Abstract

The nonlinearity of photonic crystal fibers (PCFs) can be enhanced by simutaneously tapering the fiber and doping rare-earth ions (such as Yb3+) or chalcogenide in the core. The properties of the Yb3+-doped and tapered PCF is numerically investigated by the beam propagation method. The results show that the difference of the optical field distribution between the doped and the pure silica PCF is not huge, and the mode field area of the doped PCF is only a little smaller than that of pure silica PCF. However, the nonlinearity of the doped PCF is enhanced dramatically by doping Yb ions in the core. Furthermore, the optimal boundary profile of the transverse structural parameters for maximal nonlinearity coefficient is acquired, and the boundary normalized pitch decreases exponentially with the boundary normalized hole size increasing. Finally, the longitudinal criterion for tapering is proposed, namely, that the normalized distance of the taper slope should be longer than 30μm. All these results will provide references for enhancing the nonlinearity of PCFs.

© 2006 Optical Society of America

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References

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2004 (3)

2003 (3)

2002 (1)

2001 (1)

2000 (2)

B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, "Cladding-mode resonances in air-silica microstructure optical fibers," J. Lightwave Technol. 18, 1084-1100 (2000).
[CrossRef]

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

1998 (2)

1997 (1)

1992 (1)

1991 (1)

1990 (2)

D. Yevick and B. Hermansson, "Efficient beam propagation techniques," IEEE J. Quantum Electron. 26, 109-112 (1990).
[CrossRef]

Y. Chung and N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

1980 (1)

Arkwright, J. W.

Atkins, G. R.

Bardyszewski, W.

Birks, T. A.

Bolger, J. A.

Burdge, G. L.

Chung, Y.

Dagli, N.

Y. Chung and N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

De Sario, M.

Digonnet, M. J. F.

Eggleton, B. J.

Elango, P.

Felt, M. D.

Finazzi, V.

Fleck, J. J. A.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

Han, W.

Hasegawa, T.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

Hermansson, B.

D. Yevick and B. Hermansson, "Efficient beam propagation techniques," IEEE J. Quantum Electron. 26, 109-112 (1990).
[CrossRef]

Jha, A.

Kar, A. K.

Kerbage, C.

Kim, N. S.

Kim, Y. H.

Knight, J. C.

Koshiba, M.

Leon-Saval, S. G.

Lize, Y. K.

Lizier, J. T.

Magi, E. C.

Marchese, D.

Mason, M. W.

Monro, T. M.

Mortensen, N. A.

Osgood, R. M.

Paek, U.

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

Richardson, D. J.

Russell, P.

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Russell, P. St. J.

Saitoh, K.

Sasaoka, E.

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

R. Scarmozzino and R. M. Osgood, "Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications," J. Opt. Soc. Am. A 8, 724-731 (1991).
[CrossRef]

Smith, E. C.

Steinvurzel, P.

Ta'eed, V. G.

Town, G. E.

Wadsworth, W. J.

Westbrook, P. S.

Whitbread, T.

White, C. A.

Windeler, R. S.

Yevick, D.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

D. Yevick and B. Hermansson, "Efficient beam propagation techniques," IEEE J. Quantum Electron. 26, 109-112 (1990).
[CrossRef]

Y. Chung and N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Opt. Express (5)

Opt. Lett. (3)

Science (1)

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Schematic of Yb 3 + -doped triangular PCF tapered by stretching under a brushing flame while maintaining the air holes. The right and the left insets are the transverse section of the taper waist and the untapered PCF with d Λ = 0.5 , respectively.

Fig. 2
Fig. 2

(a) and ( a ) are the electronic field distributions of the fundamental mode in Yb 3 + -doped PCF with d Λ = 0.6 and Λ λ = 5 , (b) and ( b ) are the electronic field distribution of the fundamental mode in undoped PCF with d Λ = 0.6 and Λ λ = 5 .

Fig. 3
Fig. 3

Effective MFA as a function of d Λ for the doped and the undoped PCF with Λ λ = 1.9355 and 3.2258.

Fig. 4
Fig. 4

MFA as a function of Λ λ for doped and undoped PCF with d Λ = 0.3 and 0.6.

Fig. 5
Fig. 5

Nonlinear coefficient as a function of Λ λ with d Λ = 0.6 and 0.9.

Fig. 6
Fig. 6

Nonlinear coefficient of Yb 3 + -doped PCF as a function of d Λ with Λ λ = 1.935 and 3.225.

Fig. 7
Fig. 7

Nonlinear coefficient as a function of Λ λ with different d Λ .

Fig. 8
Fig. 8

Optimal structure parameters boundary profile of the maximal nonlinear coefficient.

Fig. 9
Fig. 9

Maximum of the nonlinear coefficient as a function of d Λ .

Fig. 10
Fig. 10

Average intensity in the Yb 3 + doped core I core as a function of normalized distance of the taper slope L R 1 , where L is the distance of the taper slope and R is the taper ratio.

Fig. 11
Fig. 11

MFA (left axis) and nonlinear coefficient (right axis) versus the longitude axis z in the tapering process, The tapered PCF with R = 10 , L = 600 μ m , d Λ = 0.9 , Λ w = 0.7492 , which is the optimal pitch when λ = 1.55 μ m .

Equations (6)

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R = Λ tapered Λ untapered ,
MFA = [ E ( x , y ) E * ( x , y ) d x d y ] 2 [ E ( x , y ) E * ( x , y ) ] 2 d x d y ,
A eff = n 2 [ E ( x , y ) E * ( x , y ) d x d y ] 2 n 2 ˜ ( x , y ) [ E ( x , y ) E * ( x , y ) ] 2 d x d y ,
γ = 2 π n 2 λ A eff ,
γ = 2 π n 2 ˜ ( x , y ) [ E ( x , y ) E * ( x , y ) ] 2 d x d y λ [ E ( x , y ) E * ( x , y ) d x d y ] 2 .
I core = core E 2 d x d y core d x d y ,

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