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# Phononics and phononic crystals

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A slide presentation of the area of phononics, with a twist tpwords phononic crystals

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### Phononics and phononic crystals

1. 1. Phononics, phononic crystals, and beyond Vincent Laude Institut FEMTO-ST Université de Franche-Comté, CNRS Besançon, France vincent.laude@femto-st.fr
2. 2. What is phononics?  Phononics is the art of engineering artificial acoustic materials with tailored dispersion properties  Phononic crystals are periodically arranged materials; strong contrast in the constituents can mean:  Strong energy confinement  Band gaps = evanescent waves  Strong diffraction  Positive and negative refraction  Strong dispersion  Tunneling (evanescent waves)  Slow / fast waves (propagating waves) 21/09/2009 V. Laude, IEEE IUS 2009 #2
3. 3. Phononics: playing tricks on waves Sound Phonons Negative insulation refraction Sound Solid state Acoustics Nanoscale physics thermal control Periodicity Metamaterials Elastic waves SAW & BAW Band gaps Vibrations Electrical Applied Nonlinear waves engineering mechanics 21/09/2009 V. Laude, IEEE IUS 2009 #3 http://www.topopt.dtu.dk/
4. 4. Tutorial: band structures  Bloch-Floquet theorem: periodic media have modes of the form u (r , t ) = U (r ) exp( j (ωt − kr )) with U (r ) periodic a Band structure shows propagating waves Negative group 3 bands at low freq.: velocity 2 shear and 1 long. Full band ω / ∂konly evanescent waves v g = ∂ gap = Y π M 0 Γ π X Brillouin zone 21/09/2009 V. Laude, IEEE IUS 2009 #4
5. 5. Recent achievements in phononics Which concepts have been demonstrated?
6. 6. Ultrasonic band gaps Experimen t gap Emitting ΓX Receiving ΓM Theory transducer transducer ΓX 2D water/steel PC ΓM Khelif et al., Phys. Rev. B 68, 214301 (2003) 21/09/2009 V. Laude, IEEE IUS 2009 #6
7. 7. Tunneling 3D steel/water crystal  The evanescent character of transmission inside a band gap is analogous to the tunnel effect Yang et al., Phys. Rev. Lett. 88, 104301 (2002) 21/09/2009 V. Laude, IEEE IUS 2009 #7
8. 8. Locally resonant materials  Sound shield  Centimeter-size arrangement  stops audible sound! A “soft” silicone coating over a rigid lead sphere creates localized modes (Fano resonances). Wavelength = 85 cm @ 400 MHz Silicone Longitudinal velocity = 23 m/s Shear velocity = 5.5 m/s Liu et al., Science 289, 1735 (2000) 21/09/2009 V. Laude, IEEE IUS 2009 #8
9. 9. Confinement inside defects  The existence of complete band gaps with very high impedance contrasts enables highly confined acoustic waveguides Band gap Khelif et al., Appl. Phys. Lett. 84, 4400 (2004) 21/09/2009 V. Laude, IEEE IUS 2009 #9
10. 10. SAW and Lamb wave devices 10 µm 10 µm Benchabane et al., Phys. Rev. E 73, 065601(R) (2006) Wu et al., J. Appl. Phys. 97, 094916 (2005) Mohammadi et al., Appl. Phys. Lett. 92, 221905 (2008) Wu et al., Appl. Phys. Lett. 94, 101913 (2009) Mohammadi et al., Appl. Phys. Lett. 94, 051906 (2009) Papers 6H-1 and 6H-4 21/09/2009 V. Laude, IEEE IUS 2009 # 10
11. 11. Positive refraction  Phononic lens for sound (1700 Hz) Refraction is here positive: the dispersion is that of a homogenized medium (small wave vectors limit) Cervera et al., Phys. Rev. Lett. 88, 023902 (2002)  Gradient-index phononic crystals Lin et al., Phys. Rev. B 79, 094302 (2009) 21/09/2009 V. Laude, IEEE IUS 2009 # 11
12. 12. Negative refraction  Demonstration of negative refraction  (using a phononic band with a negative curvature) Ref. Exp. Th. Yang et al., Phys. Rev. Lett. 93, 024301 (2004) 21/09/2009 V. Laude, IEEE IUS 2009 # 12
13. 13. Acoustic metamaterials Ultrasonic metamaterial with negative modulus Cloaking via acoustic metamaterials Fang et al., Nat. Mater. 5, 452 (2006) Torrent et al., New J. Phys. 10, 083015 (2008) 21/09/2009 V. Laude, IEEE IUS 2009 # 13
14. 14. Nanophononics  Confinement of phonons inside a planar 1D GaAs/AlAs cavity Trigo et al., Phys. Rev. Lett. 89, 227402 (2002) 21/09/2009 V. Laude, IEEE IUS 2009 # 14
