Abstract

Abstract: We present a model for a Yb-doped distributed Bragg reflector (DBR) waveguide laser fabricated in phosphate glass using the femtosecond laser direct-write technique. The model gives emphasis to transverse integrals to investigate the energy distribution in a homogenously doped glass, which is an important feature of femtosecond laser inscribed waveguide lasers (WGLs). The model was validated with experiments comparing a DBR WGL and a fiber laser, and then used to study the influence of distributed rare earth dopants on the performance of such lasers. Approximately 15% of the pump power was absorbed by the doped “cladding” in the femtosecond laser inscribed Yb doped WGL case with the length of 9.8 mm. Finally, we used the model to determine the parameters that optimize the laser output such as the waveguide length, output coupler reflectivity and refractive index contrast.

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References

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  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett.21(21), 1729–1731 (1996), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-21-21-1729 .
    [CrossRef] [PubMed]
  2. G. Della Valle, S. Taccheo, R. Osellame, A. Festa, G. Cerullo, and P. Laporta, “1.5 mum single longitudinal mode waveguide laser fabricated by femtosecond laser writing,” Opt. Express15(6), 3190–3194 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6-3190 .
    [CrossRef] [PubMed]
  3. R. Mary, S. J. Beecher, G. Brown, R. R. Thomson, D. Jaque, S. Ohara, and A. K. Kar, “Compact, highly efficient ytterbium doped bismuthate glass waveguide laser,” Opt. Lett.37(10), 1691–1693 (2012), http://ol.osa.org/abstract.cfm?URI=ol-37-10-1691 .
    [CrossRef] [PubMed]
  4. G. D. Marshall, P. Dekker, M. Ams, J. A. Piper, and M. J. Withford, “Directly written monolithic waveguide laser incorporating a distributed feedback waveguide-Bragg grating,” Opt. Lett.33(9), 956–958 (2008), http://ol.osa.org/abstract.cfm?URI=ol-33-9-956 .
    [CrossRef] [PubMed]
  5. J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
    [CrossRef]
  6. I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron.34(9), 1570–1577 (1998).
    [CrossRef]
  7. M. A. Rebolledo and S. Jarabo, “Erbium-doped silica fiber modeling with overlapping factors,” Appl. Opt.33(24), 5585–5593 (1994), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-33-24-5585 .
    [CrossRef] [PubMed]
  8. I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
    [CrossRef]
  9. C. Florea and K. A. Winick, “Ytterbium-doped glass waveguide laser fabricated by ion exchange,” J. Lightwave Technol.17(9), 1593–1601 (1999).
    [CrossRef]
  10. M. Ams, G. Marshall, D. Spence, and M. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express13(15), 5676–5681 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5676 .
    [CrossRef] [PubMed]
  11. M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laser written active devices,” Laser Photonics Rev. 3, 535–544 (2009). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5676
  12. A. K. Mairaj, P. Hua, H. N. Rutt, and D. W. Hewak, “Fabrication and characterization of continuous wave direct UV (λ=244 nm) written channel waveguides in chalcogenide (Ga:La:S) glass,” J. Lightwave Technol.20(8), 1578–1584 (2002).
    [CrossRef]
  13. H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
    [CrossRef]
  14. C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
    [CrossRef]
  15. C. Henry, “Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,” J. Lightwave Technol.4(3), 288–297 (1986).
    [CrossRef]
  16. R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
    [CrossRef]
  17. A. V. Kir’yanov, Y. O. Barmenkov, I. L. Martinez, A. S. Kurkov, and E. M. Dianov, “Cooperative luminescence and absorption in ytterbium-doped silica fiber and the fiber nonlinear transmission coefficient at λ=980 nm with a regard to the ytterbium ion-pairs’ effect,” Opt. Express14(9), 3981–3992 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?id=89603 .
    [CrossRef] [PubMed]
  18. M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
    [CrossRef]
  19. T. G. Ryan and S. D. Jackson, “Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms,” Opt. Commun.273(1), 159–161 (2007).
    [CrossRef]
  20. J. Qiu and Y. Kawamoto, “Blue up-conversion luminescence and energy transfer process in Nd3+-Yb3+-Tm3+ co-doped ZrF4-based glasses,” J. Appl. Phys.91(3), 954–959 (2002).
    [CrossRef]
  21. D. G. Lancaster, S. Gross, H. Ebendorff-Heidepriem, K. Kuan, T. M. Monro, M. Ams, A. Fuerbach, and M. J. Withford, “Fifty percent internal slope efficiency femtosecond direct-written Tm³⁺:ZBLAN waveguide laser,” Opt. Lett.36(9), 1587–1589 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-9-1587 .
    [CrossRef] [PubMed]

