Abstract

We investigate the possibility of phase locking in a multicore photonic crystal fiber. We analyze the modal behavior of photonic crystal fibers with two and six cores and compare them with the usual single-core case. We also show how the strength of the coupling among modes belonging to different cores can be controlled by adjusting the size of the airholes between the waveguiding cores. We then analyze the Talbot effect in the case of the six-core photonic crystal as a pseudoperiodic structure and show that there exists the possibility of using a Talbot resonator to achieve phase locking in multicore photonic crystal fibers.

© 2004 Optical Society of America

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References

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  1. J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
    [CrossRef]
  2. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef] [PubMed]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding: Errata,” Opt. Lett. 22, 484–485 (1997).
    [CrossRef] [PubMed]
  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. P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 3, 133–140 (2001).
    [CrossRef]
  6. W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, and P. S. J. Russell, “High power air-clad photonic crystal fibre laser,” Opt. Express 11(1), 48–53 (2003).
    [CrossRef] [PubMed]
  7. M. Wrage, P. Glas, D. Fisher, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, “Phase locking in a multicore fiber laser by means of a Talbot resonator,” Opt. Lett. 25, 1436–1438 (2000).
    [CrossRef]

2003

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, and P. S. J. Russell, “High power air-clad photonic crystal fibre laser,” Opt. Express 11(1), 48–53 (2003).
[CrossRef] [PubMed]

2001

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 3, 133–140 (2001).
[CrossRef]

2000

1997

1996

Alam, S.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Atkin, D. M.

Birks, T. A.

Bouwmans, G.

Clarkson, W. A.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Fisher, D.

Glas, P.

Grudinin, A. B.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Jeong, Y.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Knight, J. C.

Leitner, M.

Napartovich, A. P.

Nilsson, J.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Percival, R. M.

Roberts, P. J.

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 3, 133–140 (2001).
[CrossRef]

Russell, P. S. J.

Russell, P. St. J.

Sahu, J. K.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Selvas, R.

J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S. Alam, “High-power fiber lasers: New developments,” in Advances in Fiber Devices, L. N. Durvasula, eds., Proc. SPIE 4974, 50–59 (2003).
[CrossRef]

Shepherd, T. J.

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 3, 133–140 (2001).
[CrossRef]

Vysotsky, D. V.

Wadsworth, W. J.

Wrage, M.

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Figures (10)

Fig. 1
Fig. 1

Single-core PCF. The circles indicate the airholes; the missing airhole in the center of the lattice is the core where the mode is confined.

Fig. 2
Fig. 2

Plot of the dispersion relation for the single-core PCF. The horizontal axis is the ratio of the lattice constant Λ to the wavelength of the mode in vacuum. The vertical axis represents the effective index of refraction or the ratio of the modal propagation constant to the wave number.

Fig. 3
Fig. 3

Two-core PCF. The regions with missing airholes act as cores. The size of the airhole residing between the cores can be adjusted to control the separation of the propagation constants between the supermodes.

Fig. 4
Fig. 4

Plot of the dispersion relation for the two-core PCF. The propagation constant of the in-phase symmetric mode is slightly higher than that of the antisymmetric mode.

Fig. 5
Fig. 5

Dispersion relation for the two-core PCF in which the size of the airhole residing between the cores is reduced by a factor of two.

Fig. 6
Fig. 6

Coupling length of the two-core photonic crystal that is sketched in Fig. 3 is plotted versus Λ/λ for both the regular-size and reduced-size airhole between the cores.

Fig. 7
Fig. 7

Six-core PCF. The size of the two airholes residing between neighboring cores is reduced to d0/Λ=0.3 for greater overlap of the modes. The cores are marked with large circles for illustration purposes only.

Fig. 8
Fig. 8

Plot of the dispersion relation for the six-core PCF. The resulting supermodes cluster themselves into doublets and quartets dictated by the symmetries of the six-core PCF.

Fig. 9
Fig. 9

Amplitude reflection coefficient of the six supermodes for the six-core PCF is plotted as a function of distance from the output facet of the waveguide in units of the lattice constant Λ at Λ/λ=4.51.

Fig. 10
Fig. 10

Amplitude reflection coefficient of the six supermodes for the six-core PCF is plotted as a function of distance from the output facet of the waveguide in units of the lattice constant Λ at Λ/λ=1.29.

Equations (13)

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Lcoupling=2π/Δβ,
Δϕm=2πm/6,m=0,,5.
ZT=2dT2/λ,
γm(z)=-Am*(x, y, z=0)Am(x, y, z)dxdy-|Am(x, y, z=0)|2dxdy.
Am(x, y, z=0)=i=n6 exp{-a[(x-xn)2+(y-yn)2]}ηmn.
aπ2λ2(nglass2-neff2),
ηmn=exp[2im(n-1)π/6],n=1,,6;m=0,,5.
γm(z)=|am(z)||am(0)|,
am(z)=-dkxdky|Amk(kx, ky)|2eikzz,
kz=ω2/c2-kx2-ky2.
am(z)=14a2-dkxdky exp-kx2+ky22a×exp(ikzz)n1,n2=16exp[ikx(xn1-xn2)]×exp[iky(yn1-yn2)]ηmn1*ηmn2.
am(z)=14a20kρdkρ exp-kρ22a×exp(ikzz)02πdθ exp[ikρ cos θ(xn1-xn2)]×exp[ikρ sin θ(yn1-yn2)]ηmn1*ηmn2.
am(z)=π2a2n1,n2=16ηmn1*ηmn20dkρkρ×exp-kρ22aexp(ikzz)J0(dn1n2kρ).

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