A layer-multiple-scattering method for phononic crystals and heterostructures of such

We present a computer program to calculate the frequency band structure of an infinite phononic crystal, and the transmission, reflection and absorption of elastic waves by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; the slice may consist of multilayers of non-overlapping spheres of given periodicity parallel to the surface and homogeneous plates. The elastic coefficients of the various components of the crystal may be complex functions of the frequency.

[1]  P. Sheng,et al.  Focusing of sound in a 3D phononic crystal. , 2004, Physical review letters.

[2]  B. K. Henderson,et al.  Elastodynamic response of a coplanar periodic layer of elastic spherical inclusions , 2000 .

[3]  李幼升,et al.  Ph , 1989 .

[4]  J. F. Cornwell.  Group theory and electronic energy bands in solids , 1969 .

[5]  P. Sheng,et al.  Ultrasound tunneling through 3D phononic crystals. , 2002, Physical review letters.

[6]  A. Modinos,et al.  Scattering of elastic waves by periodic arrays of spherical bodies , 2000 .

[7]  B. K. Henderson,et al.  Experimental investigation of acoustic band structures in tetragonal periodic particulate composite structures , 2001 .

[8]  D. Brill,et al.  Resonance theory of elastic waves ultrasonically scattered from an elastic sphere , 1987 .

[9]  P. Anderson,et al.  Stress redistribution and cavity nucleation near a diffusively growing grain boundary cavity , 2000 .

[10]  Zhen Ye,et al.  ACOUSTIC LOCALIZATION IN BUBBLY LIQUID MEDIA , 1998 .

[11]  Eleftherios N. Economou,et al.  Elastic and acoustic wave band structure , 1992 .

[12]  Z. Ye,et al.  ACOUSTIC ATTENUATION BY TWO-DIMENSIONAL ARRAYS OF RIGID CYLINDERS , 2001, cond-mat/0101442.

[13]  B. Manzanares-Martínez,et al.  Surface elastic waves in solid composites of two-dimensional periodicity , 2003 .

[14]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[15]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[16]  W. H. Reid,et al.  The Theory of Elasticity , 1960 .

[17]  B. Djafari-Rouhani,et al.  TRANSMITTIVITY THROUGH STRAIGHT AND STUBLIKE WAVEGUIDES IN A TWO-DIMENSIONAL PHONONIC CRYSTAL , 2002 .

[18]  B. Djafari-Rouhani,et al.  Acoustic band structure of periodic elastic composites. , 1993, Physical review letters.

[19]  Abdelkrim Khelif,et al.  TWO DIMENSIONAL PHONONIC CRYSTAL WITH TUNABLE NARROW PASS BAND: APPLICATION TO A WAVEGUIDE WITH SELECTIVE FREQUENCY , 2003 .

[20]  P A Deymier,et al.  Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals. , 2001, Physical review letters.

[21]  Mihail M. Sigalas,et al.  Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method , 2000 .

[22]  I.E.Psarobas,et al.  Phononic crystals with planar defects , 2000 .

[23]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

[24]  R. Martínez-Sala,et al.  SUZUKI PHASE IN TWO-DIMENSIONAL SONIC CRYSTALS , 2001 .

[25]  Fugen Wu,et al.  Elastic wave band gaps for three-dimensional phononic crystals with two structural units , 2003 .

[26]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[27]  W M Robertson,et al.  Band gaps and defect modes in periodically structured waveguides. , 2002, The Journal of the Acoustical Society of America.

[28]  Ultrasonic wedges for elastic wave bending and splitting without requiring a full band gap. , 2001, Physical review letters.

[29]  M. Sigalas,et al.  Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials. , 2000, Physical review letters.

[30]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[31]  B. Gupta,et al.  Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  R. Martínez-Sala,et al.  Refractive acoustic devices for airborne sound. , 2001 .

[33]  Yukihiro Tanaka,et al.  Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch , 2000 .

[34]  Yudell L. Luke,et al.  Algorithms for the Computation of Mathematical Functions , 1977 .

[35]  Scattering of elastic waves by a periodic monolayer of spheres , 2002 .

[36]  P. Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[37]  Garcia,et al.  Theory and experiments on elastic band gaps , 2000, Physical review letters.

[38]  B. Djafari-Rouhani,et al.  Theory of acoustic band structure of periodic elastic composites. , 1994, Physical review. B, Condensed matter.

[39]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[40]  N. Garcia,et al.  Theory for tailoring sonic devices: diffraction dominates over refraction. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Zhengyou Liu,et al.  Point defect states in two-dimensional phononic crystals , 2001 .

[42]  Zhengyou Liu,et al.  Localized states of acoustic waves in three-dimensional periodic composites with point defects , 2003 .

[43]  John H. Page,et al.  Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment , 2000 .

[44]  John B. Pendry,et al.  Low-Energy Electron Diffraction , 1990 .

[45]  E. Economou,et al.  Phonons in colloidal systems , 2003 .

[46]  Jing Shi,et al.  Theory for elastic wave scattering by a two-dimensional periodical array of cylinders: An ideal approach for band-structure calculations , 2003 .

[47]  Eleftherios N. Economou,et al.  Band structure of elastic waves in two dimensional systems , 1993 .

[48]  Eleftherios N. Economou,et al.  Multiple-scattering theory for three-dimensional periodic acoustic composites , 1999 .

[49]  P. Sheng,et al.  Three-component elastic wave band-gap material , 2002 .

[50]  M. Kafesaki,et al.  Air bubbles in water: a strongly multiple scattering medium for acoustic waves. , 2000, Physical review letters.

[51]  M. Kushwaha,et al.  CLASSICAL BAND STRUCTURE OF PERIODIC ELASTIC COMPOSITES , 1996 .