Abstract

In this paper, we investigate the spectral characteristics and bend response of fiber Bragg gratings (FBGs) in all-solid photonic bandgap fibers (PBGFs). We inscribe FBGs within the secondary bandgap by ultraviolet (UV) side illumination and observe the couplings to backward core mode, guided LP01 and LP11 supermodes and radiative LP02 supermodes. The mechanisms of these resonant couplings in the FBG are described in detail. We demonstrate that only those supermodes with certain phase relationships and symmetric mode field profiles are responsible for the supermode resonances. When the fiber grating is bent, the guided supermode resonances become chirped as a result of the strain gradient over the fiber cross section. Meanwhile, the core resonance is enhanced, due to more energy of the core mode distributed in the cladding rods. The bend response is direction dependant owing to the nonuniform UV-induced average index raises and index modulation over the high-index rod lattice.

© 2007 Optical Society of America

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  1. T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  2. J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  3. P. St. J. Russell, "Photonic-Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006).
    [CrossRef]
  4. B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, "Microstructured optical fiber devices," Opt. Express 9, 698-713 (2001).
    [CrossRef] [PubMed]
  5. N. Groothoff, J. Canning, E. Buckley, K. Lyttikainen, and J. Zagari, "Bragg gratings in air-silica structured fibers," Opt. Lett. 28, 233-235 (2003).
    [CrossRef] [PubMed]
  6. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, "Tunable photonic band gap fiber," in Optical Fiber Communications Conference, Postconference Edition, Vol. 70 of OSA Trends in Optics and Photonics Series Technical Digest (Optical Society of America, Washington D.C. 2002) pp. 4f66-468.
  7. T. T. Larsen, A. Bjarklev, and D. S. Hermann, "Optical devices based on liquid crystal photonics bandgap fibers," Opt. Express 11, 2589-2596 (2003).
    [CrossRef] [PubMed]
  8. 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]
  9. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
    [CrossRef] [PubMed]
  10. P. Steinvurzel, B. T. Kuhmley, T. P. White, M. J. Steel, C. M. de Sterke, and B. J. Eggleton, "Long- wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004).
    [CrossRef] [PubMed]
  11. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, "Guidance properties of low-contrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (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, B. T. Kuhlmey and B. J. Eggleton, "Long period grating resonances in photonic bandgap fiber," Opt. Express 14, 3007-3014 (2006).
    [CrossRef] [PubMed]
  14. P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton, "Tuning properties of long period gratings in photonic bandgap fibers," Opt. Lett. 31, 2103-2105 (2006).
    [CrossRef] [PubMed]
  15. D. Noordegraaf, L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
    [CrossRef] [PubMed]
  16. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
    [CrossRef] [PubMed]
  17. J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks, and D. M. Bird, "Solid Photonic Bandgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059-6063 (2006).
    [CrossRef]
  18. G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).
  19. Z. Wang, T. Taru, T. A. Birks, J. C. Knight, Y. Liu, and J. Du, "Coupling in dual-core photonic bandgap fibers: theory and experiment," Opt. Express 15, 4795-4803 (2007).
    [CrossRef] [PubMed]
  20. Z. Wang, Y. Liu, G. Kai, J. Liu, Y. Li, T. Sun, L. Jin, Y. Yue, W. Zhang, S. Yuan, and X. Dong, "Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers," Opt. Express 15, 8925-8930 (2007).
    [CrossRef] [PubMed]
  21. Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
    [CrossRef]
  22. L. Jin, Z. Wang, Q. Fang, B. Liu, Y. Liu, G. Kai, X. Dong, and B. O. Guan, "Bragg grating resonances in all-solid bandgap fibers," Opt. Lett. 32, 2717-2719 (2007).
    [CrossRef] [PubMed]
  23. U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, "Two-dimensional high-precision fiber waveguide arrays for coherent light propagation," Opt. Express 15, 6894-6899 (2007).
    [CrossRef]
  24. J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
    [CrossRef]
  25. J. Lægsgaard and T. T. Alkeskjold, "Designing a photonic bandgap fiber for thermo-optic switching," J. Opt. Soc. Am. B 23, 951-957 (2006).
    [CrossRef]
  26. T. B. Iredale, P. Steinvurzel, B. J. Eggleton, "Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre," Electron. Lett. 42, 739-740 (2006).
    [CrossRef]

2007 (7)

2006 (7)

2005 (2)

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

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

2004 (2)

2003 (4)

2002 (1)

2001 (1)

1997 (1)

T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Alkeskjold, T. T.

Argyros, A.

Bartelt, H.

Bird, D. M.

Birks, T. A.

Bjarklev, A.

Buckley, E.

Canning, J.

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

N. Groothoff, J. Canning, E. Buckley, K. Lyttikainen, and J. Zagari, "Bragg gratings in air-silica structured fibers," Opt. Lett. 28, 233-235 (2003).
[CrossRef] [PubMed]

Cordeiro, C. M. B.

de Sterke, C. M.