2012

2011

2010

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

2008

2007

2006

2005

2003

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

2002

J. Qiu and Y. Kawamoto, “Blue up-conversion luminescence and energy transfer process in Nd3+-Yb3+-Tm3+ co-doped ZrF4-based glasses,” J. Appl. Phys.91(3), 954–959 (2002).
[CrossRef]

A. K. Mairaj, P. Hua, H. N. Rutt, and D. W. Hewak, “Fabrication and characterization of continuous wave direct UV (λ=244 nm) written channel waveguides in chalcogenide (Ga:La:S) glass,” J. Lightwave Technol.20(8), 1578–1584 (2002).
[CrossRef]

1999

1998

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron.34(9), 1570–1577 (1998).
[CrossRef]

1997

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

1996

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett.21(21), 1729–1731 (1996), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-21-21-1729 .
[CrossRef] [PubMed]

1995

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

1994

1991

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

1986

C. Henry, “Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,” J. Lightwave Technol.4(3), 288–297 (1986).
[CrossRef]

Ams, M.

Barber, P. R.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Barmenkov, Y. O.

Baumann, I.

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

Beecher, S. J.

Bell, M. J. V.

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Brinkmann, R.

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

Brown, G.

Caplen, J. E.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

Carman, R. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Cerullo, G.

Davis, K. M.

Dawes, J. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

de la Cruz, A. R.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

de Sousa, D. F.

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Dekker, P.

Della Valle, G.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

Dianov, E. M.

Dinand, M.

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

Ebendorff-Heidepriem, H.

Ferrer, A.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

Festa, A.

Florea, C.

Fuerbach, A.

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

Gross, S.

Hanna, D. C.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Hardy, A. A.

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron.34(9), 1570–1577 (1998).
[CrossRef]

Henry, C.

C. Henry, “Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,” J. Lightwave Technol.4(3), 288–297 (1986).
[CrossRef]

Hewak, D. W.

Hirao, K.

Hua, P.

Jackson, S. D.

T. G. Ryan and S. D. Jackson, “Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms,” Opt. Commun.273(1), 159–161 (2007).
[CrossRef]

Jaque, D.

Jarabo, S.

Kar, A. K.

Kawamoto, Y.

J. Qiu and Y. Kawamoto, “Blue up-conversion luminescence and energy transfer process in Nd3+-Yb3+-Tm3+ co-doped ZrF4-based glasses,” J. Appl. Phys.91(3), 954–959 (2002).
[CrossRef]

Kelson, I.

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron.34(9), 1570–1577 (1998).
[CrossRef]

Kir’yanov, A. V.

Kuan, K.

Kurkov, A. S.

Lancaster, D. G.

Laporta, P.

Mackechnie, C. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Mairaj, A. K.

Marshall, G.

Marshall, G. D.

Martinez, I. L.

Mary, R.

Miura, K.

Monro, T. M.

Nilsson, J.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

Nunes, L. A. O.

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Ohara, S.

Oliveira, S. L.

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Osellame, R.

Paschotta, R.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

Pask, H. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Piper, J. A.

Qiu, J.

J. Qiu and Y. Kawamoto, “Blue up-conversion luminescence and energy transfer process in Nd3+-Yb3+-Tm3+ co-doped ZrF4-based glasses,” J. Appl. Phys.91(3), 954–959 (2002).
[CrossRef]

Quirino, W. G.

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Rebolledo, M. A.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

M. A. Rebolledo and S. Jarabo, “Erbium-doped silica fiber modeling with overlapping factors,” Appl. Opt.33(24), 5585–5593 (1994), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-33-24-5585 .
[CrossRef] [PubMed]

Rutt, H. N.

Ryan, T. G.

T. G. Ryan and S. D. Jackson, “Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms,” Opt. Commun.273(1), 159–161 (2007).
[CrossRef]

Sanchez-Martin, J. A.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

Sohler, W.

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

Solis, J.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

Spence, D.

Sugimoto, N.

Taccheo, S.

Thomson, R. R.

Tropper, A. C.

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

Valles, J. A.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

Westenhofer, S.

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

Winick, K. A.

Withford, M.

Withford, M. J.

Appl. Opt.

IEEE J. Quantum Electron.