15. 15. Watching waves on phononic crystals f = 206 MHz Profunser et al., Phys. Rev. Lett.. 97, 055502 (2005) Profunser et al., Phys. Rev. B 80, 014301 (2009) Kokkonen et al., Appl. Phys. Lett. 91, 083517 (2007) Papers 6B-1 & 6B-2 Invited paper 6B-3 21/09/2009 V. Laude, IEEE IUS 2009 # 15
16. 16. Phonons in photonic crystal fibers  Photonic crystal fibers are excellent guides for phonons Dainese et al., Nature Phys. 2, 388 (2006) 21/09/2009 V. Laude, IEEE IUS 2009 # 16
17. 17. Perspectives What is the state of the art in phononic crystals? What can YOU do?
18. 18. Phononic crystal for bulk waves  A lot has been done in 2D  Centimeter-size structures in air  Millimeter-size structures in water Steel beads in epoxy (3D)  Almost nothing has been achieved in 3D!  fcc (face centered cubic) crystals of metal beads in air or water  What is the next frontier?  Demonstrate 3D band gaps at the micro- and nanoscale  (Only indirect characterization by Brillouin light scattering has been performed)  Self-organized crystals 21/09/2009 V. Laude, IEEE IUS 2009 # 18
19. 19. Phononic crystals for SAW  We clearly need to move to the GHz range  Incorporate phononic crystals in SAW devices  500 MHz to 5 GHz range for present applications  This means holes around or smaller than one micron  This is difficult for deep vertical holes!  Alternative: why not use pillars instead of holes?  Pillars on a surface are resonators storing mechanical energy  Same lithography requirements as holes  Deposition or epitaxy techniques to be developed 1D high-aspect-ratio electrode array Laude et al., Appl. Phys. Lett. 89, 083515 (2006) 21/09/2009 V. Laude, IEEE IUS 2009 # 19
20. 20. Phononic crystals for Lamb waves  Plates provide vertical confinement; 2D periodic structuration is enough for 3D confinement  Holes only need to be as deep as the plate  Piezoelectric thin films (AlN, ZnO) on silicon membranes  Self-standing piezoelectric thin films  But beware: obtaining complete band gaps can be more difficult in the plate geometry than in the bulk or SAW geometries  More modes are involved  Transduction of Lamb waves can be an issue 21/09/2009 V. Laude, IEEE IUS 2009 # 20
21. 21. Phononic crystal layer on a substrate  Use a “slow velocity” phononic crystal layer on a “high velocity” substrate  Vertical confinement can be achieved in a 2D structure  Holes need only be as deep as the layer  Can be combined with a Bragg mirror for vertical confinement Bonello et al., Appl. Phys. Lett. 90, 021909 (2007) 21/09/2009 V. Laude, IEEE IUS 2009 # 21
22. 22. Other applications of phononic crystals  Sound insulation  Slow / fast sound: processing of acoustic pulses?  Store and retrieve information in phonon packets  Design really slow delay lines  Enhance nonlinearities  Create phononic circuits  Thermal management through phonon transport control  Protect microelectronic devices (processors)?  PhoXonic crystals  Achieve a nanostructure that is both a phononic crystal and a photonic crystal  Enhance acousto-optical interactions  See Sarah Benchabane, paper 6F-4 (Tuesday) 21/09/2009 V. Laude, IEEE IUS 2009 # 22
23. 23. Outlook on phononics Who’s active in phononics? Ressources
24. 24. Who’s active in phononics?  Geopolitics of phononics  Europe (Spain, France, Greece, Denmark, Russia)  Asia (China, Taiwan, Singapore, Japan)  USA, Canada  No specific phononics conference so far!  Special sessions in recent years:  IEEE Ultrasonics Symposium 2007-2009: 3 sessions this year!  Phonons 2008  Acoustics 2008  USNCCM 2005, IUTAM RAAWS 2009  First International Workshop on Phononic Crystals, in Nice, France (June 2009)  Journals?  Physical Review (APS), Appl. Phys. Lett./J. Appl. Phys. (AIP), Nature Publishing, Ultrasonics (Elsevier), JASA, J. Phys. D (IOP), IEEE Trans. on UFFC, and more. 21/09/2009 V. Laude, IEEE IUS 2009 # 24
25. 25. Ressources  Phononic crystal database  http://www.phys.uoa.gr/phononics/PhononicDatabase.html  The field is growing! Don’t join too late… 21/09/2009 V. Laude, IEEE IUS 2009 # 25