Abstract

We present the first characterisation of cladding modes of a low-index contrast all-solid photonic bandgap fiber using an acousto-optic long-period grating. We experimentally measure the relative band diagrams of the cladding, visualise the fields of the cladding modes in the near field, and find both to be in good agreement with simulations. Our measurements and simulations show that the bands of the cladding are very sensitive to actual details of the structure.

© 2008 Optical Society of America

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  1. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
    [CrossRef]
  2. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
    [CrossRef]
  3. P. Steinvurzel, C. M. de Sterke, M. J. Steel, B. T. Kuhlmey, and B. J. Eggleton, "Single scatterer Fano resonances in solid core photonic band gap fibers," Opt. Express 14, 8797-8811 (2006).
    [CrossRef] [PubMed]
  4. J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).
  5. T. A. Birks, J. A. Pearce, and D. M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483-9490 (2006).
    [CrossRef] [PubMed]
  6. N. M. Litchinitser, S. C. Dunn, P. E. Steinvurzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 1540- 1550 (2004).
    [CrossRef] [PubMed]
  7. A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005).
    [CrossRef] [PubMed]
  8. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
    [CrossRef] [PubMed]
  9. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, "All silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
    [CrossRef] [PubMed]
  10. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. Russell, "Guidance properties of lowcontrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005).
    [CrossRef] [PubMed]
  11. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. S. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005).
    [CrossRef] [PubMed]
  12. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006).
    [CrossRef] [PubMed]
  13. P. Steinvurzel, E. D. Moore, E. C. Magi, and B. J. Eggleton, "Tuning properties of long period gratings in photonic bandgap fibers," Opt. Lett. 31, 2103-2105 (2006).
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    [CrossRef] [PubMed]
  16. F. Couny, H. Sabert, P. Roberts, D. Williams, A. Tomlinson, B. Mangan, L. Farr, J. Knight, T. Birks, and P. Russell, "Visualizing the photonic band gap in hollow core photonic crystal fibers," Opt. Express 13, 558-563 (2005).
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    [CrossRef]
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    [CrossRef]
  22. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
    [CrossRef]
  23. B. Eggleton, P. Westbrook, C. White, C. Kerbage, R. Windeler, and G. Burdge, "Cladding-mode-resonances in air-silica microstructure optical fibers," J. Lightwave Technol. 18, 1084-1100 (2000).
    [CrossRef]
  24. D. I. Yeom, P. Steinvurzel, B. J. Eggleton, S. D. Lim, and B. Y. Kim, "Tunable acoustic gratings in solid-core photonic bandgap fiber," Opt. Express 15, 3513-3518 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  29. S. D. Lim, H. C. Park, I. K. Hwang, and B. Y. Kim, "Combined effects of optical and acoustic birefringence on acousto-optic mode coupling in photonic crystal fiber," Opt. Express 16, 6125-6133 (2008).
    [CrossRef] [PubMed]
  30. W. Wadsworth, N. Joly, J. Knight, T. Birks, F. Biancalana, and P. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004).
    [CrossRef] [PubMed]
  31. A. K. Abeeluck, N. M. Litchinitser, C. Headley, and B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320-1333 (2002).
    [PubMed]
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2008

2007

2006

2005

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. S. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005).
[CrossRef] [PubMed]

F. Couny, H. Sabert, P. Roberts, D. Williams, A. Tomlinson, B. Mangan, L. Farr, J. Knight, T. Birks, and P. Russell, "Visualizing the photonic band gap in hollow core photonic crystal fibers," Opt. Express 13, 558-563 (2005).
[CrossRef] [PubMed]

A. Galea, F. Couny, S. Coupland, P. Roberts, H. Sabert, J. Knight, T. Birks, and P. Russell, "Selective mode excitation in hollow-core photonic crystal fiber," Opt. Lett. 30, 717-719 (2005).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. Russell, "Guidance properties of lowcontrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005).
[CrossRef] [PubMed]

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Magi, R. C. McPhedran, and B. J. Eggleton, "Leakage of the fundamental mode in photonic crystal fiber tapers," Opt. Lett. 30, 1123-1125 (2005).
[CrossRef] [PubMed]

2004

2002

2000

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, "All silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
[CrossRef] [PubMed]

Abeeluck, A. K.

Argyros, A.

Atkin, D. M.

Bergano, N. S.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Biancalana, F.

Bird, D. M.

Birks, T.

Birks, T. A.

Bolger, J. A.

Botten, L. C.

Burdge, G.

Cordeiro, C. M. B.

Couny, F.

