Abstract

The bend-insensitive lasing characteristics of a newly designed ytterbium-doped photonic crystal fiber (YPCF) are evaluated numerically. The designed YPCF remains single-mode and possesses large-mode-area of 1400 µm2 at 1064 nm wavelength with the beam quality factor (M 2) of 1.15, suggesting a diffraction-limited and continuous-wave lasing operation. The doped-region size is optimized for maximum conversion efficiency and it is found through numerical simulations that the doped radius should be more than 21 µm. The “mode expansion”, which is the self-expansion of the fundamental mode within the doped region with wavelength increments on bending the fiber, is the basic physical mechanism to give the bend-insensitive lasing performances of YPCF. It leads to an unusual variation of overlap factor when the wavelength is increased. A 41 cm long piece of YPCF demonstrates more than 83% of slope efficiency with 75% of conversion efficiency when pumped with a 975 nm laser source delivering an input power of 1 W.

© 2008 Optical Society of America

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  1. 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, 2-13 (1995).
    [CrossRef]
  2. P.St.J. Russell, "Photonic crystal fiber," Science 288, 358-362 (2003).
    [CrossRef]
  3. J.C. Knight, "Photonic crystal fibers and fiber lasers," J. Opt. Soc. Am. B 24, 1661-1668 (2007).
    [CrossRef]
  4. T.A. Birks, J.C. Knight, and P.St.J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  5. A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic Crystal Fibres, (Kluwer Academic, The Netherlands, 2003).
    [CrossRef]
  6. A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
    [CrossRef]
  7. S. Hilaire, D. Pagnoux, P. Roy, and S , Fevrier, "Numerical study of single-mode Er-doped microstructured fibers: influence of geometrical parameters on amplifier performances," Opt. Express 14, 10865-10877 (2006).
    [CrossRef] [PubMed]
  8. W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
    [CrossRef]
  9. F. Furusawa, A. Malinowski, J.H.V. Price, T.M. Monro, J.K. Sahu, J. Nilsson, and D.J. Richardson, "Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding," Opt. Express 9, 714-720 (2001).
    [CrossRef] [PubMed]
  10. W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, and P. Russell, " High power air-clad photonic crystal fiber laser," Opt. Express 11, 48-53, 2003.
    [CrossRef] [PubMed]
  11. J. Limpert, T. Schreiber, S. Nolte, H. Zelmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, "High power air-clad large mode area photonic crystal fiber laser," Opt. Express 11, 818-823 (2003).
    [CrossRef] [PubMed]
  12. L. Dong, J. Li, and X. Peng, "Bend-resistant fundamental mode operation in ytterbium-doped leakage channel fibers with effective areas up to 3160 μm2," Opt. Express 14, 11512-11518 (2006).
    [CrossRef] [PubMed]
  13. X. Peng and L. Dong, "Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 μm2," Opt. Lett. 32, 358-360 (2007).
    [CrossRef] [PubMed]
  14. Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design of single-mode holey fibers with large-mode-area and low bending losses: the significance of the ring-core region," Opt. Express 15, 1794-1803 (2007).
    [CrossRef] [PubMed]
  15. K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 33, 927-933 (2002).
    [CrossRef]
  16. K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, "Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends," Opt. Express 14, 11128-11141 (2006).
    [CrossRef] [PubMed]
  17. R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
    [CrossRef]
  18. www.mathworks.com
  19. C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
    [CrossRef]

2007

2006

2004

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

2003

2002

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 33, 927-933 (2002).
[CrossRef]

2001

2000

W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
[CrossRef]

1997

T.A. Birks, J.C. Knight, and P.St.J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

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, 2-13 (1995).
[CrossRef]

1994

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Barber, P.R.

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, 2-13 (1995).
[CrossRef]

Barnard, C.

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Birks, T.A.

Bouwmans, G.

Broeng, J.

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, 2-13 (1995).
[CrossRef]

Chrostowski, J.

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Cucinotta, A.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

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, 2-13 (1995).
[CrossRef]

Dong, L.

Fevrier, S

Furusawa, F.

Hanna, D. D.

R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Hanna, D.C.

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, 2-13 (1995).
[CrossRef]

Hilaire, S.

Iliew, R.

Jakobsen, C.

Kakihara, K.

Kavehrad, M.

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Knight, J.

Knight, J.C.

Kono, N.

Koshiba, M.

Lederer, F.

Li, J.

Limpert, J.

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, 2-13 (1995).
[CrossRef]

Malinowski, A.

