Abstract

An all-fiber two-cavity Fabry–Perot (FP) configuration based on fiber Bragg gratings (FBGs) is proposed. The characteristics of transmission spectra for the two-cavity FP structure are theoretically analyzed and comprehensively modeled. The explicit expression of the transmission coefficient for the structures is derived. The general conditions for the lengths of two cavities and reflectivities of FBGs are presented to produce the single resonant transmission peak at the central wavelength in the FBG stop band. Based on the theoretical analysis, the transmission spectra of symmetric and asymmetric two-cavity FP structures are simulated, and the simulation results are discussed and explained qualitatively. The design guidelines of the device, including the choices of cavity lengths, grating lengths, and index modulation depths, are concluded. The results show that when the increasing of the cavity length of a single-cavity FP structure results in multiple resonant peaks in the stop band, the two-cavity FP structures of the same length can inhibit the secondary resonant peaks and keep the main peak without degrading the performance through appropriately designing the cavity lengths and FBGs. Finally, the fabrication error tolerances of the structures, including inaccurate cavity lengths and reflectivities of FBGs, are calculated and discussed.

© 2009 Optical Society of America

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  1. J. Archambault and S. G. Grubb, “Fiber gratings in lasers and amplifiers,” J. Lightwave Technol. 15, 1378-1390 (1997).
    [CrossRef]
  2. V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
    [CrossRef]
  3. G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett. 3, 613-615 (1991).
    [CrossRef]
  4. G. A. Ball and W. H. Glenn, “Design of a single-mode linear-cavity erbium fiber laser utilising Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
    [CrossRef]
  5. F. D. Pasquale, “Modeling of highly-efficient grating-feedback and Fabry-Perot Er-Yb co-doped fiber lasers,” IEEE J. Quantum Electron. 32, 326-332 (1996).
    [CrossRef]
  6. J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
    [CrossRef]
  7. G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420-422 (1992).
    [CrossRef] [PubMed]
  8. J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
    [CrossRef]
  9. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. Digiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014-2016 (1993).
    [CrossRef] [PubMed]
  10. L. Dong, W. H. Loh, J. E. Caplen, J. D. Minelly, K. Hsu, and L. Reekie, “Efficient single-frequency fiber lasers with novel photosensitive Er/Yb optical fibers,” Opt. Lett. 22, 694-697 (1997).
    [CrossRef] [PubMed]
  11. X. Liu, “A novel ultra-narrow transmission-band fiber Bragg grating and its application in a single-longitudinal-mode fiber laser with improved efficiency,” Opt. Commun. 280, 147-152 (2007).
    [CrossRef]
  12. J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
    [CrossRef]
  13. X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
    [CrossRef]
  14. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  15. C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).
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    [CrossRef]
  18. C. Lv, Z. Wang, B. Yun, and Y. Cui, “Stable single frequency Er-doped all-fiber ring laser with fiber Bragg grating Fabry-Perot filter,” Chin. Opt. Lett. 3, 212-214 (2005).
  19. J. Floriot, F. Lemarchand, and M. Lequime, “Tunable double-cavity solid-spaced bandpass filter,” Opt. Express 12, 6289-6298 (2004).
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    [CrossRef]

2008 (1)

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

2007 (1)

X. Liu, “A novel ultra-narrow transmission-band fiber Bragg grating and its application in a single-longitudinal-mode fiber laser with improved efficiency,” Opt. Commun. 280, 147-152 (2007).
[CrossRef]

2006 (2)

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

2005 (1)

2004 (2)

J. Floriot, F. Lemarchand, and M. Lequime, “Tunable double-cavity solid-spaced bandpass filter,” Opt. Express 12, 6289-6298 (2004).
[CrossRef] [PubMed]

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

1997 (5)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

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

L. Dong, W. H. Loh, J. E. Caplen, J. D. Minelly, K. Hsu, and L. Reekie, “Efficient single-frequency fiber lasers with novel photosensitive Er/Yb optical fibers,” Opt. Lett. 22, 694-697 (1997).
[CrossRef] [PubMed]

J. Archambault and S. G. Grubb, “Fiber gratings in lasers and amplifiers,” J. Lightwave Technol. 15, 1378-1390 (1997).
[CrossRef]

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

1996 (1)

F. D. Pasquale, “Modeling of highly-efficient grating-feedback and Fabry-Perot Er-Yb co-doped fiber lasers,” IEEE J. Quantum Electron. 32, 326-332 (1996).
[CrossRef]

1993 (2)

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. Digiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014-2016 (1993).
[CrossRef] [PubMed]

1992 (3)

G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420-422 (1992).
[CrossRef] [PubMed]

J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
[CrossRef]

G. A. Ball and W. H. Glenn, “Design of a single-mode linear-cavity erbium fiber laser utilising Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

1991 (1)

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett. 3, 613-615 (1991).
[CrossRef]

1985 (1)

Archambault, J.

J. Archambault and S. G. Grubb, “Fiber gratings in lasers and amplifiers,” J. Lightwave Technol. 15, 1378-1390 (1997).
[CrossRef]

Atkins, R. M.