Deyerl, H. J.

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

Dong, X.

Du, J.

Z. Wang, T. Taru, T. A. Birks, J. C. Knight, Y. Liu, and J. Du, "Coupling in dual-core photonic bandgap fibers: theory and experiment," Opt. Express 15, 4795-4803 (2007).
[CrossRef] [PubMed]

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

Dunn, S. C.

Eggleton, B. J.

Erdogan, T.

T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Fang, Q.

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

L. Jin, Z. Wang, Q. Fang, B. Liu, Y. Liu, G. Kai, X. Dong, and B. O. Guan, "Bragg grating resonances in all-solid bandgap fibers," Opt. Lett. 32, 2717-2719 (2007).
[CrossRef] [PubMed]

George, A. K.

Groothoff, N.

Guan, B. O.

Hale, A.

Hedley, T. D.

Hermann, D. S.

Iredale, T. B.

T. B. Iredale, P. Steinvurzel, B. J. Eggleton, "Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre," Electron. Lett. 42, 739-740 (2006).
[CrossRef]

Jin, L.

Kai, G.

Kerbage, C.

Knight, J. C.

Kobelke, J.

Kristensenc, M.

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

Kuhlmey, B. T.

Kuhmley, B. T.

Lægsgaard, J.

Larsen, T. T.

Leon-Saval, S. G.

Li, Y.

Litchinitser, N. M.

Liu, B.

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

L. Jin, Z. Wang, Q. Fang, B. Liu, Y. Liu, G. Kai, X. Dong, and B. O. Guan, "Bragg grating resonances in all-solid bandgap fibers," Opt. Lett. 32, 2717-2719 (2007).
[CrossRef] [PubMed]

Liu, J.

Liu, Y.

Liu, Z.

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

Luan, F.

Luo, J.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Lyttikainen, K.

Magi, E. C.

Mägi, E. C.

McPhedran, R. C.

Moore, E. D.

Noordegraaf, D.

Pearce, G. J.

Ren, G.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Rindorf, L.

Röpke, U.

Russell, P. St. J.

Schuster, K.

Scolari, L.

Shi, Q.

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

Shum, P.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Sørensen, H. R.

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

Steel, M. J.

Steinvurzel, P.

Sun, T.

Taru, T.

Tong, W.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Unger, S.

Usner, B.

Wang, A.

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks, and D. M. Bird, "Solid Photonic Bandgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059-6063 (2006).
[CrossRef]

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]

Wang, Z.

Westbrook, P. S.

White, T. P.

Windeler, R. S.

Yu, X.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Yuan, S.

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

Z. Wang, Y. Liu, G. Kai, J. Liu, Y. Li, T. Sun, L. Jin, Y. Yue, W. Zhang, S. Yuan, and X. Dong, "Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers," Opt. Express 15, 8925-8930 (2007).
[CrossRef] [PubMed]

Yue, Y.

Z. Wang, Y. Liu, G. Kai, J. Liu, Y. Li, T. Sun, L. Jin, Y. Yue, W. Zhang, S. Yuan, and X. Dong, "Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers," Opt. Express 15, 8925-8930 (2007).
[CrossRef] [PubMed]

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

Zagari, J.

Zhang, L.

G. Ren, P. Shum, L. Zhang, X. Yu, W. Tong, and J. Luo, "Low-loss all-solid photonic bandgap fiber," Opt. Lett. 32, 1203-1205 (2007).

Zhang, W.

Electron. Lett. (1)

T. B. Iredale, P. Steinvurzel, B. J. Eggleton, "Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre," Electron. Lett. 42, 739-740 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Q. Fang, Z. Wang, G. Kai, L. Jin, Y. Yue, J. Du, Q. Shi, Z. Liu, B. Liu, Y. Liu, S. Yuan, and X. Dong, "Proposal for All-Solid Photonic Bandgap Fiber with Improved Dispersion Characteristics," IEEE Photon. Technol. Lett. 19, 1239-1241 (2007).
[CrossRef]

J. Appl. Phys. (1)

J. Canning, H. J. Deyerl, H. R. Sørensen, and M. Kristensenc, "Ultraviolet-induced birefringence in hydrogen-loaded optical fiber," J. Appl. Phys. 97, 053104 (2005).
[CrossRef]

J. Lightwave Technol. (2)

P. St. J. Russell, "Photonic-Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006).
[CrossRef]

T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks, and D. M. Bird, "Solid Photonic Bandgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059-6063 (2006).
[CrossRef]

Nature (1)

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Express (11)

T. T. Larsen, A. Bjarklev, and D. S. Hermann, "Optical devices based on liquid crystal photonics bandgap fibers," Opt. Express 11, 2589-2596 (2003).
[CrossRef] [PubMed]

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, "Microstructured optical fiber devices," Opt. Express 9, 698-713 (2001).
[CrossRef] [PubMed]

