Surface acoustic wave propagation within a two-dimensional phononic band gapstructure has been studied using a heterodyne laser interferometer.Acoustic waves are launched by interdigital transducers towards a square lattice of holes etched in a piezoelectric medium. Interferometer measurements performed at frequencies lying below, within, and above the expected band gap frequency range provide direct information of the wave interaction with the phononic crystal, revealing anisotropic scattering into higher diffraction orders depending on the apparent grating pitch at the boundary between the phononic crystal and free surface. Furthermore, the measurements also confirm the existence of an elastic band gap, in accordance with previous electrical measurements and theoretical predictions.Peer reviewe

Abdelkrim Khelif

Kimmo Kokkonen

Kokkonen K.

Matti Kaivola

Sarah Benchabane

Vincent Laude

Kokkonen, Kimmo

Kaivola, Matti

Benchabane, Sarah

Khelif, Abdelkrim

Laude, Vincent

Aaltodoc Publication Archive

This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Kokkonen, Kimmo & Kaivola, Matti & Benchabane, Sarah & Khelif,Abdelkrim & Laude, VincentTitle: Scattering of surface acoustic waves by a phononic crystal revealedby heterodyne interferometryYear: 2007Version: Final published versionPlease cite the original version:Kokkonen, Kimmo & Kaivola, Matti & Benchabane, Sarah & Khelif, Abdelkrim & Laude,Vincent. 2007. Scattering of surface acoustic waves by a phononic crystal revealed byheterodyne interferometry. Applied Physics Letters. Volume 91, Issue 8. ISSN0003-6951 (printed). DOI: 10.1063/1.2768910.Rights: © 2007 American Intitute of Physics (AIP). This article may be downloaded for personal use only. Any otheruse requires prior permission of the author and the American Institute of Physics.http://scitation.aip.org/content/aip/journal/aplAll material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)Scattering of surface acoustic waves by a phononic crystal revealed by heterodyneinterferometryKimmo Kokkonen, Matti Kaivola, Sarah Benchabane, Abdelkrim Khelif, and Vincent Laude  Citation: Applied Physics Letters 91, 083517 (2007); doi: 10.1063/1.2768910 View online: http://dx.doi.org/10.1063/1.2768910 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/8?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Local resonances in phononic crystals and in random arrangements of pillars on a surface J. Appl. Phys. 114, 104503 (2013); 10.1063/1.4820928  Analysis of surface acoustic wave propagation in a two-dimensional phononic crystal J. Appl. Phys. 112, 023524 (2012); 10.1063/1.4740050  Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for highfrequency applications J. Appl. Phys. 111, 014504 (2012); 10.1063/1.3673874  Observation of surface-guided waves in holey hypersonic phononic crystal Appl. Phys. Lett. 98, 171908 (2011); 10.1063/1.3583982  Propagation of acoustic waves and waveguiding in a two-dimensional locally resonant phononic crystal plate Appl. Phys. Lett. 97, 193503 (2010); 10.1063/1.3513218    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 10:24:01Scattering of surface acoustic waves by a phononic crystal revealedby heterodyne interferometryKimmo Kokkonena and Matti KaivolaOptics and Molecular Materials Laboratory, Helsinki University of Technology, P.O Box 3500, FI-02015,TKK, FinlandSarah Benchabane, Abdelkrim Khelif, and Vincent LaudeInstitut FEMTO-ST, CNRS UMR 6174, Université de Franche-Comté, 32 Avenue de l’Observatoire, 25044Besançon Cedex, FranceReceived 27 June 2007; accepted 16 July 2007; published online 24 August 2007Surface acoustic wave propagation within a two-dimensional phononic band gap structure has beenstudied using a heterodyne laser interferometer. Acoustic waves are launched by interdigitaltransducers towards a square lattice of holes etched in a piezoelectric medium. Interferometermeasurements performed at frequencies lying below, within, and above the expected band gapfrequency range provide direct information of the wave interaction with the phononic crystal,revealing anisotropic scattering into higher diffraction orders depending on the apparent gratingpitch at the boundary between the phononic crystal and free surface. Furthermore, the measurementsalso confirm the existence of an elastic band gap, in accordance with previous electricalmeasurements and theoretical predictions. © 2007 American Institute of Physics.DOI: 10.1063/1.2768910Phononic crystals PCs are two- or three-dimensionalperiodic structures that consist of two materials with differ-ent elastic constants, giving rise to absolute stop bands foracoustic wave propagation in the material.1,2 They offer in-teresting new possibilities to engineer sophisticated transferfunctions for microacoustic components. Recently, elasticstop bands for surface acoustic waves SAWs have been atthe center of a growing research effort.3–7 Experimental dem-onstrations of directional8 as well as full band gaps9 in pi-ezoelectric crystals at the micrometer scale have been re-ported. These studies have taken advantage of the possibilityto directly generate and