Abstract

When the mode field and refractive index mismatches between two spliced fibers are small, the splice loss is generally evaluated by calculating an overlap integral without reflection waves. A single-polarization circular-hole holey fiber with a core consisting of an elliptical-hole lattice (EC-CHF) has a strikingly different mode field caused by elliptical holes in the core region from those of conventional single-mode fibers (SMFs), and thus reflected radiation modes may significantly appear in splicing an EC-CHF to conventional SMFs. We study the influence of reflected radiation modes on the splice loss evaluation of optical fibers with large mode field and large refractive index mismatches through numerical analyses using a bidirectional eigenmode propagation method and a three-dimensional finite-element method.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (4)

2009 (3)

2008 (2)

2007 (2)

2006 (2)

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
[CrossRef]

G. Brambilla, F. Xu, and X. Feng, “Fabrication of optical fibre nanowires and their optical and mechanical characterisation,” Electron. Lett. 42, 517–519 (2006).
[CrossRef]

2004 (1)

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

1997 (2)

1996 (1)

1995 (1)

T. Conese, G. Barbarossa, and M. N. Armenise, “Accurate loss analysis of single-mode fiber/D-fiber splice by vectorial finite-element method,” IEEE Photon. Technol. Lett. 7, 523–525(1995).
[CrossRef]

1994 (2)

M. Koshiba, S. Maruyama, and K. Hirayama, “A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).
[CrossRef]

1991 (1)

J. P. Meunier and S. I. Hosain, “An efficient model for splice loss evaluation in single-mode graded-index fibers,” J. Lightwave Technol. 9, 1457–1463 (1991).
[CrossRef]

1983 (1)

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983).
[CrossRef]

1978 (1)

1977 (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

1973 (1)

J. S. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints,” Bell Syst. Tech. J. 52, 1439–1448 (1973).

1952 (1)

G. Goubau, “On the excitation of surface waves,” Proc. IRE 40, 865–868 (1952).
[CrossRef]

Abdou-Ahmed, M.

Aghaie, K. Z.

Armenise, M. N.

T. Conese, G. Barbarossa, and M. N. Armenise, “Accurate loss analysis of single-mode fiber/D-fiber splice by vectorial finite-element method,” IEEE Photon. Technol. Lett. 7, 523–525(1995).
[CrossRef]

Atkin, D. M.

Barbarossa, G.

T. Conese, G. Barbarossa, and M. N. Armenise, “Accurate loss analysis of single-mode fiber/D-fiber splice by vectorial finite-element method,” IEEE Photon. Technol. Lett. 7, 523–525(1995).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).
[CrossRef]

Birks, T. A.

Brambilla, G.

Conese, T.

T. Conese, G. Barbarossa, and M. N. Armenise, “Accurate loss analysis of single-mode fiber/D-fiber splice by vectorial finite-element method,” IEEE Photon. Technol. Lett. 7, 523–525(1995).
[CrossRef]

Cook, J. S.

J. S. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints,” Bell Syst. Tech. J. 52, 1439–1448 (1973).

Digonnet, M. J. F.

Duan, K.

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Eguchi, M.

Fan, S.

Feng, X.

Goubau, G.

G. Goubau, “On the excitation of surface waves,” Proc. IRE 40, 865–868 (1952).
[CrossRef]

Graf, T.

Grow, R. J.

J. S. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints,” Bell Syst. Tech. J. 52, 1439–1448 (1973).

Hirayama, K.

M. Koshiba, S. Maruyama, and K. Hirayama, “A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Ho, H. L.

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

Hoo, Y. L.

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

Horak, P.

Hosain, S. I.

J. P. Meunier and S. I. Hosain, “An efficient model for splice loss evaluation in single-mode graded-index fibers,” J. Lightwave Technol. 9, 1457–1463 (1991).
[CrossRef]

Jin, W.

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

Ju, J.

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

Jung, Y.

Kimura, T.

Knight, J. C.

Koizumi, F.

Koshiba, M.

M. Koshiba, S. Maruyama, and K. Hirayama, “A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Koukharenko, E.

Liu, Z.