J. A. Valles, A. Ferrer, J. A. Sanchez-Martin, A. R. de la Cruz, M. A. Rebolledo, and J. Solis, “New characterization technique for femtosecond laser written waveguides in Yb/Er-codoped glass,” IEEE J. Quantum Electron.46(6), 996–1002 (2010).
[CrossRef]

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron.34(9), 1570–1577 (1998).
[CrossRef]

I. Baumann, R. Brinkmann, M. Dinand, W. Sohler, and S. Westenhofer, “Ti:Er:LiNbO3 waveguide laser of optimized efficiency,” IEEE J. Quantum Electron.32(9), 1695–1706 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron.1(1), 2–13 (1995).
[CrossRef]

J. Appl. Phys.

J. Qiu and Y. Kawamoto, “Blue up-conversion luminescence and energy transfer process in Nd3+-Yb3+-Tm3+ co-doped ZrF4-based glasses,” J. Appl. Phys.91(3), 954–959 (2002).
[CrossRef]

J. Lightwave Technol.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

C. Henry, “Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,” J. Lightwave Technol.4(3), 288–297 (1986).
[CrossRef]

C. Florea and K. A. Winick, “Ytterbium-doped glass waveguide laser fabricated by ion exchange,” J. Lightwave Technol.17(9), 1593–1601 (1999).
[CrossRef]

A. K. Mairaj, P. Hua, H. N. Rutt, and D. W. Hewak, “Fabrication and characterization of continuous wave direct UV (λ=244 nm) written channel waveguides in chalcogenide (Ga:La:S) glass,” J. Lightwave Technol.20(8), 1578–1584 (2002).
[CrossRef]

J. Phys. Condens. Matter

M. J. V. Bell, W. G. Quirino, S. L. Oliveira, D. F. de Sousa, and L. A. O. Nunes, “Cooperative luminescence in Yb3+ -doped phosphate glasses,” J. Phys. Condens. Matter15(27), 4877–4887 (2003).
[CrossRef]

Opt. Commun.

T. G. Ryan and S. D. Jackson, “Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms,” Opt. Commun.273(1), 159–161 (2007).
[CrossRef]

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibres,” Opt. Commun.136(5-6), 375–378 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laser written active devices,” Laser Photonics Rev. 3, 535–544 (2009). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5676

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Figures (7)

Fig. 1
Fig. 1

(a) DIC top-view image of a waveguide (b) respective end-on cross section image.

Fig. 2
Fig. 2

Schematic of the DBR waveguide laser. HR-High Reflectivity grating. OC-Output Coupler grating. DUT- Device Under Test. WDM- Wavelength-Division Multiplexer. OSA- Optical Spectrum Analyser.

Fig. 3
Fig. 3

Schematic illustration of the end-pumped waveguide laser.

Fig. 4
Fig. 4

Experimental (black dots) and theoretical (red line) output power versus pump power of the DBR fiber and waveguide laser.

Fig. 5
Fig. 5

(a) Output power versus pump power of the DBR waveguide laser (L = 9.8 mm) and (b) slope efficiency and threshold of the WGL as a function of waveguide length in fully doped glass and inhomogeneously doped glass (r = 10 μm).

Fig. 6
Fig. 6

Slope efficiency for various waveguide length and OC reflectivities.

Fig. 7
Fig. 7

Slope efficiency and output power (with incident power of 300 mW) as a function of refractive index contrasts.

Tables (1)

Tables Icon

Table 1 Parameters used for the Yb3+-doped DBR waveguide and fiber laser model.

Equations (7)

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± d P p ± dz = σ ep P p ± (z) 0 2π 0 i p (r,ϕ) n 2 (r,ϕ,z)rdrdϕ σ ap P p ± (z) 0 2π 0 i p (r,ϕ)( n t (r,ϕ,z) n 2 (r,ϕ,z))rdrdϕ α p P p ± (z)
± d P s ± dz = σ es P s ± (z) 0 2π 0 i s (r,ϕ) n 2 (r,ϕ,z)rdrdϕ σ as P s ± (z) 0 2π 0 i s (r,ϕ)( n t (r,ϕ,z) n 2 (r,ϕ,z))rdrdϕ α s P s ± (z)
n 2 (r,ϕ,z)= n t (r,ϕ,z) τ σ ap h v p ( P p + + P p ) i p + τ σ as h v s ( P s + + P s ) i s 1+ τ( σ ap + σ ep ) h v p ( P p + + P p ) i p + τ( σ as + σ es ) h v s ( P s + + P s ) i s
P s (L)= P s + (L) R sL T 2 ,
P s + (0)= P s (0) R s0 T 2 ,
P p + (0)= P p (0) R p0 T 2 +P(0),
P p (L)= P p + (L) R pL T 2 +P(L),

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