Abstract

We propose a general geometric definition of the V-parameter in photonic crystal fibers (PCF). We argue that the fundamental modal field in both square-lattice and triangular-lattice PCFs can be approached by certain proper assemblies of the fundamental mode in a one-dimensional planar waveguide. This observation suggests a geometric definition of the effective core radius and the single-mode regime of Vπ/2 in various PCFs. The numerical results imply that the suggestion is valid for all of the one-rod, seven-rod, 19-rod, and 37-rod core triangular-lattice PCFs and the one-rod, nine-rod, and 25-rod core square-lattice PCFs.

© 2014 Optical Society of America

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References

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  1. P. St. J. Russell, Science 299, 358 (2003).
    [CrossRef]
  2. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, Opt. Lett. 28, 393 (2003).
    [CrossRef]
  3. M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.
  4. S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
    [CrossRef]
  5. H. Li, A. Mafi, A. Schlzgen, L. Li, V. L. Temyanko, N. Peyghambarian, and J. V. Moloney, J. Lightwave Technol. 25, 1224 (2007).
    [CrossRef]
  6. F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
    [CrossRef]
  7. F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
    [CrossRef]
  8. F. Poli, E. Coscelli, T. T. Alkeskjold, D. Passaro, A. Cuci-notta, L. Leick, J. Broeng, and S. Selleri, Opt. Express 19, 9896 (2011).
    [CrossRef]
  9. F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
    [CrossRef]
  10. H. Demir and S. Ozsoy, Opt. Fiber Technol. 17, 594 (2011).
    [CrossRef]
  11. T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
    [CrossRef]
  12. T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.
  13. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
    [CrossRef]
  14. M. Koshiba and K. Saitoh, Opt. Lett. 29, 1739 (2004).
    [CrossRef]
  15. K. Saitoh, Y. Tsuchida, M. Koshiba, and N. A. Mortensen, Opt. Express 13, 10833 (2005).
    [CrossRef]
  16. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, Opt. Lett. 28, 1879 (2003).
    [CrossRef]
  17. A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
    [CrossRef]
  18. M. Qiu, Microw. Opt. Technol. Lett. 30, 327 (2001).
    [CrossRef]

2011 (2)

2009 (2)

F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
[CrossRef]

2007 (1)

2005 (3)

2004 (1)

2003 (3)

2002 (1)

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

2001 (1)

M. Qiu, Microw. Opt. Technol. Lett. 30, 327 (2001).
[CrossRef]

2000 (1)

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

1997 (1)

Alkeskjold, T. T.

Allan, D. C.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Birks, T. A.

Birkst, T. A.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Bottacini, M.

Brechet, F.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

Broeng, J.

F. Poli, E. Coscelli, T. T. Alkeskjold, D. Passaro, A. Cuci-notta, L. Leick, J. Broeng, and S. Selleri, Opt. Express 19, 9896 (2011).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
[CrossRef]

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Burani, N.

Coscelli, E.

Cucinotta, A.

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
[CrossRef]

F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

Cuci-notta, A.

Demir, H.

H. Demir and S. Ozsoy, Opt. Fiber Technol. 17, 594 (2011).
[CrossRef]

Fajardo, J. C.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Folkenberg, J. R.

Foroni, M.

F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
[CrossRef]

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

Fuochi, M.

Hansen, K. P.

Knight, J. C.

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef]

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Koshiba, M.

Lægsgaard, J.

Leick, L.

Li, H.

Li, L.

Mafi, A.

Marcou, J.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

Mogilevtsev, D.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Moloney, J. V.

Mortensen, N. A.

Nielsen, M. D.

Ozsoy, S.

H. Demir and S. Ozsoy, Opt. Fiber Technol. 17, 594 (2011).
[CrossRef]

Pagnoux, D.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

Passaro, D.

Petersson, A.

Peyghambarian, N.

Poli, F.

F. Poli, E. Coscelli, T. T. Alkeskjold, D. Passaro, A. Cuci-notta, L. Leick, J. Broeng, and S. Selleri, Opt. Express 19, 9896 (2011).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
[CrossRef]

F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
[CrossRef]

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

Qiu, M.

M. Qiu, Microw. Opt. Technol. Lett. 30, 327 (2001).
[CrossRef]

Roberts, P. J.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Rosa, L.

F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
[CrossRef]

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

Roy, P.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef]

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Saitoh, K.

