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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References

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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]
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    [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.
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    [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 (1)

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]

Kalli, K.

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

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]

Kashyap, Raman

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

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.

Mansuripur, Masud

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]

Moloney, Jerome

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]

Othonos, A.

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

Peyghambarian, N.

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]

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]

Polynkin, Alexander

Polynkin, Pavel

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]

Svelto, Orazio

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

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]

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)

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

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]

Opt. Lett. (3)

Other (4)

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

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.

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]

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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)

Equations on this page are rendered with MathJax. Learn more.

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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