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Mammel, W. L.

J. S. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints,” Bell Syst. Tech. J. 52, 1439–1448 (1973).

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972).

Maruyama, S.

M. Koshiba, S. Maruyama, and K. Hirayama, “A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Meunier, J. P.

J. P. Meunier and S. I. Hosain, “An efficient model for splice loss evaluation in single-mode graded-index fibers,” J. Lightwave Technol. 9, 1457–1463 (1991).
[CrossRef]

Murugan, G. S.

Petermann, K.

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983).
[CrossRef]

Richardson, D. J.

Russell, P. St. J.

Sakai, J.

Sessions, N. P.

Tsuji, Y.

Vogel, M. M.

Voss, A.

Wang, Y.

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Wilkinson, J. S.

Xu, F.

Xu, Z.

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Zhao, W.

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Bell Syst. Tech. J. (2)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

J. S. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints,” Bell Syst. Tech. J. 52, 1439–1448 (1973).

Electron. Lett. (2)

G. Brambilla, F. Xu, and X. Feng, “Fabrication of optical fibre nanowires and their optical and mechanical characterisation,” Electron. Lett. 42, 517–519 (2006).
[CrossRef]

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Eguchi and Y. Tsuji, “Bending loss evaluations of holey fibers having a core consisting of an elliptical-hole lattice by various approaches,” IEEE J. Quantum Electron. 46, 601–609 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Conese, G. Barbarossa, and M. N. Armenise, “Accurate loss analysis of single-mode fiber/D-fiber splice by vectorial finite-element method,” IEEE Photon. Technol. Lett. 7, 523–525(1995).
[CrossRef]

J. Comp. Physiol. (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).
[CrossRef]

J. Lightwave Technol. (3)

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
[CrossRef]

M. Koshiba, S. Maruyama, and K. Hirayama, “A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

J. P. Meunier and S. I. Hosain, “An efficient model for splice loss evaluation in single-mode graded-index fibers,” J. Lightwave Technol. 9, 1457–1463 (1991).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

Y. L. Hoo, W. Jin, J. Ju, and H. L. Ho, “Loss analysis of single-mode fiber/photonic-crystal fiber splice,” Microwave Opt. Technol. Lett. 40, 378–380 (2004).
[CrossRef]

Opt. Commun. (1)

Z. Xu, K. Duan, Z. Liu, Y. Wang, and W. Zhao, “Numerical analysis of splice losses of photonic crystal fibers,” Opt. Commun. 282, 4527–4531 (2009).
[CrossRef]

Opt. Lett. (8)

Proc. IRE (1)

G. Goubau, “On the excitation of surface waves,” Proc. IRE 40, 865–868 (1952).
[CrossRef]

Other (1)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972).

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Figures (21)

Fig. 1.
Fig. 1.

Elliptical-hole core circular-hole holy fiber (EC-CHF).

Fig. 2.
Fig. 2.

Calculation of the overlap-integral of the evaluation formula for a butt-joint splice loss.

Fig. 3.
Fig. 3.

Schematic drawing of BEP method.

Fig. 4.
Fig. 4.

Tetrahedral edge element (blue-colored arrows: edge vector).

Fig. 5.
Fig. 5.

Fiber splice between an EC-CHF and an SMF.

Fig. 6.
Fig. 6.

Splicing efficiency caused by the mode field mismatch in the 2D planar waveguide model corresponding to a large air-hole EC-CHF. Solid curve, overlap integral method. Open circles, BEP method. Pluses, xz-plane FEM.

Fig. 7.
Fig. 7.

Splicing efficiency caused by the mode field mismatch in the 2D planar waveguide model corresponding to a small air-hole EC-CHF. Solid curve, overlap integral method. Open circles, BEP method. Pluses, xz-plane FEM.

Fig. 8.
Fig. 8.

Wave propagation through the interface between a symmetric three-layer slab waveguide with a core layer width of 2aSMF and a multilayer planar waveguide with thick air layers. (a) aSMF=1μm. (b) aSMF=3μm. (c) aSMF=5μm.

Fig. 9.
Fig. 9.