Monro, T.M.

Myslinski, P.

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Nilsson, J.

Nolte, S.

Pagnoux, D.

Paschotta, R.

R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (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, 2-13 (1995).
[CrossRef]

Peng, X.

Percival, R.

Petersson, A.

Poli, F.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

Price, J.H.V.

Reeves, W.H.

W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
[CrossRef]

Richardson, D.J.

Roy, P.

Russell, P.

Russell, P.St.J.

P.St.J. Russell, "Photonic crystal fiber," Science 288, 358-362 (2003).
[CrossRef]

W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
[CrossRef]

T.A. Birks, J.C. Knight, and P.St.J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

Sahu, J.K.

Saitoh, K.

Schreiber, T.

Selleri, S.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

Tropper, A.C.

R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (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, 2-13 (1995).
[CrossRef]

Tsuchida, Y.

Tunnermann, T.

Vienne, G.

Wadsworth, W.

Wadsworth, W.J.

W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
[CrossRef]

Zelmer, H.

Electron. Lett.

W.J. Wadsworth, J.C. Knight, W.H. Reeves, and P.St.J. Russell," Yb3+-doped photonic crystal fiber laser," Electron. Lett. 36, 1452-1453 (2000).
[CrossRef]

IEEE J. Quantum Electron.

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 33, 927-933 (2002).
[CrossRef]

R. Paschotta, J. Nilsson, A.C. Tropper, and D. D. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[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, 2-13 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic crystal fiber based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

F. Furusawa, A. Malinowski, J.H.V. Price, T.M. Monro, J.K. Sahu, J. Nilsson, and D.J. Richardson, "Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding," Opt. Express 9, 714-720 (2001).
[CrossRef] [PubMed]

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, and P. Russell, " High power air-clad photonic crystal fiber laser," Opt. Express 11, 48-53, 2003.
[CrossRef] [PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zelmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, "High power air-clad large mode area photonic crystal fiber laser," Opt. Express 11, 818-823 (2003).
[CrossRef] [PubMed]

L. Dong, J. Li, and X. Peng, "Bend-resistant fundamental mode operation in ytterbium-doped leakage channel fibers with effective areas up to 3160 μm2," Opt. Express 14, 11512-11518 (2006).
[CrossRef] [PubMed]

S. Hilaire, D. Pagnoux, P. Roy, and S , Fevrier, "Numerical study of single-mode Er-doped microstructured fibers: influence of geometrical parameters on amplifier performances," Opt. Express 14, 10865-10877 (2006).
[CrossRef] [PubMed]

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, "Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends," Opt. Express 14, 11128-11141 (2006).
[CrossRef] [PubMed]

Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design of single-mode holey fibers with large-mode-area and low bending losses: the significance of the ring-core region," Opt. Express 15, 1794-1803 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Science

P.St.J. Russell, "Photonic crystal fiber," Science 288, 358-362 (2003).
[CrossRef]

Other

A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic Crystal Fibres, (Kluwer Academic, The Netherlands, 2003).
[CrossRef]

www.mathworks.com

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Figures (12)

Fig. 1.
Fig. 1.

A 3-D schematic of Ytterbium-doped PCF. The parameters r d, d, d 1, d 2, and Λ stand for the radius of the doped region, hole-diameters of small, large, medium air-holes, and the pitch constant of the PCF, are d/Λ=0.45, d 1/Λ=0.95, d 2/Λ=0.51, and Λ=20 µm.

Fig. 2.
Fig. 2.

The variation of effective mode area of pump (975 nm, solid blue curve) and the output lasing wavelengths (1064 nm, solid red curve) as a function of bending radius in a passive PCF. It can be seen from the results that both curves closely follows each other as the bending radius is increased and attains nearly similar effective mode area of 1400 µm2.

Fig. 3.
Fig. 3.

The overlap factor Γ as a function of wavelength for doping radius of (a) 10 µm, (b) 15 µm, and (c) 25 µm when the YPCF is straight (solid green curve), bended in 10 cm (dashed red curve) and 5 cm (dotted blue curve) bending radii. The overlap factor curves for bent cases show contrary behavior with increasing wavelength i.e. the overlap values increase as the wavelength increases on bending the YPCF due to the “mode expansion” mechanism that occurs when the YPCF is bent into smaller bending radius.

Fig. 4.
Fig. 4.