receive SAWs by using interdigitaltransducers IDTs,10 thus allowing testing of PCs in realisticdevice configurations via electrical measurements. This char-acterization method, however, yields only indirect informa-tion on the wave interaction with the PC. In contrast, opticalimaging of SAWs on the crystal surface is expected to revealdirect information on scattering and diffraction of waves insuch anisotropic structures. In Refs. 11 and 12, laser genera-tion and detection of ultrasound was used to obtain the dis-persion of SAWs in one- and two-dimensional PCs. Anothertechnique for probing SAW fields is scanning laser interfer-ometry see, e.g., Refs. 13 and 14 for recent accounts of themethod. This technique is especially suited to characterizingSAWs electrically generated by standard IDTs on a piezo-electric substrate.In this letter, a scanning heterodyne laser interferometerhas been used to directly image the actual acoustic wavefields within a PC SAW device. The interferometric measure-ments have been performed below, within, and above thetheoretically predicted and electrically confirmed forbiddenfrequency range. Besides confirming the existence of a bandgap, the measurements reveal the existence of anisotropicscattering, as well as provide direct observation of higherorder diffraction above the band gap.The samples were fabricated onto standard 500 mthick Y-cut LiNbO3 substrates and they feature a PC in adelay line configuration similar to that presented in Ref. 9.The PC structure between the two IDTs is composed of asquare lattice of 10 m deep holes with a diameter of9.4 m and a pitch of 10 m. According to finite elementsimulations,9 the resulting filling fraction of 69% theoreti-cally ensures a full band gap for SAWs in a frequency rangebetween 175 and 230 MHz. The actual full band gap wasdetermined through electrical characterization of the devicesand was found to extend from 200 up to 230 MHz. Thedifference between the predicted and experimental full bandgap widths is attributed to the conicity of the holes.9Direct optical measurements of the SAW fields in the PCdevices for the M direction were carried out with the scan-ning heterodyne laser interferometer presented in Ref. 14,featuring phase-sensitive absolute-amplitude detection of theSAW field at each measurement point. A set of three devicesoperating, respectively, below, within, and above the bandgap was selected, with center frequencies of 176, 206, and260 MHz, and a 12% fractional bandwidth for each of them.In order to study the device behavior, large area scans,consisting of an area of 650600 m2, were measured overthe whole delay line structure with a lateral scanning step of2.1 m. The amplitude fields at three selected frequenciesare presented on the first row of Fig. 1. More detailed mea-surements of the wave interaction with the PC are providedon the second to fourth rows of Fig. 1. In these measure-ments, only the center of the acoustic beam, including thespace in between the two IDTs, corresponding to an area of205205 m2, is scanned with a lateral scanning stepsmaller than 1 m. The scanning step was chosen to besmall enough to also facilitate probing of the wave field inbetween the etch holes. The amplitude data have been aver-aged in the y direction at each frequency to provide an aver-aged line profile of the wave amplitude along the propaga-tion path see the third row of Fig. 1.aElectronic mail: kimmo.kokkonen@tkk.fiAPPLIED PHYSICS LETTERS 91, 083517 20070003-6951/2007/918/083517/3/$23.00 © 2007 American Institute of Physics91, 083517-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 10:24:01At frequencies below the onset frequency of the bandgap at 200 MHz, the SAWs pass through the PC latticewith relatively undisturbed phase fronts, revealing that thewave motion corresponds to a fairly pure traveling wave seeFig. 1a. Furthermore, no significant reflection, scattering,or other losses are observed, indicating that the PC does notsignificantly interfere with the wave motion. The beam steer-ing angle due to the anisotropy of SAW propagation onlithium niobate is clearly observed and is in accordance withthe theoretical value of 6° for the direction considered.When operating at a frequency within the band gap, thePC structure is very reflective, resulting in a strong standingwave pattern seen on the left side of the PC in Fig. 1b,between the transmitting IDT and the PC. This behavior isaccompanied by a low transmission leading nearly to an ab-sence of wave amplitude on the other side of the PC struc-ture. The phase fronts of the wave field, however, remainrelatively undisturbed. These measurements thus confirm theexistence of the predicted band gap along the M propaga-tion direction.9Above the acoustic band gap, good transmission ofSAWs is expected. However, the PC is observed to scatterthe wave field at angles different from normal incidence,which results in a lobe structure visible both in the measuredamplitude and phase fields see Fig. 1c. Despite the scat-tering, the PC does not cause as significant an attenuation toFIG. 