inverse design of phononic
devices
7. Conclusion
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 34/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 35/41
Inverse design of phononic
devices
Wave source(s) Material dist.(m) Observabledata d=[G(m)]sPerformanced=[G(m)]s
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 36/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 37/41
Inverse Design-Tool
Direct Solver – Multiple Scattering Theory
• Semi analytical
• Fast
Optimization Method – Genetic Algorithm
• Great history
• Easy implementation
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 38/41
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)
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 39/41
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
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 40/41
Inverse design of highly directional
sound sources
Theoretical prediction Practical realization
APL, 90, 224107 (2007).
Onmidirectional
point source
8/14/2019 Towards the Full Control of Elastic Waves propagation.pdf
http://slidepdf.com/reader/full/towards-the-full-control-of-elastic-waves-propagationpdf 41/41
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!