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

Ball, G. A.

G. A. Ball and W. H. Glenn, “Design of a single-mode linear-cavity erbium fiber laser utilising Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420-422 (1992).
[CrossRef] [PubMed]

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett. 3, 613-615 (1991).
[CrossRef]

Bayon, J. F.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Bernage, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Caplen, J. E.

Cheng, X. P.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Cordier, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Cui, Y.

C. Lv, Z. Wang, B. Yun, and Y. Cui, “Stable single frequency Er-doped all-fiber ring laser with fiber Bragg grating Fabry-Perot filter,” Chin. Opt. Lett. 3, 212-214 (2005).

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

Delavaux, J. P.

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

Delevaque, E.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Digiovanni, D. J.

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. Digiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014-2016 (1993).
[CrossRef] [PubMed]

J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
[CrossRef]

Digonnet, M. J. F.

Dong, L.

L. Dong, W. H. Loh, J. E. Caplen, J. D. Minelly, K. Hsu, and L. Reekie, “Efficient single-frequency fiber lasers with novel photosensitive Er/Yb optical fibers,” Opt. Lett. 22, 694-697 (1997).
[CrossRef] [PubMed]

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Douay, M.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Erdogan, T.

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

Floriot, J.

Glenn, W. H.

G. A. Ball and W. H. Glenn, “Design of a single-mode linear-cavity erbium fiber laser utilising Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett. 3, 613-615 (1991).
[CrossRef]

Grubb, S. G.

J. Archambault and S. G. Grubb, “Fiber gratings in lasers and amplifiers,” J. Lightwave Technol. 15, 1378-1390 (1997).
[CrossRef]

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

Hsu, K.

Huang, D.

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

Lemarchand, F.

Lequime, M.

Liu, X.

X. Liu, “A novel ultra-narrow transmission-band fiber Bragg grating and its application in a single-longitudinal-mode fiber laser with improved efficiency,” Opt. Commun. 280, 147-152 (2007).
[CrossRef]

Loh, W. H.

Lv, C.

C. Lv, Z. Wang, B. Yun, and Y. Cui, “Stable single frequency Er-doped all-fiber ring laser with fiber Bragg grating Fabry-Perot filter,” Chin. Opt. Lett. 3, 212-214 (2005).

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

Minelly, J. D.

Mizrahi, V.

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
[CrossRef]

Morey, W. W.

G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420-422 (1992).
[CrossRef] [PubMed]

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett. 3, 613-615 (1991).
[CrossRef]

Muller, J. M.

Niay, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Park, Y.

V. Mizrahi, D. J. Digiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” J. Lightwave Technol. 11, 2021-2025 (1993).
[CrossRef]

Pasquale, F. D.

F. D. Pasquale, “Modeling of highly-efficient grating-feedback and Fabry-Perot Er-Yb co-doped fiber lasers,” IEEE J. Quantum Electron. 32, 326-332 (1996).
[CrossRef]

Poignant, H.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Poumellec, B.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Reekie, L.

Shaw, H. J.

Shum, P.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Stadt, H.

Sulhoff, J. W.

J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
[CrossRef]

Sun, J.

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

Tan, W. C.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Tang, M.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Taunay, T.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Tse, C. H.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Wagener, J. L.

Wang, Z.

C. Lv, Z. Wang, B. Yun, and Y. Cui, “Stable single frequency Er-doped all-fiber ring laser with fiber Bragg grating Fabry-Perot filter,” Chin. Opt. Lett. 3, 212-214 (2005).

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

Wu, R. F.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Wysocki, P. F.

Xie, W. X.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329-1342 (1997).
[CrossRef]

Yuan, X.

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

Yun, B.

C. Lv, Z. Wang, B. Yun, and Y. Cui, “Stable single frequency Er-doped all-fiber ring laser with fiber Bragg grating Fabry-Perot filter,” Chin. Opt. Lett. 3, 212-214 (2005).

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

Zhang, J.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Zhang, X.

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based Fabry-Perot filters and variable saturable absorbers,” Opt. Commun. 267, 177-181 (2006).
[CrossRef]

Zhow, J. L.

X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhow, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry-Perot etalon,” IEEE Photon. Technol. Lett. 20, 976-978 (2008).
[CrossRef]

Zyskind, J. L.

J. L. Zyskind, V. Mizrahi, D. J. DiGiovanni, and J. W. Sulhoff, “Short single frequency erbium-doped fiber laser,” Electron. Lett. 28, 1385-1387 (1992).
[CrossRef]

Acta Phys. Sin. (1)

C. Lv, Y. Cui, Z. Wang, and B. Yun, “A study on the longitudinal mode behavior of Fabry-Perot cavity composed of fiber Bragg grating,” Acta Phys. Sin. 54, 145-150 (2004).

Chin. Opt. Lett. (1)

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Figures (12)

Fig. 1
Fig. 1

Schematic of two-cavity FP structure.