Schlzgen, A.

Selleri, S.

F. Poli, E. Coscelli, T. T. Alkeskjold, D. Passaro, A. Cuci-notta, L. Leick, J. Broeng, and S. Selleri, Opt. Express 19, 9896 (2011).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, J. Lightwave Technol. 27, 4935 (2009).
[CrossRef]

F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A. Cucinotta, and S. Selleri, J. Opt. Soc. Am. A 22, 1655 (2005).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

Simonsen, H. R.

Temyanko, V. L.

Tsuchida, Y.

Vicetti, L.

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

West, J. A.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

Zoboli, M.

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

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

F. Poli, A. Cucinotta, D. Passaro, and J. Broeng, IEEE J. Sel. Top. Quantum Electron. 15, 54 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Cucinotta, S. Selleri, L. Vicetti, and M. Zoboli, IEEE Photon. Technol. Lett. 14, 1530 (2002).
[CrossRef]

J. Lightwave Technol. (2)

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

Microw. Opt. Technol. Lett. (1)

M. Qiu, Microw. Opt. Technol. Lett. 30, 327 (2001).
[CrossRef]

Opt. Express (2)

Opt. Fiber Technol. (2)

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Opt. Fiber Technol. 6, 181 (2000).
[CrossRef]

H. Demir and S. Ozsoy, Opt. Fiber Technol. 17, 594 (2011).
[CrossRef]

Opt. Lett. (4)

Proc. SPIE (1)

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, Proc. SPIE 5950, 59500U (2005).
[CrossRef]

Science (1)

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef]

Other (2)

M. Foroni, F. Poli, L. Rosa, A. Cucinotta, and S. Selleri, in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components (2005), pp. 41–46.

T. A. Birkst, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 1999), paper FG4.

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Figures (6)

Fig. 1.
Fig. 1.

Normalized FM intensity distribution that are obtained by FDTD for T-PCFs with (a) one-rod core and (b) seven-rod core, S-PCFs with (d) one-rod core and (e) nine-rod core, and that given by Eq. (4) with γ=1 for (c) seven-rod T-PCF and (f) nine-rod S-PCF. The white circles denote circular unit cells containing airholes in the cladding.

Fig. 2.
Fig. 2.

Geometric definition of the effective core radius in multirod T-PCFs and an example of a seven-rod core.

Fig. 3.
Fig. 3.

Effective area of FM as function of V for (a) T-PCFs and (b) S-PCFs, where the solid lines are obtained by PDWA, and the square blocks and the circles are given by FDTD with d/Λ=0.3 and d/Λ=0.15, respectively.

Fig. 4.
Fig. 4.

Comparing the profiles of the FM intensity obtained by FDTD (scatter points) and by PDWA (lines) for PCFs with (a) seven-rod core, (b) 19-rod core, (c) nine-rod core, and (d) 25-rod core, where d/Λ=0.3.

Fig. 5.
Fig. 5.

Second-order cutoff wavelengths versus d/Λ for various different core structures, where the scatter points are obtained by FDTD and the solid lines are given by PDWA. The dashed line denotes a known result for the seven-rod core [3].

Fig. 6.
Fig. 6.

Second-order cutoff of the V-parameter versus d/Λ for (a) T-PCFs and (b) S-PCFs with different core structures.

Equations (13)

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

VSIF=kρnco2ncl2<2.405,
V1=kρeffnco2nFSM2,
V2=kΛnFM2nFSM2.
ϕTPCF(x,y)={ϕPDW(x)ϕPDW(x+3y2)×ϕPDW(x3y2)}γ,
ϕSPCF(x,y)={[ϕPDW(x)]1+q[ϕPDW(x+y2)]q×[ϕPDW(y)]1+q[ϕPDW(xy2)]q}γ.
ϕPDW(x)={cos(Ux/ρ)/cosU|x|ρ,exp[W(|x|/ρ1)]|x|>ρ,
tanU=W/U=V2U2/U.
V3=kΛ2NA<π2.
V3(λ)=kρeffnFM2(λ)nFSM2(λ)<π2.
ρeff=3nmr12Λ,(nmr=2,3,),
ρeff=1+q21+qΛ2q,q=12nmr1.
γ=nmr+VPDW*nmr+VPDW,
nHOM1(k*Λ)=nFSM(k*Λ).

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