D. Noordegraaf, L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

P. Steinvurzel, B. T. Kuhmley, T. P. White, M. J. Steel, C. M. de Sterke, and B. J. Eggleton, "Long- wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, "Guidance properties of low-contrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (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]

P. Steinvurzel, E. D. Moore, E. C. Magi, B. T. Kuhlmey and B. J. Eggleton, "Long period grating resonances in photonic bandgap fiber," Opt. Express 14, 3007-3014 (2006).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, "Two-dimensional high-precision fiber waveguide arrays for coherent light propagation," Opt. Express 15, 6894-6899 (2007).
[CrossRef]

Z. Wang, T. Taru, T. A. Birks, J. C. Knight, Y. Liu, and J. Du, "Coupling in dual-core photonic bandgap fibers: theory and experiment," Opt. Express 15, 4795-4803 (2007).
[CrossRef] [PubMed]

Z. Wang, Y. Liu, G. Kai, J. Liu, Y. Li, T. Sun, L. Jin, Y. Yue, W. Zhang, S. Yuan, and X. Dong, "Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers," Opt. Express 15, 8925-8930 (2007).
[CrossRef] [PubMed]

Opt. Lett. (6)

Other (1)

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, "Tunable photonic band gap fiber," in Optical Fiber Communications Conference, Postconference Edition, Vol. 70 of OSA Trends in Optics and Photonics Series Technical Digest (Optical Society of America, Washington D.C. 2002) pp. 4f66-468.

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Figures (6)

Fig. 1.
Fig. 1.

Microscopic photograph for the cross section of the all-solid bandgap fiber. The bright spots represent Ge-doped rods.

Fig. 2.
Fig. 2.

(a). Simulated effective indices of the core modes versus wavelength and the bandgap map for the PBGF. Supermodes are discretely distributed in between the bandgap cutoffs. Due to the large quantity of supermodes in our experiment, they are not given in this figure. (b) Intensity distributions of the core modes in the middle of the bandgap (upper, at 1050nm) and at the edge of the bandgap (lower, at 950nm). Core modes near the bandgap edges have larger mode field areas, and more energy fractions of these modes are distributed over the high-index rods. (c) Some typical phase relationships for the eigen supermodes in our PBGF. The supermodes are distinguished by phase relationship of rod mode fields in adjacent high-index rods, which are represented by different color combinations. (d) The calculated overlap integrals between each LP01 (upper) and LP11 (lower) supermode and the core mode over the rod lattice. The calculation involves considering both the symmetric profiles of the phase relationships and the specific LP01 and LP11 rod modes. As shown in these two figures, only the 60°-symmetric LP01 supermodes are responsible for the LP01 supermode resonances, while the LP11 supermodes with 180°-antisymmetric phase relationships for the LP11 supermode resonances. Mode numbers are ordered with decreased propagation constants.

Fig. 3
Fig. 3

Transmission (upper, solid curve) and reflection (dashed curve) spectra of the FBG in straight all-solid PBGF. Peaks A-C correspond to the resonant couplings to backward LP01 supermodes, LP11 supermodes, and core mode respectively. The green, blue, and red curves represent simulated resonant wavelengths for them, respectively. Note that each of the green and blue ones is actually made up of many closely spaced lines, because of the discretion of the guided supermodes. Peak D and its adjacent peaks at the short wavelength side of peak C arise from couplings to discrete, radiative LP02 supermodes. The lower solid curve represents a typical transmission spectrum of the FBG when it is bent against the UV launch direction. The core mode resonance is enhanced and the two guided supermode resonances are chirped.

Fig. 4.
Fig. 4.

(a). Shift of the short wavelength edge of the fundamental bandgap during exposure (resolution: 1nm); (b). UV-induced shifts for peaks A, B, and C. The result indicates that the effective indices of the LP01, LP11 supermodes and the core mode present different sensitivities to average index raise of the high-index rods; (c). Simulated sensitivities of wavelength variation of peaks A, B, and C to the average index raise of high index rods over the secondary bandgap. The LP01 and LP11 supermodes present much higher sensitivities than that of the core mode.

Fig. 5.
Fig. 5.

Evolution for depths of peaks B and C with directional curvature along the UV launch direction. When applying bendings, peak B will broadens and splits, which causes decreased resonant strength. The core mode resonance is enhanced, because of the energy extension to the high-index rods of the core mode, induced by the narrowed bandgap.

Fig. 6.
Fig. 6.

Scheme for strain gradient over the cross section of the bent PBGF. The neutral layer experiences a zero strain. The outside half of the fiber is stretched while the inner half is compressed. The amplitude of strain of the local cladding rod is determined by its distance x to the neutral layer and the bent radius R by ε = x/R.

Equations (3)

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e sup , i = j N m i , j e rod , j ( x x j , y y j )
κ = ∫∫ rods ωε 0 2 ( Δ n UV ) 2 E core × E res dA
d λ m d ( Δ n ) = 2 d m + 1 2 2 n 0 Δ n

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