Coupland, S.

Davidson, C. R.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

de Sterke, C.

de Sterke, C. M.

Dunn, S. C.

Eggleton, B.

Eggleton, B. J.

D. I. Yeom, P. Steinvurzel, B. J. Eggleton, S. D. Lim, and B. Y. Kim, "Tunable acoustic gratings in solid-core photonic bandgap fiber," Opt. Express 15, 3513-3518 (2007).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. Magi, and B. J. Eggleton, "Tuning properties of long period gratings in photonic bandgap fibers," Opt. Lett. 31, 2103-2105 (2006).
[CrossRef] [PubMed]

B. T. Kuhlmey, H. C. Nguyen, M. J. Steel, and B. J. Eggleton, "Confinement loss in adiabatic photonic crystal fiber tapers," J. Opt. Soc. Am. B 23, 1965-1974 (2006).

P. Steinvurzel, C. M. de Sterke, M. J. Steel, B. T. Kuhlmey, and B. J. Eggleton, "Single scatterer Fano resonances in solid core photonic band gap fibers," Opt. Express 14, 8797-8811 (2006).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
[CrossRef] [PubMed]

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Magi, R. C. McPhedran, and B. J. Eggleton, "Leakage of the fundamental mode in photonic crystal fiber tapers," Opt. Lett. 30, 1123-1125 (2005).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, P. E. Steinvurzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 1540- 1550 (2004).
[CrossRef] [PubMed]

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

A. K. Abeeluck, N. M. Litchinitser, C. Headley, and B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320-1333 (2002).
[PubMed]

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
[CrossRef]

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Farr, L.

Fuerbach, A.

Galea, A.

Headley, C.

Hwang, I. K.

Joly, N.

Judkins, J. B.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Kerbage, C.

Kim, B. Y.

Knight, J.

Knight, J. C.

Kuhlmey, B.

Kuhlmey, B. T.

Laegsgaard, J.

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

Leon-Saval, S. G.

Lim, S. D.

Litchinitser, N. M.

Luan, F.

Magi, E. C.

Mangan, B.

Maystre, D.

McPhedran, R.

McPhedran, R. C.

Moore, E. D.

Nguyen, H. C.

Nulsen, A.

Park, H. C.

Pathmanandavel, K.

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10,851-10,864 (2006).
[CrossRef]

Pearce, G. J.

Pearce, J. A.

Pedrazzani, J. R.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

Renversez, G.

Roberts, P.

Russell, P.

Russell, P. S.

Russell, P. S. J.

Sabert, H.

Shum, P.

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Smith, C. L.

Steel, M. J.

Steinvurzel, P.

Steinvurzel, P. E.

Tomlinson, A.

Vengsarkar, A. M.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Wadsworth, W.

Wang, A.

Westbrook, P.

White, C.

White, T.

White, T. P.

Williams, D.

Windeler, R.

Yan, M.

Yeom, D. I.

J. Lightwave Technol.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long Period Fiber Gratings as Band Rejection Filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

B. Eggleton, P. Westbrook, C. White, C. Kerbage, R. Windeler, and G. Burdge, "Cladding-mode-resonances in air-silica microstructure optical fibers," J. Lightwave Technol. 18, 1084-1100 (2000).
[CrossRef]

J. Opt. A

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).

J. Opt. Soc. Am. B

Opt. Express

P. Steinvurzel, C. M. de Sterke, M. J. Steel, B. T. Kuhlmey, and B. J. Eggleton, "Single scatterer Fano resonances in solid core photonic band gap fibers," Opt. Express 14, 8797-8811 (2006).
[CrossRef] [PubMed]

T. A. Birks, J. A. Pearce, and D. M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483-9490 (2006).
[CrossRef] [PubMed]

D. I. Yeom, P. Steinvurzel, B. J. Eggleton, S. D. Lim, and B. Y. Kim, "Tunable acoustic gratings in solid-core photonic bandgap fiber," Opt. Express 15, 3513-3518 (2007).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. Russell, "Guidance properties of lowcontrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005).
[CrossRef] [PubMed]

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006).
[CrossRef] [PubMed]

S. D. Lim, H. C. Park, I. K. Hwang, and B. Y. Kim, "Combined effects of optical and acoustic birefringence on acousto-optic mode coupling in photonic crystal fiber," Opt. Express 16, 6125-6133 (2008).
[CrossRef] [PubMed]

A. K. Abeeluck, N. M. Litchinitser, C. Headley, and B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320-1333 (2002).
[PubMed]

