Abstract

Fiber Bragg gratings inscribed with a femtosecond laser using the point-by-point (PbP) technique have polarization dependent grating strength (PDGS) and exhibit birefringence. In this paper we quantify the dependence of these two properties on the ellipticity, position in the core and size of the micro-voids at the center of each refractive index modulation. We demonstrate that the effective modal index for type II gratings written with a femtosecond laser using the PbP method must be lower than that of the pristine fiber, and for the first time associate an axis with a polarization such that the long axis of the elliptically-shaped index modulations corresponds to the slow axis of the gratings. We exploit the PDGS of two gratings used as frequency-selective feedback elements as well as appropriate coiling, to realize a linearly-polarized fiber laser with a low birefringence fiber cavity. We show that the polarization-dependent grating strength is a function of the writing pulse energy and that only gratings optimized for this property will linearly polarize the fiber laser. The fiber lasers have high extinction ratios (>30 dB) for fiber lengths of up to 10 m and very stable polarized output powers (<0.5% amplitude fluctuations) in the range of 20–65 mW at 1540 nm. This method of polarization discrimination allows the realization of highly robust and simplified linearly polarized fiber lasers.

© 2009 Optical Society of America

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  1. Y. Lai, A. Martinez, I. Khrushchev and I. Bennion, "Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription," Opt. Lett. 31, 1672-1674 (2006).
    [CrossRef] [PubMed]
  2. E. Wikszak, J. Thomas, J. Burghoff, B. Ortaç, J. Limpert, S. Nolte, U. Fuchs, and A. Tünnermann, "Erbium fiber laser based on intracore femtosecond-written fiber Bragg grating," Opt. Lett. 31, 2390-2392 (2006).
    [CrossRef] [PubMed]
  3. N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, "Stable high-power continuous-wave Yb3+ - doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating," Opt. Lett. 32, 1486-1488 (2007).
    [CrossRef] [PubMed]
  4. C. W. Smelser, S. J. Mihailov and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
    [CrossRef] [PubMed]
  5. A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
    [CrossRef]
  6. N. Jovanovic, M. Åslund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, "Narrow linewidth, 100W cw Yb3+-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core," Opt. Lett. 32, 2804-2806 (2007).
    [CrossRef] [PubMed]
  7. N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
    [CrossRef]
  8. P. Lu, D. Grobnic and S. J. Mihailov, "Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser," IEEE J. Lightwave Technology 25, 779-786 (2007).
    [CrossRef]
  9. Y. Lai, K. Zhou, K Sugden, and I. Bennion, "Point-by-point inscription of first order fiber Bragg grating for C band applications," Opt. Express 15, 18318-18325 (2007).
    [CrossRef] [PubMed]
  10. E. Wikszak, J. Thomas, S. Klingebiel, B. Ortaç, J. Limpert, S. Nolte, and A. Tünnermann, "Linearly polarized ytterbium fiber laser based on intracore femtosecond-written fiber Bragg gratings," Opt. Lett. 32, 2756-2758 (2007).
    [CrossRef] [PubMed]
  11. A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
    [CrossRef]
  12. C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
    [CrossRef]
  13. Comsol, Perpendicular Hybrid Mode Waves Package, www.comsol.com
  14. RSoft, BandSOLVE, www.rsoftdesign.com
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    [CrossRef]
  16. SMF 28e specification sheet, http://www.corning.com/WorkArea/showcontent.aspx?id=15535
  17. I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
    [CrossRef]
  18. R. B. Dyott, Elliptical fiber waveguides, (Artech House, London, 1995).
  19. M. J. Steel and R. M. Osgood, Jr, "Elliptical hole photonic crystal fibers," Opt. Lett. 26, 229-231 (2001).
    [CrossRef]
  20. T. Erdogan, "Fiber grating spectra," IEEE J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  21. S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
    [CrossRef]
  22. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999).
    [CrossRef]
  23. F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
    [CrossRef]

2008

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
[CrossRef]

2007

2006

Y. Lai, A. Martinez, I. Khrushchev and I. Bennion, "Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription," Opt. Lett. 31, 1672-1674 (2006).
[CrossRef] [PubMed]

E. Wikszak, J. Thomas, J. Burghoff, B. Ortaç, J. Limpert, S. Nolte, U. Fuchs, and A. Tünnermann, "Erbium fiber laser based on intracore femtosecond-written fiber Bragg grating," Opt. Lett. 31, 2390-2392 (2006).
[CrossRef] [PubMed]

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

2005

A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
[CrossRef]

C. W. Smelser, S. J. Mihailov and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

2004

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
[CrossRef]

I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
[CrossRef]

2001

1999

1997

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

1965

Åslund, M.

