Two-dimensional phononic crystals and scattering of elastic waves by an array of voids

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 458, Issue 2026, 2002, Pages 2327-2347

  Platts, S B ^a   Movchan, N V ^a   McPhedran, R C ^a   Movchan, A B ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Elastic waves; Multipole expansions; Phononic crystals; Scattering

Indexed keywords

EID: 57249116864     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2002.0960     Document Type: Article

References (28)

1. Asatryan, A. A., Robinson, P. A., Botten, L. C., McPhedran, R. C., Nicorovici, N. A. & de Sterke, C. M. 1999 Effects of disorder on wave propagation in two-dimensional photonic crystals. Phys. Rev. E 60, 6118-6127.
2. Asatryan, A. A., Robinson, P. A., Botten, L. C., McPhedran, R. C., Nicorovici, N. A. & de Sterke, C. M. 2000 Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals. Phys. Rev. E 62, 5711-5720.
3. Birks, T. A., Knight, J. C. & Russell. P. St. J. 1997 Endlessly single-mode photonic crystal fibre. Opt. Lett. 22, 961-963.
4. Botten, L. C., McPhedran, R. C., Nicorovici, N. A. & Movchan, A. B. 1998 Off-axis diffraction by perfectly conducting capacitive grids: modal formulation and verification. J. Electromag. Waves Appl. 12, 847-882.
5. Botten, L. C., Nicorovici, N. A., Asatryan, A. A., McPhedran, R. C., de Sterke, C. M. & Robinson, P. A. 2000a Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 1. Method. J. Opt. Soc. Am. A 17, 2165-2176.
6. Botten, L. C., Nicorovici, N. A., Asatryan, A. A., McPhedran, R. C., de Sterke, C. M. & Robinson, P. A. 2000b Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 2. Properties and implementation. J. Opt. Soc. Am. A 17, 2177-2190.
7. Dowling, J. P., Everitt, H. & Yablonovitch, E. 2000 Photonic and sonic band-gap bibliography. (Available at http://home.earthlink.net/~jpdowling/pbgbib.html.)
8. García-Pablos, D., Sigalas, M., Montero de Espinosa, F. R., Torres, M., Kafesaki, M. & García, N. 2000 Theory and experiment on elastic band gaps. Phys. Rev. Lett. 84, 4349-4352.
9. Kafesaki, M. & Economou, E. N. 1999 Multiple-scattering theory for three-dimensional periodic acoustic composites. Phys. Rev. B 60, 11 993-12001.
10. Knight, J. C., Birks, T. A., Russell, P. St. J. & Rarity, J. G. 1998 Bragg scattering from an obliquely illuminated photonic crystal fiber. Appl. Opt. 37, 449-452.
11. Kushwaha, M. S. 1997 Stop-bands for periodic metallic rods: sculptures that can filter the noise. Appl. Phys. Lett. 70, 3218-3220.
12. Kushwaha, M. S. & Halevi, P. 1994 Band-gap engineering in periodic elastic composites. Appl. Phys. Lett. 64, 1085-1087.
13. Kushwaha, M. S. & Halevi, P. 1996 Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders. Appl. Phys. Lett. 69, 31-33.
14. Kushwaha, M. S., Halevi, P., Martinez, G., Dobrzynski, L. & Djafari-Rouhani, B. 1994 Theory of acoustic band structure of periodic elastic composites. Phys. Rev. B 49, 2313-2322.
15. Liu, Z., Chan, C. T., Sheng, P., Goertzen, A. L. & Page, J. H. 2000 Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys. Rev. B 62, 2446-2457.
16. McPhedran, R. C. & Movchan, A. B. 1994 The Rayleigh multipole method for linear elasticity. J. Mech. Phys. Solids 42, 711-727.
17. McPhedran, R. C., Botten, L. C., Asatryan, A. A., Nicorovici, N. A., Robinson, P. A. & de Sterke, C. M. 1999a Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders. Phys. Rev. E 60, 7614-7617.
18. McPhedran, R. C., Botten, L. C., Asatryan, A. A., Nicorovici, N. A., de Sterke, C. M. & Robinson, P. A. 1999b Ordered and disordered photonic band gap materials. Austral. J. Phys. 52, 779-789.
19. Movchan, A. B., Nicorovici, N. A. & McPhedran, R. C. 1997 Green's tensors and lattice sums for elastostatics and elastodynamics. Proc. R. Soc. Lond. A 453, 643-662.
20. Poulton, C. G., Movchan, A. B., McPhedran, R. C., Nicorovici, N. A. & Antipov, Y. A. 2000 Eigenvalue problems for doubly periodic elastic structures and phononic band gaps. Proc. R. Soc. Lond. A 456, 2543-2559.
21. Psarobas, I. E., Stefanou, N. & Modinos, A. 2000 Phononic crystals with planar defects. Phys. Rev. B 62, 5536-5540.
22. Rayleigh, Lord 1892 On the influence of obstacles arranged in rectangular order upon the properties of medium. Phil. Mag. 34, 481-502.
23. Sigalas, M. M. & Economou, E. N. 1994 Elastic waves in plates with periodically placed inclusions. J. Appl. Phys. 75, 2845-2850.
24. Sigalas, M. M. & Soukoulis, C. M. 1995 Elastic-wave propagation through disordered and/or absorptive layered systems. Phys. Rev. B 51, 2780-2789.
25. Twersky, V. 1961 Elementary function representations of Schlömilch series. Arch. Ration. Mech. Analysis 8, 323-332.
26. von Ignatowsky, W. 1914 Zur theorie der gitter. Annln Phys. 44, 369-436.
27. Zalipaev, V. V., Movchan, A. B., Poulton, C. G. & McPhedran, R. C. 2002 Elastic waves and homogenization in oblique periodic structures. Proc. R. Soc. Lond. A 458, 1887-1912.
28. Ziman, J. M. 1972 Principles of the theory of solids, 2nd edn. Cambridge University Press.