1. Color Measured wave fields for the same phononic crystal structure with IDTs operating a below the band gap, at 176 MHz b within the bandgap, at 206 MHz, and c above the band gap, at 256 MHz. The acoustic band gap exists for frequencies between 200 and 230 MHz. In each case, the left handside IDT is emitting while the right hand side IDT is receiving. The first row shows large area scans with the PC structure overlayed on the amplitude image.The locations of the IDTs and their busbars are indicated with dashed black lines. More detailed scans of the amplitude and phase of the wave field arepresented in rows 2 and 4, respectively. The PC structure is overlayed on the amplitude images to indicate the locations of the holes. The amplitude data ofrow two are averaged in the y direction and the resulting line profiles of the averaged amplitude along the wave propagation direction x are presented asgraphs in the third row. The location of the PC structure is marked with gray area. Due to the PC geometry, filling fraction, and scan step used, there arex-coordinate values at which only few good data points are available for the averaging. These locations are marked on the graphs by arrows and lines.083517-2 Kimmo et al. Appl. Phys. Lett. 91, 083517 2007 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 10:24:01the wave field as within the band gap. The observed scatter-ing can be explained by noting that, above a certain thresholdfrequency, the PC acts as an anisotropic diffraction grating.The apparent grating pitch is p=2a in the M directionconsidered here. The evanescent or propagative nature of thediffraction orders can be obtained from the slowness curveconstruction of Fig. 2, by requesting that the wave vectoralong the boundary between the PC and the free surface isky =2n / p for the nth diffraction order. Diffraction appearswhen the wave vector component along y of the first ordersatisfies ky =2 / ps, where s is the slowness in the ydirection. This gives a threshold frequency of 248 MHz,which lies below the frequency of 256 MHz of the measure-ment data presented in Fig. 1c. In comparison, the thresh-old frequency for the appearance of diffraction for the X orY directions would be approximately 350 MHz, because inthis case the grating pitch is smaller p=a. As a side effectof diffraction, we note that for efficient reception of the waveat the receiving IDT, the phase fronts of the wave shouldmatch the finger geometry of the IDT. Therefore it is to beexpected that if the phase fronts of the transmitted wave aredistorted due to, e.g., scattering, electrical measurements willlikely result in a low value of transmission.In conclusion, the surface-acoustic wave fields within atwo-dimensional phononic crystal structure have been im-aged in amplitude and phase by the use of a scanning het-erodyne interferometer. These measurements confirm the ex-istence of a band gap for surface acoustic waves previouslypredicted theoretically and via electrical measurements. Theyreveal that SAWs are transmitted almost unaffected belowthe band gap and strongly reflected within it. Above the bandgap, scattering to higher diffraction orders appears dependingon the apparent grating pitch as seen at the boundary be-tween the PC and the free surface. These results open upinteresting prospects for probing more complex spatial ge-ometries such as elastic waveguides, defect modes, and dif-fractive structures managed in phononic crystals.K.K. thanks the Finnish Cultural Foundation and NokiaFoundation for Scholarships.1M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Phys.Rev. Lett. 71, 2022 1993.2M. Sigalas and E. N. Economou, Solid State Commun. 86, 141 1993.3T. Aono and S.-I. Tamura, Phys. Rev. B 58, 4838 1998.4Y. Tanaka and S. I. Tamura, Phys. Rev. B 60, 13294 1999.5M. Torres, F. R. Montero de Espinosa, D. García-Pablos, and N. García,Phys. Rev. Lett. 82, 3054 1999.6T. Wu, Z. Huang, and S. Lin, Phys. Rev. B 69, 094301 2004.7V. Laude, M. Wilm, S. Benchabane, and A. Khelif, Phys. Rev. E 71,036607 2005.8T. Wu, L. Wu, and Z. Huang, J. Appl. Phys. 97, 094916 2005.9S. Benchabane, A. Khelif, J.-Y. Rauch, L. Robert, and V. Laude, Phys.Rev. E 73, 065601R 2006.10R. M. White and F. W. Voltmer, Appl. Phys. Lett. 17, 314 1965.11L. Dhar and J. A. Rogers, Appl. Phys. Lett. 77, 1402 2000.12D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97,055502 2006.13J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, Opt. Lett. 25, 613 2000.14K. Kokkonen, J. V. Knuuttila, V. P. Plessky, and M. M. Salomaa, Proc.-IEEE Ultrason. Symp. 2, 1145 2003.FIG. 2. Color online Construction of diffraction orders on both sides of thephononic crystal from the slowness curve for SAW on the free surface oflithium niobate. p=2a is the apparent grating pitch. The frequency  /2=256 MHz is used for the construction of diffraction orders shown. Below248 MHz all diffraction orders except the zeroth are evanescent. The direc-tion of the Poynting vector for diffraction orders corresponding to propagat-ing waves is indicated by an arrow.083517-3 Kimmo et al. Appl. Phys. Lett. 91, 083517 2007 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 10:24:01

Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry

International audienceSurface acoustic wave propagation within a two-dimensional phononic band gap structure has been studied using a heterodyne laser interferometer. Acoustic waves are launched by interdigital transducers towards a square lattice of holes etched in a piezoelectric medium. Interferometer measurements performed at frequencies lying below, within, and above the expected band gap frequency range provide direct information of the wave interaction with the phononic crystal, revealing anisotropic scattering into higher diffraction orders depending on the apparent grating pitch at the boundary between the phononic crystal and free surface. Furthermore, the measurements also confirm the existence of an elastic band gap, in accordance with previous electrical measurements and theoretical predictions

HAL - Université de Franche-Comté

Aaltodoc

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s): Kokkonen, Kimmo & Kaivola, Matti & Benchabane, Sarah & Khelif,
Abdelkrim & Laude, Vincent
Title: Scattering of surface acoustic waves by a phononic crystal revealed
by heterodyne interferometry
Year: 2007
Version: Final published version
Please cite the original version:
Kokkonen, Kimmo & Kaivola, Matti & Benchabane, Sarah & Khelif, Abdelkrim & Laude,
Vincent. 2007. Scattering of surface acoustic waves by a phononic crystal revealed by
heterodyne interferometry. Applied Physics Letters. Volume 91, Issue 8. ISSN
0003-6951 (printed). DOI: 10.1063/1.2768910.
Rights: © 2007 American Intitute of Physics (AIP). This article may be downloaded for personal use only. Any other
use requires prior permission of the author and the American Institute of Physics.
http://scitation.aip.org/content/aip/journal/apl
All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and
duplication or sale of all or part of any of the repository collections is not permitted, except that material may
be duplicated by you for your research use or educational purposes in electronic or print form. You must
obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or
otherwise to anyone who is not an authorised user.
Powered by TCPDF (www.tcpdf.org)
Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne
interferometry
Kimmo Kokkonen, Matti Kaivola, Sarah Benchabane, Abdelkrim Khelif, and Vincent Laude 
 
Citation: Applied Physics Letters 91, 083517 (2007); doi: 10.1063/1.2768910 
View online: http://dx.doi.org/10.1063/1.2768910 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/8?ver=pdfcov 
Published by the AIP Publishing 
 
Articles you may be interested in 
Local resonances in phononic crystals and in random arrangements of pillars on a surface 
J. Appl. Phys. 114, 104503 (2013); 10.1063/1.4820928 
 
Analysis of surface acoustic wave propagation in a two-dimensional phononic crystal 
J. Appl. Phys. 112, 023524 (2012); 10.1063/1.4740050 
 
Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for high
frequency applications 
J. Appl. Phys. 111, 014504 (2012); 10.1063/1.3673874 
 
Observation of surface-guided waves in holey hypersonic phononic crystal 
Appl. Phys. Lett. 98, 171908 (2011); 10.1063/1.3583982 
 
Propagation of acoustic waves and waveguiding in a two-dimensional locally resonant phononic crystal plate 
Appl. Phys. Lett. 97, 193503 (2010); 10.1063/1.3513218 
 
 
 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.240 On: Tue, 19 May 2015 10:24:01
Scattering of surface acoustic waves by a phononic crystal revealed
by heterodyne interferometry
Kimmo Kokkonena and Matti Kaivola
Optics and Molecular Materials Laboratory, Helsinki University of Technology, P.O Box 3500, FI-02015,
TKK, Finland
Sarah Benchabane, Abdelkrim Khelif, and Vincent Laude
Institut FEMTO-ST, CNRS UMR 6174, Université de Franche-Comté, 32 Avenue de l’Observatoire, 25044
Besançon Cedex, France
Received 27 June 2007; accepted 16 July 2007; published online 24 August 2007
Surface acoustic wave propagation within a two-dimensional phononic band gap structure has been
studied using a heterodyne laser interferometer. Acoustic waves are launched by interdigital
transducers towards a square lattice of holes etched in a piezoelectric medium. Interferometer
measurements performed at frequencies lying below, within, and above the expected band gap
frequency range provide direct information of the wave interaction with the phononic crystal,
revealing anisotropic scattering into higher diffraction orders depending on the apparent grating
pitch at the boundary between the phononic crystal and free surface. Furthermore, the measurements
also confirm the existence of an elastic band gap, in accordance with previous electrical
measurements and theoretical predictions. © 2007 American Institute of Physics.
DOI: 10.1063/1.2768910
Phononic crystals PCs are two- or three-dimensional
periodic structures that consist of two materials with differ-
ent elastic constants, giving rise to absolute stop bands for
acoustic wave propagation in the material.1,2 They offer in-
teresting new possibilities to engineer sophisticated transfer
functions for microacoustic components. Recently, elastic
stop bands for surface acoustic waves SAWs have been at
the center of a growing research effort.3–7 Experimental dem-
onstrations of directional8 as well as full band gaps9 in pi-
ezoelectric crystals at the micrometer scale have been re-
ported. These studies have taken advantage of the possibility
to directly generate and receive SAWs by using interdigital
transducers IDTs,10 thus allowing testing of PCs in realistic
device configurations via electrical measurements. This char-
acterization method, however, yields only indirect informa-
tion on the wave interaction with the PC. In contrast, optical
imaging of SAWs on the crystal surface is expected to reveal
direct information on scattering and diffraction of waves in
such anisotropic structures. In Refs. 11 and 12, laser genera-
tion and detection of ultrasound was used to obtain the dis-
persion of SAWs in one- and two-dimensional PCs. Another
technique for probing SAW fields is scanning laser interfer-
ometry see, e.g., Refs. 13 and 14 for recent accounts of the
method. This technique is especially suited to characterizing
SAWs electrically generated by standard IDTs on a piezo-
electric substrate.
In this letter, a scanning heterodyne laser interferometer
has been used to directly image the actual acoustic wave
fields within a PC SAW device. The interferometric measure-
ments have been performed below, within, and above the
theoretically predicted and electrically confirmed forbidden
frequency range. Besides confirming the existence of a band
gap, the measurements reveal the existence of anisotropic
scattering, as well as provide direct observation of higher
order diffraction above the band gap.
The samples were fabricated onto standard 500 m
thick Y-cut LiNbO3 substrates and they feature a PC in a
delay line configuration similar to that presented in Ref. 9.
The PC structure between the two IDTs is composed of a
square lattice of 10 m deep holes with a diameter of
9.4 m and a pitch of 10 m. According to finite element
simulations,9 the resulting filling fraction of 69% theoreti-
cally ensures a full band gap for SAWs in a frequency range
between 175 and 230 MHz. The actual full band gap was
determined through electrical characterization of the devices