Wave propagation through the interface between a symmetric three-layer slab waveguide with a core layer width of 2aSMF and a multilayer planar waveguide with thin air layers. (a) aSMF=1μm. (b) aSMF=3μm. (c) aSMF=5μm.

Fig. 10.
Fig. 10.

Reflection power of a large air-hole EC-CHF calculated by the BEP method. Blue-colored solid and red-colored dashed lines represent the reflected fundamental mode and total reflection powers, respectively.

Fig. 11.
Fig. 11.

Reflection power of a small air-hole EC-CHF calculated by the BEP method. Blue-colored solid and red-colored dashed lines represent the reflected fundamental mode and total reflection powers, respectively.

Fig. 12.
Fig. 12.

Splicing efficiency caused by the mode field mismatch between a small air hole EC-CHF and an SMF. (a) Splicing efficiency against the core radius of SMF. Solid curve and open circles correspond to the EC-CHF and the equivalent SI fiber, respectively. Closed circles represent the MFD of SMF. (b) Mode field distributions of the fundamental modes of the EC-CHF and SMFs with aSMF=2,3, and 4 μm.

Fig. 13.
Fig. 13.

Mode fields on the x axis of a small air hole EC-CHF (red-colored solid curve), equivalent SI fiber (dashed curve), and SMF (blue-colored solid curve).

Fig. 14.
Fig. 14.

Splicing efficiency caused by the mode field mismatch between a large air hole EC-CHF and an SMF. (a) Splicing efficiency against the core radius of SMF. Solid curve and open circles correspond to the EC-CHF and the equivalent SI fiber, respectively. Closed circles represent the MFD of SMF. (b) Mode field distributions of the fundamental modes of the EC-CHF and SMFs with aSMF=2,2.9,and3.5μm.

Fig. 15.
Fig. 15.

Mode fields on the x axis of a large air hole EC-CHF (red-colored solid curve), equivalent SI fiber (dashed curve), and SMF (blue-colored solid curve).

Fig. 16.
Fig. 16.

Splicing efficiency caused by butt-joint splice with an offset misalignment between a small air hole EC-CHF and an SMF.

Fig. 17.
Fig. 17.

Splicing efficiency caused by butt-joint splice with an offset misalignment between a large air hole EC-CHF and an SMF.

Fig. 18.
Fig. 18.

Element division at the splice interface for an SMF with aSMF=4μm.

Fig. 19.
Fig. 19.

Splicing efficiency caused by the mode field mismatch between a large air hole EC-CHF and an SMF calculated using the 3D FEM (blue-colored solid curve). Red-colored dashed curve, overlap integral method.

Fig. 20.
Fig. 20.

Mode fields on the xz- and yz-plane cross sections around the splice interfaces between the EC-CHF and three incident SMFs with aSMF= (a) 0.5, (b) 2.0, and (c) 2.5 μm.

Fig. 21.
Fig. 21.

Mode fields before (z=0.8μm), at (z=0μm), and after (z=0.8μm) the fiber splice interface calculated by 3D FEM.

Equations (48)

