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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 20 — Oct. 6, 2003
  • pp: 2555–2560
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Sonic band gaps in PCF preforms: enhancing the interaction of sound and light

P. St. J. Russell, E. Marin, A. Díez, S. Guenneau, and A. B. Movchan  »View Author Affiliations


Optics Express, Vol. 11, Issue 20, pp. 2555-2560 (2003)
http://dx.doi.org/10.1364/OE.11.002555


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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

There is currently keen interest in materials that are periodically microstructured so as to exhibit photonic band gaps - frequency ranges where all optical vibrations are switched off [1

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)

3

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

]. Sonic vibrations can be controlled in a similar way [4

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]

8

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]

]. Here we report the observation of high frequency (~25 MHz) sonic band gaps (SBGs) in rods of silica glass with square-lattice arrays of hollow micro-channels running along their length. By incorporating point defects in the form of filled-in channels, localised resonances appear [9

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

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.

]. Driving a dual-defect structure with a piezoelectric transducer, we monitor the vibrations using laser interferometry. Numerical solutions of the full acoustic wave equation, for the sonic band structure and the fields at the defects, are in good agreement with the measurements. The results point to a new class of ultra-efficient photo-sonic device in which both sound and light are controlled with great precision and their interactions enhanced.

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).

The glass samples were prepared following a procedure commonly used to fabricate photonic crystal fibres [11

11. P.St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

,12

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).

]. First of all, precision-made tubes and rods of silica glass (~1 mm in diameter) were stacked into a large-scale “preform” of the desired structure. This was then fused together and reduced in size, roughly by a factor of 20 in transverse linear dimension, using an optical fibre drawing tower. These intermediate preforms were used directly in the work reported here (normally they are drawn down once more to form a fibre). A scanning electron micrograph of the cross-section of the sample used in the experiments is given in Fig. 1 - note the small interstitial holes. Two structural defects were placed in next-nearest-neighbour sites. Their effect is to “clear a space” for localised resonances to form at frequencies within the SBG. These resonances can be excited by placing a transducer directly inside the defects themselves [13

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]

]. In this work we excite them by means of evanescent wave tunnelling through the SBG region. When the frequency of the transducer (attached to the side of the preform) coincides with the frequency of a defect resonance, energy is efficiently transferred. At other intra-SBG frequencies this transfer is suppressed, while at frequencies outside the SBG there will be no localisation of energy at the defect - the entire preform will vibrate.

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. 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.

(λ+2μ)·u(r)μ××u(r)+ρω2u(r)=0
(1)

where u(r)=(u(r),ν(r)) is the displacement vector at position r=(x,y) and ω is the angular frequency of vibration. The boundary conditions assume traction-free surfaces at each hole, i.e., the components of the stress tensor vanish at the boundaries. As the cylinders are considered to be infinitely long, the problem is inherently two-dimensional. Finally, the periodicity implies that u must satisfy Bloch’s theorem:

u(r+Rp)=u(r)exp(jkB·Rp)
(2)

where the Bloch vector k B lies entirely in the (x,y) plane and R p points to the center of the pth cavity. Using the multi-pole method described in [15

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]

], we find the set of normal frequencies ω for a given k B, corresponding to propagating modes. The resulting sonic band structure, for a defect-free lattice with the same hole size and spacing as the preform, is presented in Fig. 4. A full SBG appears in the frequency range 21.8–25.0 MHz. The resonances observed in the experiments sit well within this range, suggesting that the sound is indeed trapped in the cores by a SBG.

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. 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.

In conclusion, the ability to precisely manipulate high frequency acoustic fields suggests many possibilities for new devices. For example, consider a laser beam launched equally into the two cores of a dual-core preform resonating in its odd mode, and then re-combined at the output. As the relative phase between the cores changes, the wave amplitude at the output will oscillate. The result is an efficient optical modulator. If the structures are scaled down in size to the point where the cores become single mode waveguides (as in a photonic crystal fibre), the acoustic resonant frequencies scale up to into the GHz range (although the acoustic losses increase with frequency, they only become significant at multi-GHz frequencies). The almost perfect spatial overlap of acoustic and optical fields, in a very small area, points to a new family of highly efficient acousto-optic devices based on photo-sonic effects, such as optically pumped acoustic oscillators [17

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

18. J.M. Worlock and M.L. Roukes, “Son et Lumière,” Nature 421, 802–803 (2003). [CrossRef] [PubMed]

]. It may even prove possible to suppress acoustic vibrations in the fibre core, suggesting that high power single-frequency laser light could be transmitted without the onset of stimulated Brillouin scattering.

Acknowledgments

A. Dièz acknowledges the financial support of the Comisión Interministerial de Ciencia y Tecnologia (CICYT) of Spain. His current address is Departamento de Física Aplicada, Universidad de Valencia, Dr. Moliner 50, E-46100, Spain. E. Marin’s current address is Laboratoire TSI - UMR CNRS 5516, Bâtiment F-10, rue Barrouin, 42000 Saint-Etienne, France. The authors would like to thank M. Franczyk and B.J. Mangan for preform fabrication. The work was supported by the UK Engineering and Physical Sciences Research Council.

References and links

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, 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]

OCIS Codes
(160.1050) Materials : Acousto-optical materials
(230.1040) Optical devices : Acousto-optical devices

ToC Category:
Research Papers

History
Original Manuscript: July 17, 2003
Revised Manuscript: September 26, 2003
Published: October 6, 2003

Citation
P. Russell, E. Marin, A. Diez, S. Guenneau, and A. Movchan, "Sonic band gaps in PCF preforms: enhancing the interaction of sound and light," Opt. Express 11, 2555-2560 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-20-2555


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References

  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]

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