and was found to extend from 200 up to 230 MHz. The
difference between the predicted and experimental full band
gap widths is attributed to the conicity of the holes.9
Direct optical measurements of the SAW fields in the PC
devices for the M direction were carried out with the scan-
ning heterodyne laser interferometer presented in Ref. 14,
featuring phase-sensitive absolute-amplitude detection of the
SAW field at each measurement point. A set of three devices
operating, respectively, below, within, and above the band
gap was selected, with center frequencies of 176, 206, and
260 MHz, and a 12% fractional bandwidth for each of them.
In order to study the device behavior, large area scans,
consisting of an area of 650600 m2, were measured over
the whole delay line structure with a lateral scanning step of
2.1 m. The amplitude fields at three selected frequencies
are presented on the first row of Fig. 1. More detailed mea-
surements of the wave interaction with the PC are provided
on the second to fourth rows of Fig. 1. In these measure-
ments, only the center of the acoustic beam, including the
space in between the two IDTs, corresponding to an area of
205205 m2, is scanned with a lateral scanning step
smaller than 1 m. The scanning step was chosen to be
small enough to also facilitate probing of the wave field in
between the etch holes. The amplitude data have been aver-
aged in the y direction at each frequency to provide an aver-
aged line profile of the wave amplitude along the propaga-
tion path see the third row of Fig. 1.aElectronic mail: kimmo.kokkonen@tkk.fi
APPLIED PHYSICS LETTERS 91, 083517 2007
0003-6951/2007/918/083517/3/$23.00 © 2007 American Institute of Physics91, 083517-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.240 On: Tue, 19 May 2015 10:24:01
At frequencies below the onset frequency of the band
gap at 200 MHz, the SAWs pass through the PC lattice
with relatively undisturbed phase fronts, revealing that the
wave motion corresponds to a fairly pure traveling wave see
Fig. 1a. Furthermore, no significant reflection, scattering,
or other losses are observed, indicating that the PC does not
significantly interfere with the wave motion. The beam steer-
ing angle due to the anisotropy of SAW propagation on
lithium niobate is clearly observed and is in accordance with
the theoretical value of 6° for the direction considered.
When operating at a frequency within the band gap, the
PC structure is very reflective, resulting in a strong standing
wave pattern seen on the left side of the PC in Fig. 1b,
between the transmitting IDT and the PC. This behavior is
accompanied by a low transmission leading nearly to an ab-
sence of wave amplitude on the other side of the PC struc-
ture. The phase fronts of the wave field, however, remain
relatively undisturbed. These measurements thus confirm the
existence of the predicted band gap along the M propaga-
tion direction.9
Above the acoustic band gap, good transmission of
SAWs is expected. However, the PC is observed to scatter
the wave field at angles different from normal incidence,
which results in a lobe structure visible both in the measured
amplitude and phase fields see Fig. 1c. Despite the scat-
tering, the PC does not cause as significant an attenuation to
FIG. 1. Color Measured wave fields for the same phononic crystal structure with IDTs operating a below the band gap, at 176 MHz b within the band
gap, at 206 MHz, and c above the band gap, at 256 MHz. The acoustic band gap exists for frequencies between 200 and 230 MHz. In each case, the left hand
side IDT is emitting while the right hand side IDT is receiving. The first row shows large area scans with the PC structure overlayed on the amplitude image.
The locations of the IDTs and their busbars are indicated with dashed black lines. More detailed scans of the amplitude and phase of the wave field are
presented in rows 2 and 4, respectively. The PC structure is overlayed on the amplitude images to indicate the locations of the holes. The amplitude data of
row two are averaged in the y direction and the resulting line profiles of the averaged amplitude along the wave propagation direction x are presented as
graphs in the third row. The location of the PC structure is marked with gray area. Due to the PC geometry, filling fraction, and scan step used, there are
x-coordinate values at which only few good data points are available for the averaging. These locations are marked on the graphs by arrows and lines.