The snapshots of the electric field distribution of fundamental mode at 1064 nm in YPCF when the fiber is straight (a), (d), (g); bent into 10 cm bending radius (b), (e), (h); 5 cm bending radius (c), (f), (i) for different doping radii r d=10 µm, 15 µm, and 25 µm, respectively.

Fig. 5.
Fig. 5.

The electric field distributions of fundamental mode in a 25 µm doping radius YPCF bent into a 10 cm bending radius at (a) 900 nm and (b) 1200 nm wavelengths. It can be clearly seen that the modal field expands within the doped region towards the center of the core as indicated by solid black arrow when the wavelength increases. This “mode expansion” mechanism gives unusual variation of the modal overlap which leads to the bend-insensitive lasing performance of the YPCF.

Fig. 6.
Fig. 6.

Overlap factor as a function of the inverse of the bending radius at pump 975 nm (dashed blue curve) and the output lasing signal 1064 nm (solid red curve).

Fig. 7.
Fig. 7.

(a) The plot between fiber length L and the reflectivity R out of FBG corresponding to the lasing wavelength with conversion efficiency as a parameter when the input pump power is 1 W. The fiber length can be deduced from the above graph for maximum conversion efficiency. The length of YPCF is 1.22 m for maximum conversion efficiency of 75% at 90% of reflectivity of output FBG, (b) the output lasing characteristics of 1.22 m long YPCF as a function of input pump power when the YPCF is straight (solid green curve), bent into 10 cm (dashed red curve) and 5 cm (dotted blue curve) bending radii. The corresponding slope efficiencies are 83 %, 48%, and 0%, respectively.

Fig. 8.
Fig. 8.

(a) The plot between fiber length L and the reflectivity R out of FBG corresponding to the lasing wavelength with conversion efficiency as a parameter when the input pump power is 1 W. The fiber length can be deduced from the above graph for maximum conversion efficiency. The length of YPCF is 0.65 m for maximum conversion efficiency of 75% at 90% of reflectivity of output FBG, (b) the output lasing characteristics of 0.65 m long YPCF as a function of input pump power when the YPCF is straight (solid green curve), bent into 10 cm (dashed red curve) and 5 cm (dotted blue curve) bending radii. The corresponding slope efficiencies are 84 %, 81%, and 19%, respectively.

Fig. 9.
Fig. 9.

(a) The plot between fiber length L and the reflectivity R out of FBG corresponding to the lasing wavelength with conversion efficiency as a parameter when the input pump power is 1 W. The fiber length can be deduced from the above graph for maximum conversion efficiency. The length of YPCF is 0.41 m for maximum conversion efficiency of 75% at 90% of reflectivity of output FBG, (b) the output lasing characteristics of 0.41 m long YPCF as a function of input pump power when the YPCF is straight (solid green curve), bent into 10 cm (dashed red curve) and 5 cm (dotted blue curve) bending radii. The corresponding slope efficiencies are 83 %, 85%, and 86%, respectively.

Fig. 10.
Fig. 10.

Comparison between two approaches used to obtain lasing performances of the proposed YPCF. The solid red curve corresponds to the laser output power calculated from the analytical relations mentioned in Ref. [19], whereas the solid blue curve stands for the laser characteristics obtained numerically by solving the rate equations. A 7% of error is estimated in slope efficiencies between two curves.

Fig. 11.
Fig. 11.

Slope efficiency as a function of doped radius r d. On vertical axis, the difference of slope efficiencies (ΔS=S 5cm-S straight, where S 5cm and S straight are the slope efficiencies when the YPCF is bent in 5 cm bending radius and it is kept straight) is plotted. It is apparent from the numerical result that a high and an almost constant slope efficiency can be obtained if the doped radius is assumed larger than 21 µm i.e. r d≥21 µm.

Fig. 12.
Fig. 12.

The contour plot between the overlap factors for pump Γp and lasing signal Γs with output lasing power P o as a parameter for 41 cm long YPCF with 25 µm doped radius. It can be observed from the graph that Γsp when the YPCF is bent, which is opposite to what is found in conventional Yb-doped fibers and PCFs. The larger value of Γs on bending can lead to high powers from YPCF laser. Also, note that the output power P o increases on shortening the bending radius.

Tables (2)

Tables Icon

Table 1. The optical parameters for YPCF laser.

Tables Icon

Table 2. Summary of the bend-insensitive lasing characteristics of YPCF

Equations (1)

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Γ s , p = S d E s , p ( x , y ) 2 dx dy S E s , p ( x , y ) 2 dx dy

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