Bennetts, S.

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
[CrossRef]

Bennion, I.

Y. Lai, K. Zhou, K Sugden, and I. Bennion, "Point-by-point inscription of first order fiber Bragg grating for C band applications," Opt. Express 15, 18318-18325 (2007).
[CrossRef] [PubMed]

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

Y. Lai, A. Martinez, I. Khrushchev and I. Bennion, "Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription," Opt. Lett. 31, 1672-1674 (2006).
[CrossRef] [PubMed]

A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
[CrossRef]

Borrelli, N. F.

Burghoff, J.

Douay, M.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Dubov, M.

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

Dürr, F.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Erdogan, T.

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

Fertein, E.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Fuchs, U.

Fuerbach, A.

Gaeta, A. L.

Gamaly, E.

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

Grobnic, D.

P. Lu, D. Grobnic and S. J. Mihailov, "Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser," IEEE J. Lightwave Technology 25, 779-786 (2007).
[CrossRef]

C. W. Smelser, S. J. Mihailov and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

Hashimoto, T.

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

Hindle, F.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Homoelle, D.

Hwang, I. K.

I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
[CrossRef]

Jackson, S. D.

Jamison, A. O.

C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
[CrossRef]

Jovanovic, N.

Juodkazis, S.

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

Khrushchev, I.

Khrushchev, I. Y.

A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
[CrossRef]

Khrushchev, I.Y.

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

Klingebiel, S.

Lai, Y.

Lancaster, D. G.

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
[CrossRef]

Lee, Y. H.

I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
[CrossRef]

Limberger, H. G.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Limpert, J.

Lu, P.

P. Lu, D. Grobnic and S. J. Mihailov, "Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser," IEEE J. Lightwave Technology 25, 779-786 (2007).
[CrossRef]

Luther-Davies, B.

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

Malitson, I. H.

Marshall, G. D.

Martinez, A.

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

Y. Lai, A. Martinez, I. Khrushchev and I. Bennion, "Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription," Opt. Lett. 31, 1672-1674 (2006).
[CrossRef] [PubMed]

A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
[CrossRef]

Mazur, E.

C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
[CrossRef]

Mihailov, S. J.

P. Lu, D. Grobnic and S. J. Mihailov, "Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser," IEEE J. Lightwave Technology 25, 779-786 (2007).
[CrossRef]

C. W. Smelser, S. J. Mihailov and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

Misawa, H.

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

Nolte, S.

Oh, K.

I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
[CrossRef]

Ortaç, B.

Osgood, R. M.

Payne, D. N.

I. K. Hwang, Y. H. Lee, K. Oh and D.N. Payne, "High birefringence in elliptical hollow optical fiber," Opt. Express 20, 1916 (2004).
[CrossRef]

Przygodski, C.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Salathe, R. P.

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Schaffer, C. B.

C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
[CrossRef]

Smelser, C. W.

Smith, C.

Steel, M. J.

Sugden, K

Thomas, J.

Town, G. E.

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
[CrossRef]

Tünnermann, A.

Wielandy, S.

Wikszak, E.

Withford, M. J.

Zhou, K.

Appl. Phys. Lett.

C. B. Schaffer, A. O. Jamison and E. Mazur, "Morphology of femtosecond laser-induced structural changes in bulk transparent materials," Appl. Phys. Lett. 84, 1441-1443 (2004).
[CrossRef]

S. Juodkazis, H. Misawa, T. Hashimoto, E. Gamaly, B. Luther-Davies, "Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids," Appl. Phys. Lett. 88, 201909 (2006)
[CrossRef]

F. Dürr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertein, and C. Przygodski, "Tomographic measurement of femtosecond-laser induced stress changes in optical fibers," Appl. Phys. Lett. 84, 4983-4985 (2004).
[CrossRef]

Electron. Lett.

A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fiber Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-177 (2005).
[CrossRef]

IEEE J. Lightwave Technol.