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

E1t+crE1t+0cr(ρ)E1t(ρ)dρ=ctE2t+0ct(ρ)E2t(ρ)dρ,
H1tcrH1t0cr(ρ)H1t(ρ)dρ=ctH2t+0ct(ρ)H2t(ρ)dρ,
(1+cr)I12=ctI11,
(1cr)I21=ctI22
Iij=S(Eit×Hjt)izdS,i,j=1,2,
η=ct2I22I11=4I212I122I11I22(I21+I12)2.
η=4neff,1neff,2[Sϕ1ϕ2dS]2(neff,1+neff,2)2Sϕ12dSSϕ22dS,
ϕi={AJ0(k02(n1,i2neff,i2)r)(rai)BK0(k02(neff,i2n2,i2)r)(r>ai),
B=AJ0(k02(n1,i2neff,i2)ai)K0(k02(neff,i2n2,i2)ai),
Ek=lekl{Aklexp[jβkl(zzk)]+Bklexp[jβkl(zzk)]},
Hk=lhkl{Aklexp[jβkl(zzk)]Bklexp[jβkl(zzk)]},
lekl(Akl+Bkl)=le(k+1)l{A(k+1)lexp(jβ(k+1)ldk+1)+B(k+1)lexp(jβ(k+1)ldk+1)},
lhkl(AklBkl)=lh(k+1)l{A(k+1)lexp(jβ(k+1)ldk+1)B(k+1)lexp(jβ(k+1)ldk+1)},
dk+1=zk+1zk.
[{A}k{B}k]=[F]k+1[{A}k+1{B}k+1]=[[P]k+1[Q]k+1[R]k+1[S]k+1][{A}k+1{B}k+1],
P(k+1)il=12(fkil(1)fkii(0)+gkil(1)gkii(0))exp(jβ(k+1)ldk+1),
Q(k+1)il=12(fkil(1)fkii(0)gkil(1)gkii(0))exp(jβ(k+1)ldk+1),
R(k+1)il=12(fkil(1)fkii(0)gkil(1)gkii(0))exp(jβ(k+1)ldk+1),
S(k+1)il=12(fkil(1)fkii(0)+gkil(1)gkii(0))exp(jβ(k+1)ldk+1),
fkil(ξ)=S(e(k+1)l×hki*)izdS,
gkil(ξ)=S(ekl*×h(k+1)i)izdS,ξ=0,1.
[{A}0{B}0]=[F][{A}N{B}N]=[[P][Q][R][S]][{A}N{B}N],
[F]=k=1N[F]k.
{A}N=[P]1{A}0,
{B}0=[R]{A}N=[R][P]1{A}0.
×([p]×Φ)k02[q]Φ=0,
[p]=[μr]1,[q]=[εr]forε0E,
[p]=[εr]1,[q]=[μr]forμ0H.
Φ=({U}Tix+{V}Tiy+{W}Tiz){Φe}={N}T{Φe},
[Pi]{Φi}=([Ki]k02[Mi]){Φi}={ui},i=A,B,
[Ki]=eiei(×{N})([p]×{N}T)dV,
[Mi]=eiei{N}([q]{N}T)dV,
{ui}=SiSi{N}Si{in×([p]×Φ)}SidS,
[[Pi]00[Pi]0Γ[Pi]Γ0[Pi]ΓΓ][{Φi}0{Φi}Γ]=[{ui}0{ui}Γ].
Φi|Γ=Φi,in|Γ+Φi,scat|Γ.
in×(×ΦA,scat)Γ=in×(×ΦB,scat)Γ,
ΦA,scat|Γ=ΦB,scat|Γ=Φscat|Γ.
[[PA]00[0][PA]0Γ[0][PB]00[PB]0Γ[PA]Γ0[PB]Γ0[PA]ΓΓ+[PB]ΓΓ][{ΦA}0{ΦB}0{Φscat}Γ]=[{uA}0[PA]0Γ{ΦA,in}Γ{uB}0[PB]0Γ{ΦB,in}Γ{uA,in}Γ+{uB,in}Γ[PA]ΓΓ{ΦA,in}Γ[PB]ΓΓ{ΦB,in}Γ].
ΦA,in|Γ=ΦB,in|Γ=Φin|Γ,
[[P]00[P]0Γ[P]Γ0[P]ΓΓ][{Φ}0{Φ}Γ]=[{u}02{uin}Γ],
[P]00=[[PA]00[0][0][PB]00],
[P]0Γ=[[PA]0Γ[PB]0Γ],
[P]Γ0=[[PA]Γ0[PB]Γ0],
[P]ΓΓ=[[PA]ΓΓ+[PB]ΓΓ].
Φ(x,y)=({U}Tix+{V}Tiy){Φt}+jβ{N}T{Φz}iz,
{ui,in}Γ=ΓiΓi[{N}Γip{(jβΦx+Φzx)ix+(jβΦy+Φzy)iy}Γi]dS=jβΓiΓi[p({U}{U}T+{V}{V}T){Φt}+p({U}{N}Tx+{V}{N}Ty){Φz}]dS,
{ui}0={0}.
WM2=20ϕ2(r)rdr0(dϕ(r)dr)2rdr.

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