Abstract

We study the localisation and control of high frequency sound in a dual-core square-lattice photonic crystal fibre preform. The coupled states of two neighboring acoustic resonances are probed using an interferometric set up, and experimental evidence is obtained for odd and even symmetry trapped states. Full numerical solutions of the acoustic wave equation show the existence of a two-dimensional sonic band gap, and numerical modelling of the strain field at the defects gives results that agree well with the experimental observations. The results suggest that sonic band gaps can be used to manipulate sound with great precision and enhance its interaction with light.

© 2003 Optical Society of America

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References

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  1. C.M. Bowden, J.P. Dowling and H.O. Everitt (Editors), �??Development and applications of materials exhibiting photonic band gaps,�?? J. Opt. Soc. Am. 10, 279-413 (1993)
  2. J.D. Joannopoulos, R.D. Meade, R.D. and J.N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995)
  3. C. Soukoulis (Editor), Photonic Band Gap Materials (Kluwer Academic, Dordrecht, 1996)
    [CrossRef]
  4. E.N. Economou and M. Sigalas, �??Stop bands for elastic-waves in periodic composite-materials,�?? J. Acoust. Soc. Am. 95, 1734-1740 (1994).
    [CrossRef]
  5. M. Shen and W. Cao, �??Acoustic band-gap engineering using finite-size layered structures of multiple periodicity,�?? Appl. Phys. Lett. 75, 3713-3715 (1999).
    [CrossRef]
  6. A. Díez, G. Kakarantzas, T.A. Birks and P.St.J. Russell, �?? Acoustic stop-bands in periodically microtapered optical fibers,�?? Appl. Phys. Lett. 76, 3481-3483 (2000).
    [CrossRef]
  7. C. Rubio, et al., �??The existence of full gaps and deaf bands in two-dimensional sonic crystals,�?? J. Lightwave Technol. 17, 2202-2207 (1999).
    [CrossRef]
  8. Y. Tanaka, Y. Tomoyasu and S. Tamura, �?? Band structure of acoustic waves in phononic lattices: Two dimensional composites with large acoustic mismatch,�?? Phys. Rev. B 62, 7387-7392 (2000).
    [CrossRef]
  9. E. Marin, A. Díez and P.St.J. Russell, �??Optical measurement of trapped acoustic mode at defect in square lattice photonic crystal fibre preform,�?? Proc. Conf. Lasers & Electro-Optics (CLEO, Baltimore) May 2001, p 123.
  10. E. Marin, B.J. Mangan, A. Díez, and P.St.J. Russell, �??Acoustic modes of a dual-core square-lattice photonic crystal fibre preform,�?? Proc. European Conf. Opt. Commun. (ECOC, Amsterdam) October 2001, pp 518-519.
  11. P.St.J. Russell, �??Photonic crystal fibers,�?? Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  12. J.C. Knight, T.A. Birks and P.St.J. Russell, �??Holey silica fibres�?? in Optics of Nanostructured Materials, Editors V.A. Markel and T.F. George, pp 39-71 (John Wiley & Sons, New York, 2001).
  13. M. Torres, F.R.M. de Espinosa, D. Garcia-Pablos, and N. Garcia, �??Sonic band gaps in finite elastic media: Surface states and localization phenomena in linear and point defects,�?? Phys. Rev. Lett. 82, 3054-3057 (1999).
    [CrossRef]
  14. A. Yariv, and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, New York, 1984).
  15. C.G. Poulton, A.B. Movchan, R.C. McPhedran, N.A. Nicorovici and Y.A. Antipov, �??Eigenvalue problems for doubly periodic elastic structures and phononic band gaps,�?? Proc. Roy. Soc. Lond. A. 456, 2543-2559 (2000).
    [CrossRef]
  16. B.A. Auld, Acoustic Fields and Waves in Solids (Robert E. Krieger Publishing Company, Florida, 2nd Edition, 1990).
  17. P.St.J. Russell, �??Light in a tight space: enhancing matter-light interactions using photonic crystals,�?? Proc. Conf. Nonlinear Optics (Optical Society of America) 79, 377-379 (2002).
  18. J.M. Worlock and M.L. Roukes, �??Son et Lumière,�?? Nature 421, 802-803 (2003).
    [CrossRef] [PubMed]

Appl. Phys. Lett.

M. Shen and W. Cao, �??Acoustic band-gap engineering using finite-size layered structures of multiple periodicity,�?? Appl. Phys. Lett. 75, 3713-3715 (1999).
[CrossRef]

A. Díez, G. Kakarantzas, T.A. Birks and P.St.J. Russell, �?? Acoustic stop-bands in periodically microtapered optical fibers,�?? Appl. Phys. Lett. 76, 3481-3483 (2000).
[CrossRef]

CLEO 2001

E. Marin, A. Díez and P.St.J. Russell, �??Optical measurement of trapped acoustic mode at defect in square lattice photonic crystal fibre preform,�?? Proc. Conf. Lasers & Electro-Optics (CLEO, Baltimore) May 2001, p 123.