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

IEEE J. Lightwave Technology

P. Lu, D. Grobnic and S. J. Mihailov, "Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser," IEEE J. Lightwave Technology 25, 779-786 (2007).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Y. Lai, A. Martinez, I. Khrushchev and I. Bennion, "Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription," Opt. Lett. 31, 1672-1674 (2006).
[CrossRef] [PubMed]

E. Wikszak, J. Thomas, J. Burghoff, B. Ortaç, J. Limpert, S. Nolte, U. Fuchs, and A. Tünnermann, "Erbium fiber laser based on intracore femtosecond-written fiber Bragg grating," Opt. Lett. 31, 2390-2392 (2006).
[CrossRef] [PubMed]

N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, "Stable high-power continuous-wave Yb3+ - doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating," Opt. Lett. 32, 1486-1488 (2007).
[CrossRef] [PubMed]

E. Wikszak, J. Thomas, S. Klingebiel, B. Ortaç, J. Limpert, S. Nolte, and A. Tünnermann, "Linearly polarized ytterbium fiber laser based on intracore femtosecond-written fiber Bragg gratings," Opt. Lett. 32, 2756-2758 (2007).
[CrossRef] [PubMed]

N. Jovanovic, M. Åslund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, "Narrow linewidth, 100W cw Yb3+-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core," Opt. Lett. 32, 2804-2806 (2007).
[CrossRef] [PubMed]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999).
[CrossRef]

M. J. Steel and R. M. Osgood, Jr, "Elliptical hole photonic crystal fibers," Opt. Lett. 26, 229-231 (2001).
[CrossRef]

Photon. Technol. Lett.

A. Martinez, M. Dubov, I.Y. Khrushchev, and I. Bennion, "Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation," Photon. Technol. Lett. 18, 2266-2268 (2006).
[CrossRef]

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-901 (2008).
[CrossRef]

Other

Comsol, Perpendicular Hybrid Mode Waves Package, www.comsol.com

RSoft, BandSOLVE, www.rsoftdesign.com

SMF 28e specification sheet, http://www.corning.com/WorkArea/showcontent.aspx?id=15535

R. B. Dyott, Elliptical fiber waveguides, (Artech House, London, 1995).

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Figures (10)

Fig. 1.
Fig. 1.

(a). Transmission spectra for two orthogonal states of linear polarization for a PbP FBG written with 160 nJ. (b). Transmission image of a typical PbP FBG taken orthogonal to the writing direction. (c). Schematic diagram of the cross section of a single RIM in the PbP FBG.

Fig. 2.
Fig. 2.

(a). CAD idealization of the cross-sectional refractive index profile of a RIM in a PbP FBG. (b) Energy flux profile for the x-polarized mode. (c) Energy flux profile for the y-polarized mode, magnified around the void region.

Fig. 3.
Fig. 3.

(a). Birefringence and (b) difference in coupling coefficients as a function of void area for constant ellipticities. The dashed lines join the points of maximum birefringence and Δκ.

Fig. 4.
Fig. 4.

(a). Absolute R, for two orthogonal states of linear polarization as a function of Av for grating lengths of 4, 6, and 8 mm. Dotted lines represent the y-polarization and solid lines represent the x-polarization. (b) Displays the corresponding ΔR.

Fig. 5.
Fig. 5.

(a) Energy flux profile when a PbP RIM is vertically offset in the core. (b) ΔnB and Δκ as a function of vertical offset of the PbP RIM.

Fig. 6.
Fig. 6.

Birefringence, difference in cross-coupling coefficient, κ, and power confined within the densified region as a function of Δnd . The dimensions of the modulation used in the calculation are displayed in the figure.

Fig. 7.
Fig. 7.

Linear grating reflectivity for two orthogonal states of linear polarization, the difference between them and the birefringence as a function of pulse energy.

Fig. 8.
Fig. 8.

Schematic of fiber laser architecture with various laser cavities. (a) HR silver mirror and a low reflecting splice as OC, (b) HR FBG and OC FBG, (c) HR Silver mirror and an OC FBG, (d) HR FBG and a low reflecting splice. Note: yellow lightning bolts represent splices.

Fig. 9.
Fig. 9.

(a). Transmission spectra for a PDGS optimized HR and OC and a non-optimized HR. The dotted curves correspond to light polarized parallel to the long axis of the REVIs while the solid curves correspond to light polarized perpendicular to the long axis of the REVIs. (b) Output power as a function of time for cavity configuration (b). Inset to (b) shows a typical laser spectrum from fiber lasers with cavity configurations (b), (c) and (d).

Fig. 10.
Fig. 10.

ER for different cavity lengths for cavity configuration (b).

Tables (1)

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Table 1. Extinction ratio of 3 m long fiber lasers with the four cavity configurations shown in Fig. 8.

Equations (3)

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n mvi = 1 Λ P [ ( w v · n v ) + ( Λ P w v ) · n core ] ,
κ m = π 4 · ω ε 0 8 m ∫∫ mod dxdy [ 2 n core Δ n ( x , y ) + Δ n ( x , y ) 2 ] · ( E t · E t * ) ,
R = tan h 2 ( κ m L ) .

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