Fig. 2
Fig. 2

Transmission spectrum of single-cavity FP structure with about 60.1 mm length.

Fig. 3
Fig. 3

Transmission spectra of symmetric two-cavity FP structures of about 60.1 mm for s = ( a ) 3, (b) 4, (c) 7, and (d) 9.

Fig. 4
Fig. 4

(a) Transmission spectra for symmetric two-cavity FP structures with different index modulation depths of fiber gratings, (b) spectral responses of the transmission resonant peaks.

Fig. 5
Fig. 5

Transmission spectra of asymmetric two-cavity FP structures for q ( a ) 3 and (b) 7. (The dashed curve presents the transmission spectrum of a symmetric two-cavity FP structure with the same structure parameters except the cavity lengths.)

Fig. 6
Fig. 6

Transmission spectrum of symmetric two-cavity FP structure.

Fig. 7
Fig. 7

Transmission spectra of asymmetric two-cavity FP structures for q 3 .

Fig. 8
Fig. 8

Transmission spectra of asymmetric two-cavity FP structures for q 7 . The inset is the comparison of spectral responses of the transmission resonant main peaks between symmetric (solid curve) and asymmetric (dashed curve) structures.

Fig. 9
Fig. 9

Transmission spectra of symmetric two-cavity FP structures with inaccurate cavity lengths: s = ( a ) 3 and (b) 9.

Fig. 10
Fig. 10

Transmission spectra of symmetric two-cavity FP structures with inaccurate grating index modulations: (a) Δ n 2 is inaccurate, (b) Δ n 1 is inaccurate, (c) both Δ n 1 and Δ n 2 are inaccurate, (d) Δ n 1 , Δ n 2 and cavity lengths are imperfect.

Fig. 11
Fig. 11

Transmission spectra of asymmetric two-cavity FP structures with inaccurate cavity lengths: q ( a ) 3 and (b) 7.

Fig. 12
Fig. 12

Transmission spectra of asymmetric two-cavity FP structures with inaccurate grating index modulations: (a) Δ n 2 is inaccurate, (b) Δ n 1 is inaccurate, (c) both Δ n 1 and Δ n 2 are inaccurate, (d) Δ n 1 , Δ n 2 and cavity lengths are imperfect.

Tables (4)

Tables Icon

Table 1 Influence of the Cavity Length on Transmission Spectral Parameters

Tables Icon

Table 2 Influence of the Grating Index Modulations on Transmission Spectral Parameters

Tables Icon

Table 3 Influence of the Cavity Length on Transmission Spectral Parameters

Tables Icon

Table 4 Influence of the Grating Index Modulations on Transmission Spectral Parameters

Equations (11)

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[ T G ] = [ G 11 G 12 G 12 * G 11 * ] = [ 1 t r * t * r t 1 t * ] ,
G 11 = cosh ( γ B l ) i Δ γ B sinh ( γ B l ) ,
G 12 = i κ γ B sinh ( γ B l ) ,
[ C ] = [ P 1 0 0 P ] ,
[ T ] = [ T 11 T 12 T 21 T 22 ] = [ T G 1 ] [ C 1 ] [ T G 2 ] [ C 2 ] [ T G 3 ] = [ 1 t 1 r 1 * t 1 * r 1 t 1 1 t 1 * ] [ P 1 1 0 0 P 1 ] [ 1 t 2 r 2 * t 2 * r 2 t 2 1 t 2 * ] [ P 2 1 0 0 P 2 ] [ 1 t 3 r 3 * t 3 * r 3 t 3 1 t 3 * ] ,
t F P = 1 T 11 = t 1 t 2 t 3 P 1 P 2 1 + t 1 t 1 * r 1 * r 2 P 1 2 + t 2 t 2 * r 2 * r 3 P 2 2 + t 1 t 2 t 1 * t 2 * r 1 * r 3 P 1 2 P 2 2 ,
T F P = t F P t F P * = ( 1 R 1 ) ( 1 R 2 ) ( 1 R 3 ) 1 + R 1 R 2 + R 2 R 3 + R 1 R 3 + 2 R 1 R 2 ( 1 + R 3 ) cos ( 2 ϕ 1 ) + 2 R 2 R 3 ( 1 + R 1 ) cos ( 2 ϕ 2 ) + 2 R 1 R 3 cos ( 2 ϕ 1 + 2 ϕ 2 ) + 2 R 1 R 2 R 3 cos ( 2 ϕ 1 2 ϕ 2 ) ,
T F P = ( 1 R 1 ) 2 ( 1 R 2 ) ( 1 R 1 ) 2 ( 1 R 2 ) + [ R 2 ( 1 + R 1 ) 2 R 1 ] 2 .
R 2 = 4 R 1 ( 1 + R 1 ) 2 .
L 1 = ( 2 m + 1 ) λ B 4 n eff , L 2 = ( 2 n + 1 ) λ B 4 n eff ,
T F P = ( 1 R 1 ) 2 ( 1 R 1 ) 2 + 2 R 1 [ cos ( 2 ϕ ) + 1 ] .

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