Abstract

Multifilament core (MFC) fibers are a new type of microstructured fiber recently introduced. We investigate their properties using finite element modeling and show that the equivalent step index fiber based on moments theory does not provide similar properties. We propose an effective index theory based on the fundamental space filling mode which allows to predict the MFC properties using a semi-analytical modeling. Good resistance to bending is thus attributed to increased core effective index due to the high index filaments.

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References

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2009

2008

2007

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for Optical Fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[CrossRef]

2006

2005

2003

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

2000

1997

1984

1982

1976

Abdou-Ahmed, M.

Baggett, J. C.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Birks, T. A.

Black, R. J.

Bourdon, P.

Canat, G.

Codemard, C.

Cole, J. H.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for Optical Fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[CrossRef]

Dolfi, A.

Dong, L.

Dupriez, P.

Finazzi, V.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Furusawa, K.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Graf, T.

Jetschke, S.

Jolivet, V.

Kim, J.

Kirchhof, J.

Knight, J. C.

Lombard, L.

Marcuse, D.

McLaughlin, J. M.

Midrio, M.

Monro, T. M.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Nilsson, J.

Pask, C.

Peng, X.

Richardson, D.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Russell, P. S.

Sahu, J. K.

Samson, B.

K. Tankala, B. Samson, and ., “New developments in High Power Eye-Safe LMA fibers,” Proc. SPIE 6102, 610206 (2006).
[CrossRef]

Schermer, R. T.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for Optical Fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[CrossRef]

Singh, M.

Someda, C.

Tankala, K.

K. Tankala, B. Samson, and ., “New developments in High Power Eye-Safe LMA fibers,” Proc. SPIE 6102, 610206 (2006).
[CrossRef]

Unger, S.

Vasseur, O.

Vogel, M. M.

Voss, A.

Wong, W. S.

Appl. Opt.

IEEE J. Quantum Electron.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for Optical Fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

K. Tankala, B. Samson, and ., “New developments in High Power Eye-Safe LMA fibers,” Proc. SPIE 6102, 610206 (2006).
[CrossRef]

Other

A. W. Snyder, and J. D. Love, “Optical Waveguide Theory”, Chapman and Hall, New York, 1983.

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Figures (10)

Fig. 1
Fig. 1

Cleave of a 28 x 31 µm multifilament core fiber with N = 37 filaments.

Fig. 2
Fig. 2

The multifilament fiber core with hexagonal lattice. The high index filament (red disks) radius is a and the lattice pitch is Λ.

Fig. 3
Fig. 3

Evolution of the effective index and effective area of the fundamental mode as a function of wavelength computed with the finite element method.

Fig. 4
Fig. 4

Modelling of the bending loss as a function of the bending radius for the MFC fiber using the finite element method (circles) and the equivalent step index fiber from moments (squares).

Fig. 5
Fig. 5

Variation of the effective index of the fundamental mode in the MFC and in the equivalent step index fiber (ESI). The dashed line corresponds to λ = 1545nm where the bending loss modeling has been performed.

Fig. 6
Fig. 6

The unit cell of the infinite hexagonal lattice in the fundamental space filling mode theory.

Fig. 7
Fig. 7

Variation of the core equivalent index from FSM as function of the normalized wavelength. The dashed line corresponds to the equivalent step index computed by the ESI-FSM theory.

Fig. 8
Fig. 8

Comparison of the effective index of the fundamental mode computed using the finite elements method (FEM) (squares) and the Effective Step Index Approximation (ESI-FSM) (disks) for a = 0.9 µm and Λ = 4.5 µm, 5.1 µm and 6.5 µm.

Fig. 9
Fig. 9

Variation of the effective normalized frequency Veff with the normalized wavelength and the a/Λ parameter. The single mode region is in the direction of the arrows. The black circle shows the fiber described in Fig. 2.

Fig. 10
Fig. 10

Comparison of the fundamental mode effective area (a) and bending loss (b) computed at λ = 1545 nm using the Marcuse equations and the effective index computed with the ESI-FSM compared (line) to numerical calculations using COMSOL (squares).

Equations (22)

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n b e n d ( r ) = n ( r ) ( 1 + 2 x ξ R b e n d ) = n ( r ) ( 1 + 2 x R e f f )
α ( d B / m ) = 20 ln ( 10 ) Im β
G 0 = 1 2 π [ n ( r , θ ) 2 n c l a d 2 ] r d r d θ
G 2 p = 1 2 π [ n ( r , θ ) 2 n c l a d 2 ] r 2 p + 1 d r d θ
G 0 = ( n c o r e 2 n c l a d 2 ) a 2 2
G 2 = ( n c o r e 2 n c l a d 2 ) a 4 4
a e q E S I = 2 G 2 G 0
N A e q E S I = G 0 G 2
R c r i t = 8 π 2 n s t e p 2 a s t e p 3 λ 2 W 3 8 π 2 n c l a d 2 λ 2 w 3
R = Λ ( 3 / 2 π ) 1 / 2
E z ( r , θ ) = A J l ( u r ) exp i l θ H z ( r , θ ) = B J l ( u r ) exp i l θ
E z ( r , θ ) = C P l ( w r ) exp i l θ H z ( r , θ ) = D P l ( w r ) exp i l θ
P l ( W ) = I l ( W ) K l ( W R a ) K l ( W ) I l ( W R a )
U = u a
W = w a
[ j ^ l ( U ) + p ^ l ( W ) ] [ n 1 2 j ^ l ( U ) + n 2 2 p ^ l ( W ) ] = l 2 ( 1 U 2 + 1 W 2 ) ( n 1 2 U 2 + n 2 2 W 2 )
j ^ l ( U ) = J l ' ( U ) U J l ( U ) p ^ l ( W ) = P l ' ( W ) W P l ( W )
lim λ n e q F S M = f n 1 + ( 1 f ) n 2 = n a v
a e q F S M = Λ ( N 3 2 π ) 1 / 2
V e f f = 2 π λ Λ ( N 3 2 π ) 1 / 2 ( n F S M 2 ( λ ) n c l a d 2 ) 1 / 2
ω e q = N 3 2 π Λ ( 0.65 + 1.619 V e f f 3 / 2 + 2.879 V e f f 6 )
2 α = π 1 / 2 u 2 exp ( 2 3 w 3 R e f f k 2 n e f f 2 ) 2 R e f f 1 / 2 w 3 / 2 V e f f 2 K ( w a e q ) 2

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