M. Yan and P. Shum, "Antiguiding in microstructured optical fibers," Opt. Express 12, 104-116 (2004).
[CrossRef] [PubMed]

W. Wadsworth, N. Joly, J. Knight, T. Birks, F. Biancalana, and P. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, P. E. Steinvurzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 1540- 1550 (2004).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. S. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005).
[CrossRef] [PubMed]

F. Couny, H. Sabert, P. Roberts, D. Williams, A. Tomlinson, B. Mangan, L. Farr, J. Knight, T. Birks, and P. Russell, "Visualizing the photonic band gap in hollow core photonic crystal fibers," Opt. Express 13, 558-563 (2005).
[CrossRef] [PubMed]

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10,851-10,864 (2006).
[CrossRef]

Opt. Lett.

J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, "All silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, "Long period fiber-grating-based gain equalizers," Opt. Lett. 21, 1746-1758 (1996).
[CrossRef]

A. Galea, F. Couny, S. Coupland, P. Roberts, H. Sabert, J. Knight, T. Birks, and P. Russell, "Selective mode excitation in hollow-core photonic crystal fiber," Opt. Lett. 30, 717-719 (2005).
[CrossRef] [PubMed]

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
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Supplementary Material (2)

» Media 1: MOV (1602 KB)     
» Media 2: MOV (1214 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

A schematic diagram of the acoustic grating setup for spectral measurements (a) and for mode imaging (b). Pol: polariser, Obj: microscope objective, Mono: Monochromator, SC source: supercontinuum source, OSA: optical spectrum analyser, CCD: CCD camera. For spectral measurements the SC source is butt-coupled to the SC-PBGF. (c): Optical microscope image of the SC-PBGF.

Fig. 2.
Fig. 2.

Spectral power density at the output of the fibre when the acoustic grating is turned off (blue) and on (red, acoustic frequency is 750kHz).

Fig. 3.
Fig. 3.

Density plot of the acoustic grating’s transmission normalized to the SC-PBGF’s transmission in the absence of grating, as a function of acoustic frequency and optical wavelength. Blue crosses indicate wavelength and acoustic frequency of the mode images shown in Fig. 8.

Fig. 4.
Fig. 4.

Index profiles within the unit cell used for simulations, normalized to the background refractive index, as a distance from the rod’s center. blue: Profile used for plane wave expansion simulations; red: profile used for multipole method simulations.

Fig. 5.
Fig. 5.

(a): calculated effective index of core and cladding modes as a function of wavelength, relative to the background index. Blue lines: modes of the infinite periodic photonic crystal (plane wave simulations). Green curves: core modes of a 5×5 supercell with a missing rod at its center, as obtained using the plane wave method. For both plane wave simulations no material dispersion is taken into account, but the graded index profile of each cylinder is accurately described. Black +symbols: modes of a 5 ring finite structure as calculated by the multipole method using an approximate radial index profile, but with material dispersion taken into account. Insets show examples of field distributions of modes of the upper and lower bands. (b): same bands, but relative to the core mode’s refractive index. (c): Experimentally reconstructed bands of the PBGF’s cladding: Map of acoustic grating resonances as a function of wavelength and difference between effective index of higher order and fundamental modes. -see Figs. 6 and 7 for details.

Fig. 6.
Fig. 6.

Band of the cladding around 600nm wavelength: Experimentally determined (bottom) and simulated (top): lines using plane wave method, crosses using multipole method. Left: using Δn eff=-λ/Λ, right: using Δn eff=λ/Λ. Blue crosses indicate wavelength and acoustic frequency of the mode images shown in Fig. 8.

Fig. 7.
Fig. 7.

Band of the cladding around 900nm wavelength: Experimentally determined (bottom) and simulated (top): lines using plane wave method, crosses using multipole method. Left: using Δn eff=-λ/Λ, right: using Δn eff =λ/Λ.

Fig. 8.
Fig. 8.

Field distribution of modes in the upper (top) and lower (bottom) bands. Left: simulated (multipole), right: experiment. The experimental mode images link to an animation showing switching between the acoustic grating being on and off. Video file sizes are 1.6MB for (b)(Media 1), 1.2MB for (d) (Media 2). Simulated field distributions show the field intensity (norm of the electric field squared).

Equations (3)

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Δ n eff = λ Λ ,
n ( r ) = { n silica ( 1 + Δ n GI ( 1 ( r r 0 ) α ) ) r < r 0 n silica r r 0 ,
n ( r ) = { n silica ( 1 + Δ n GI ) r < r 1 n silica ( 1 + 0.45 Δ n GI ) r 1 < r < r 0

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