Localization of surface acoustic waves in a one-dimensional quasicrystal

Macon, Louis; Jp, Desideri; Sornette, Didier

doi:10.1103/physrevb.44.6755

Cited by 22 publications

(13 citation statements)

References 69 publications

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“…As a complementary picture, we present a heuristic model for the SAW propagation, which relies on the tightbinding Schrodinger discrete equation (2) and which allows us to interpret quantitatively our experimental results. 9 Our approach amounts to replacing the exact expression (3) for the <p n by the following Ansatz:…”

Section: =(2jr/x)[c -(C -S)int{fmc(n(t -D) -1}] (3)mentioning

confidence: 99%

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Observation of critical modes in quasiperiodic systems

Desideri¹,

Macon²,

Sornette³

1989

Phys. Rev. Lett.

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We present experimental results and their interpretation on the propagation of surface acoustic waves on a quasiperiodically corrugated solid. The surface is made of a thousand grooves engraved according to a Fibonacci sequence. For the first time, we observe the spatial structure of the critical proper modes obtained from an optical diffraction experiment. These special modes are characteristic of quasiperiodic systems and exhibit remarkable scaling features. PACS numbers: 68.35.Gy, 03.40.Kf, 71.55.Jv It is usually accepted that wave propagation in disordered structures leads to the phenomenon of Anderson localization 1 at any nonvanishing disorder for space dimensions rf=l and 2 and at sufficiently high disorder for rf = 3. The localization regime is a nonperturbative effect involving coherent interferences between all the wavelets partially reflected by the quenched disordered set of scatterers, for which only partial scenarios exist. According to the present wisdom, wave propagation in random media is characterized by the existence of a remarkable localization transition separating an "extended regime" at small disorder and a "localized regime" at large disorder, only at space dimension d > 2. At lower dimensions, any nonvanishing disorder leads to the second regime. The existence of a transition between two regimes is always exciting because one can hope that understanding the crucial features which trigger the transition will reveal the physics of the different regimes.In this respect, wave propagation in one-dimensional id = 1) quasiperiodic systems is very interesting since it has been discovered 2 that there exists a transition between an extended and a localized regime similarly to what occurs in d = 3 disordered systems.' d = 1 quasiperiodic systems are thus natural intermediate cases between periodicity and randomness. Another motivation for studying these systems follows from the recent experimental discovery of the quasicrystal phase in metallic alloys. 3 From a different point of view, since we have studied this problem in the context of surface acoustic waves (SAW's), the understanding of the interaction of elastic surface acoustic waves with complex surface topography 4,5 is of major importance to underwater acoustics, seismology, surface-acoustic-wave devices, nondestructive testing, and ultrasonic applications in medicine.In this Letter, we report experimental measurements on the spectrum and the proper modes of a Rayleigh surface acoustic wave propagating on the quasiperiodically corrugated surface of a piezoelectric lithium niobate (KZ-LiNbCh) substrate with a thousand grooves engraved according to a Fibonacci sequence. It is shown that this system is in the critical regime of the localization transition predicted to occur in certain quasiperiodic systems. With our choice of studying surface waves, an optical diffraction experiment using the Raman-Nath effect 6 allows us to probe for the first time the spatial structure of the proper modes with a remarkable precision, and to obtain informa...

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Section: =(2jr/x)[c -(C -S)int{fmc(n(t -D) -1}] (3)mentioning

confidence: 99%

“…Dependence of the SAW reflection modulus as a function of frequency. Each peak probes the existence of a stop band (see Ref 9. for more details about the peak pattern).…”

mentioning

confidence: 99%

Observation of critical modes in quasiperiodic systems

Desideri¹,

Macon²,

Sornette³

1989

Phys. Rev. Lett.

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“…Moreover, phononic crystals are of interest as functional elements of SAW devices. Measurements and calculations of SAW localization have been reported in onedimensional Fibonacci superlattices [133], as well as in twodimensional periodic elastic structures [59,134].…”

Section: Scatteringmentioning

confidence: 99%

Surface acoustic wave-assisted scanning probe microscopy—a summary

Hesjedal

2009

Rep. Prog. Phys.

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Elastic properties of nanoscopic materials, structures and thin films are important parameters controlling their growth, as well as their optical and electronic properties. Acoustic microscopy is a well-established method for elastic imaging. In order to overcome its micrometer-scale diffraction-limited lateral resolution, scanning probe microscopy-based acoustic near-field techniques have been developed. Among the acoustic modes used for microscopy, surface acoustic waves (SAWs) are especially suited for probing very small and thin objects due to their localization in the vicinity of the surface. Moreover, the study of SAWs is crucial for the design of frequency filter devices as well as for fundamental physical studies, for instance, the probing of composite fermions in two-dimensional electron systems. This review discusses the capabilities and limitations of SAW-based scanning probe microscopy techniques. Particular emphasis is laid on the review of surface acoustic waves and their interaction with elastic inhomogeneities. Scattering, diffraction and wave localization phenomena will be discussed in detail. Finally, the possibilities for quantitative acoustic microscopy of objects on the nanoscale, as well as practical applications, are presented.

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“…The spectral and response properties of these structures as well as their imaging are of current interest. One can mention the investigation of surface acoustic shape resonances [8][9][10] or the scattering of acoustic waves by single resonating elements [11][12][13][14] and by periodic or quasi-periodic [15] solid surfaces. In Ref.…”

Section: Adsorbed Wire On a Planar Surfacementioning

confidence: 99%

Elastic Vibrations of Planar and Deterministic Rough Surfaces

et al. 1996

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We present a few recent or new theoretical results about surface acoustic localized and resonant modes associated with planar or deterministic rough surfaces. The following composite systems are considered: one or two adlayers deposited on a semi-infinite substrate and wires or grooves integrated near a planar surface. The surface modes can be obtained as well-defined features of the density of states resulting from a calculation of the Green functions in these heteróstructures. In this work, the materials are described in the framework of the elasticity theory.

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Localization of surface acoustic waves in a one-dimensional quasicrystal

Cited by 22 publications

References 69 publications

Observation of critical modes in quasiperiodic systems

Observation of critical modes in quasiperiodic systems

Surface acoustic wave-assisted scanning probe microscopy—a summary

Elastic Vibrations of Planar and Deterministic Rough Surfaces

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