083517-2 Kimmo et al. Appl. Phys. Lett. 91, 083517 2007
 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.240 On: Tue, 19 May 2015 10:24:01
the wave field as within the band gap. The observed scatter-
ing can be explained by noting that, above a certain threshold
frequency, the PC acts as an anisotropic diffraction grating.
The apparent grating pitch is p=2a in the M direction
considered here. The evanescent or propagative nature of the
diffraction orders can be obtained from the slowness curve
construction of Fig. 2, by requesting that the wave vector
along the boundary between the PC and the free surface is
ky =2n / p for the nth diffraction order. Diffraction appears
when the wave vector component along y of the first order
satisfies ky =2 / ps, where s is the slowness in the y
direction. This gives a threshold frequency of 248 MHz,
which lies below the frequency of 256 MHz of the measure-
ment data presented in Fig. 1c. In comparison, the thresh-
old frequency for the appearance of diffraction for the X or
Y directions would be approximately 350 MHz, because in
this case the grating pitch is smaller p=a. As a side effect
of diffraction, we note that for efficient reception of the wave
at the receiving IDT, the phase fronts of the wave should
match the finger geometry of the IDT. Therefore it is to be
expected that if the phase fronts of the transmitted wave are
distorted due to, e.g., scattering, electrical measurements will
likely result in a low value of transmission.
In conclusion, the surface-acoustic wave fields within a
two-dimensional phononic crystal structure have been im-
aged in amplitude and phase by the use of a scanning het-
erodyne interferometer. These measurements confirm the ex-
istence of a band gap for surface acoustic waves previously
predicted theoretically and via electrical measurements. They
reveal that SAWs are transmitted almost unaffected below
the band gap and strongly reflected within it. Above the band
gap, scattering to higher diffraction orders appears depending
on the apparent grating pitch as seen at the boundary be-
tween the PC and the free surface. These results open up
interesting prospects for probing more complex spatial ge-
ometries such as elastic waveguides, defect modes, and dif-
fractive structures managed in phononic crystals.
K.K. thanks the Finnish Cultural Foundation and Nokia
Foundation for Scholarships.
1M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Phys.
Rev. Lett. 71, 2022 1993.
2M. Sigalas and E. N. Economou, Solid State Commun. 86, 141 1993.
3T. Aono and S.-I. Tamura, Phys. Rev. B 58, 4838 1998.
4Y. Tanaka and S. I. Tamura, Phys. Rev. B 60, 13294 1999.
5M. Torres, F. R. Montero de Espinosa, D. García-Pablos, and N. García,
Phys. Rev. Lett. 82, 3054 1999.
6T. Wu, Z. Huang, and S. Lin, Phys. Rev. B 69, 094301 2004.
7V. Laude, M. Wilm, S. Benchabane, and A. Khelif, Phys. Rev. E 71,
036607 2005.
8T. Wu, L. Wu, and Z. Huang, J. Appl. Phys. 97, 094916 2005.
9S. Benchabane, A. Khelif, J.-Y. Rauch, L. Robert, and V. Laude, Phys.
Rev. E 73, 065601R 2006.
10R. M. White and F. W. Voltmer, Appl. Phys. Lett. 17, 314 1965.
11L. Dhar and J. A. Rogers, Appl. Phys. Lett. 77, 1402 2000.
12D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97,
055502 2006.
13J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, Opt. Lett. 25, 613 2000.
14K. Kokkonen, J. V. Knuuttila, V. P. Plessky, and M. M. Salomaa, Proc.-
IEEE Ultrason. Symp. 2, 1145 2003.
FIG. 2. Color online Construction of diffraction orders on both sides of the
phononic crystal from the slowness curve for SAW on the free surface of
lithium niobate. p=2a is the apparent grating pitch. The frequency  /2
=256 MHz is used for the construction of diffraction orders shown. Below
248 MHz all diffraction orders except the zeroth are evanescent. The direc-
tion of the Poynting vector for diffraction orders corresponding to propagat-
ing waves is indicated by an arrow.
083517-3 Kimmo et al. Appl. Phys. Lett. 91, 083517 2007
 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.240 On: Tue, 19 May 2015 10:24:01


English

Crossref

https://aaltodoc.aalto.fi/bitstream/handle/123456789/16114/A1_kokkonen_kimmo_2007.pdf?sequence=1&isAllowed=y

Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry

Abstract

Similar works

Full text

Available Versions

Aaltodoc Publication Archive

HAL - Université de Franche-Comté

Aaltodoc

Crossref