Abstract

In this paper, we describe the properties of Fabry-Perot fiber cavity formed by two fiber Bragg gratings in terms of the grating effective length. We show that the grating effective length is determined by the group delay of the grating, which depends on its diffraction efficiency and physical length. We present a simple analytical formula for calculation of the effective length of the uniform fiber Bragg grating and the frequency separation between consecutive resonances of a Fabry-Perot cavity. Experimental results on the cavity transmission spectra for different values of the gratings’ reflectivity support the presented theory.

© 2006 Optical Society of America

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  1. J.S. Zyskind, V. Mizrahi, D.J. DiGiovanni and J.W. Sulhoff, "Short single-frequency erbium-doped fiber laser," Electron. Lett. 28, 1385-1387 (1992).
    [CrossRef]
  2. Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
    [CrossRef]
  3. Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
    [CrossRef]
  4. Pavel Polynkin, Alexander Polynkin, Masud Mansuripur, Jerome Moloney and N. Peyghambarian, "Single-frequency laser oscillator with watts-level output power at 1.5 μm by use of a twisted-mode technique," Opt. Lett. 30, 2745-2747 (2005).
    [CrossRef] [PubMed]
  5. J. Canning, N. Groothoff, E. Buckley, T. Ryan, K. Lyytikainen and J. Digweed, "All-fibre photonic crystal distributed Bragg reflector (PC-DBR) fibre laser," Opt. Express 11, 1995-2000 (2003).
    [CrossRef] [PubMed]
  6. J.J. Zayhowski, "Limits imposed by spatial hole burning on the single-mode operation of standing-wave laser cavities," Opt. Lett. 15, 431-433 (1990).
    [CrossRef] [PubMed]
  7. J. Canning, M. Janos and M.G. Sceats, "Rayleigh longitudinal profile of optical resonances within waveguide grating structures using sidescattered light," Opt. Lett. 21, 609-611 (1996).
    [CrossRef] [PubMed]
  8. Orazio Svelto, Principles of Lasers, (New York: Plenum Press, 1989), chapter 4.
  9. T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  10. A. Othonos and K. Kalli, Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing, (Boston: Artech House, 1999), chapter 5.
  11. Raman Kashyap, "Fiber Bragg Gratings," San Diego: Academic Press, 1999, chapter 4.
  12. H. Renner, "Effective-index increase, form birefringence and transition losses in UV-side-illuminated photosensitive fibers," Opt. Express 11, 546-560 (2001).
    [CrossRef]
  13. K. Dossou, S. LaRochelle and M. Fontaine, "Numerical Analysis of the Contribution of the Transverse Asymmetry in the Photo-Induced Index Change Profile to the Birefringence of Optical Fiber," J. Lightwave Technol. 20, 1463-1470 (2002).
    [CrossRef]

2005 (2)

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

Pavel Polynkin, Alexander Polynkin, Masud Mansuripur, Jerome Moloney and N. Peyghambarian, "Single-frequency laser oscillator with watts-level output power at 1.5 μm by use of a twisted-mode technique," Opt. Lett. 30, 2745-2747 (2005).
[CrossRef] [PubMed]

2004 (1)

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

H. Renner, "Effective-index increase, form birefringence and transition losses in UV-side-illuminated photosensitive fibers," Opt. Express 11, 546-560 (2001).
[CrossRef]

1997 (1)

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

1996 (1)

1992 (1)

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

1990 (1)

Andrés, M.V.

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

Barmenkov, Yu.O.

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

Buckley, E.

Canning, J.

Cruz, J.L.

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

DiGiovanni, D.J.

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

Digweed, J.

Dossou, K.

Erdogan, T.

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

Fontaine, M.

Geng, J.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Groothoff, N.

Hu, Y.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Janos, M.

Jiang, S.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Kaneda, Yu.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Kir’yanov, A.V.

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

LaRochelle, S.

Lyytikainen, K.

Mizrahi, V.

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

Mora, J.

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

Peyghambarian, N.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Renner, H.

H. Renner, "Effective-index increase, form birefringence and transition losses in UV-side-illuminated photosensitive fibers," Opt. Express 11, 546-560 (2001).
[CrossRef]

Ryan, T.

Sceats, M.G.

Spiegelberg, Ch.

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

Sulhoff, J.W.

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

Zayhowski, J.J.

Zyskind, J.S.

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

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett. (1)

Yu.O. Barmenkov, A.V. Kir’yanov, J. Mora, J.L. Cruz and M.V. Andrés, The continuous-wave and giant-pulse operations of a single-frequency Erbium-doped fiber laser.IEEE Photon. Technol. Lett. 17, 28-30 (2005).
[CrossRef]

J. Lightwave Techn. (1)

Ch. Spiegelberg, J. Geng, Y. Hu, Yu. Kaneda, S. Jiang and N. Peyghambarian, "Low-noise narrow-linewidth fiber laser at 1550 nm (June 2003)," J. Lightwave Techn. 22, 57-62 (2004).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (2)

J. Canning, N. Groothoff, E. Buckley, T. Ryan, K. Lyytikainen and J. Digweed, "All-fibre photonic crystal distributed Bragg reflector (PC-DBR) fibre laser," Opt. Express 11, 1995-2000 (2003).
[CrossRef] [PubMed]

H. Renner, "Effective-index increase, form birefringence and transition losses in UV-side-illuminated photosensitive fibers," Opt. Express 11, 546-560 (2001).
[CrossRef]

Opt. Lett. (3)

Other (3)

A. Othonos and K. Kalli, Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing, (Boston: Artech House, 1999), chapter 5.

Raman Kashyap, "Fiber Bragg Gratings," San Diego: Academic Press, 1999, chapter 4.

Orazio Svelto, Principles of Lasers, (New York: Plenum Press, 1989), chapter 4.

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Figures (5)

Fig. 1.
Fig. 1.

Fabry-Perot fiber cavity formed by two FBGs (FBG1 and FBG2). L 1,2 are the physical lengths of FBGs and L 0 is the distance between them.

Fig. 2.
Fig. 2.

Relative effective length Leff /L of a uniform 4-cm fiber Bragg grating versus its diffraction efficiency for λ 0=1530 nm. The labels near the curves correspond to detuning from the peak wavelength.

Fig. 3.
Fig. 3.

Group delay calculated for uniform 4-cm fiber Bragg grating versus detuning from the grating peak wavelength (1530 nm). The labels near the curves correspond to the diffraction efficiency values.

Fig. 4.
Fig. 4.

(a) Theoretical and (b) experimental transmittance spectra of the Fabry-Perot fiber cavity formed by two equal uniform 4-cm FBGs separated by 5 cm. Gratings are centered at 1531.08 nm. The diffraction efficiency values are labeled near the corresponding curves.

Fig. 5.
Fig. 5.

Comparison between theoretical (solid line) and experimental (stars) mode-spacing values.

Equations (8)

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T = ( 1 R 1 ) ( 1 R 2 ) ( 1 R 1 R 2 ) 2 + 4 R 1 R 2 sin 2 ( β L 0 + φ 1 + φ 2 2 ) ,
Δ λ = λ 2 2 n g ( L 0 + L eff 1 + L eff 2 ) ,
L eff = v g τ 1,2 2 ,
ρ = κ sinh ( εL ) ξ sinh ( εL ) + cosh ( εL ) ,
τ = λ 2 2 π c d φ d λ ,
φ = atan ( ε ξ cotanh ( εL ) ) .
L eff = λ 0 2 π n 1 tanh ( π n 1 λ 0 L ) .
L eff = L R 2 atanh ( R ) .

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