Conf. Nonlinear Optics 2002

P.St.J. Russell, �??Light in a tight space: enhancing matter-light interactions using photonic crystals,�?? Proc. Conf. Nonlinear Optics (Optical Society of America) 79, 377-379 (2002).

ECOC 2001

E. Marin, B.J. Mangan, A. Díez, and P.St.J. Russell, �??Acoustic modes of a dual-core square-lattice photonic crystal fibre preform,�?? Proc. European Conf. Opt. Commun. (ECOC, Amsterdam) October 2001, pp 518-519.

J. Acoust. Soc. Am.

E.N. Economou and M. Sigalas, �??Stop bands for elastic-waves in periodic composite-materials,�?? J. Acoust. Soc. Am. 95, 1734-1740 (1994).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

C.M. Bowden, J.P. Dowling and H.O. Everitt (Editors), �??Development and applications of materials exhibiting photonic band gaps,�?? J. Opt. Soc. Am. 10, 279-413 (1993)

Nature

J.M. Worlock and M.L. Roukes, �??Son et Lumière,�?? Nature 421, 802-803 (2003).
[CrossRef] [PubMed]

Optics of Nanostructured Materials

J.C. Knight, T.A. Birks and P.St.J. Russell, �??Holey silica fibres�?? in Optics of Nanostructured Materials, Editors V.A. Markel and T.F. George, pp 39-71 (John Wiley & Sons, New York, 2001).

Phys. Rev. B

Y. Tanaka, Y. Tomoyasu and S. Tamura, �?? Band structure of acoustic waves in phononic lattices: Two dimensional composites with large acoustic mismatch,�?? Phys. Rev. B 62, 7387-7392 (2000).
[CrossRef]

Phys. Rev. Lett.

M. Torres, F.R.M. de Espinosa, D. Garcia-Pablos, and N. Garcia, �??Sonic band gaps in finite elastic media: Surface states and localization phenomena in linear and point defects,�?? Phys. Rev. Lett. 82, 3054-3057 (1999).
[CrossRef]

Proc. Roy. Soc. Lond. A.

C.G. Poulton, A.B. Movchan, R.C. McPhedran, N.A. Nicorovici and Y.A. Antipov, �??Eigenvalue problems for doubly periodic elastic structures and phononic band gaps,�?? Proc. Roy. Soc. Lond. A. 456, 2543-2559 (2000).
[CrossRef]

Science

P.St.J. Russell, �??Photonic crystal fibers,�?? Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other

A. Yariv, and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, New York, 1984).

B.A. Auld, Acoustic Fields and Waves in Solids (Robert E. Krieger Publishing Company, Florida, 2nd Edition, 1990).

J.D. Joannopoulos, R.D. Meade, R.D. and J.N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995)

C. Soukoulis (Editor), Photonic Band Gap Materials (Kluwer Academic, Dordrecht, 1996)
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Scanning electron micrograph of the preform used in the experiments. It has two solid defects, an inter-hole period of 80 µm, a hole diameter of 59 µm, and an interstitial hole diameter of 8 µm; (b) A detail of the structure used in the numerical modelling (the lines are guidelines only).

Fig. 2.
Fig. 2.

Schematic diagram of the experimental set up. BS1 and BS2 are beam splitters and L1 and L2 are microscopic objectives. M1 and M2 are travelling mirrors that were used to adjust the initial phase of the interferometers. One of the interferometers (solid laser beam) was used to measure the phase change induced by the acoustic wave while the second interferometer (dashed laser beam, inside box (b)) was used to keep constant the vibration of the transducer. In this interferometer, the piezoelectric transducer was used as one of the mirrors (see detailed sketch inside box (a)).

Fig. 3.
Fig. 3.

Phase change of the light propagating in the cores of the PCF preform, induced by the acoustic wave, as a function of frequency. Two sharp resonances are apparent at 23.00 MHz and 23.25 MHz.

Fig. 4.
Fig. 4.

Sonic band structure for in-plane mixed-polarized shear and dilatational waves in the sonic crystal depicted in Figure 1, with defects removed but including interstitial holes. The experimentally observed resonances (at 23 and 23.25 MHz - the dashed lines) sit near the middle of the sonic band gap, which extends from 21.8 to 25 MHz.

Fig. 5.
Fig. 5.

Field patterns for four of the acoustic resonances (the lowest frequency mode, at 23.04 MHz, has extremely small dilatational strain and is omitted from the plot). In each case the shear amplitudes are plotted on the right and the dilatation on the left (the strain scale is in units of 0.01). The resonant frequencies are (a) 23.47 MHz, (b) 23.55 MHz, (c) 24.15 MHz and (d) 24.32 MHz.

Equations (2)

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( λ + 2 μ ) · u ( r ) μ × × u ( r ) + ρ ω 2 u ( r ) = 0
u ( r + R p ) = u ( r ) exp ( j k B · R p )

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