Abstract

In this work, we propose a new technique for modeling light propagation in photonic crystal fibers where the electric field is evaluated from a purely transverse linearly polarized vector potential. The vector potential in a nonuniform dielectric obeys a wave equation coupled to the scalar potential, but it can be reduced to a scalar wave equation when the coupling term is ignored to the lowest order approximation. We show that this method gives reliable results for photonic crystal fibers when the scalar analysis is improved by a perturbational correction.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2007

P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A: Pure Appl. Opt. 9, 728–740 (2007).
[CrossRef]

2006

2005

2004

S. Campbell, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “Differential multipole method for microstructured optical fibers,” J. Opt. Soc. Am. B 21, 1919–1928 (2004).
[CrossRef]

T.-L. Wu and C.-H. Chao, “Photonic crystal fiber analysis through the vector boundary-element method: Effect of elliptical air hole,” IEEE Photonics Technol. Lett. 16, 126–128 (2004).
[CrossRef]

H. Uranus and H. Hoekstra, “Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions,” Opt. Express 12, 2795–2809 (2004).
[CrossRef] [PubMed]

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).
[CrossRef]

2003

2002

2001

M. Qiu, “Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,” Microw. Opt. Tech. Lett. 30, 327–330 (2001).
[CrossRef]

2000

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Modeling large air fraction holey optical fibers,” J. Lightwave Technol. 18, 50–56 (2000).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

1999

1998

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

1997

Andrés, M. V.

Andrés, P.

Aristizábal, V. H.

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

Bassi, P.

Bellanca, G.

Bennett, P. J.

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. S. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystals,” J. Lightwave Technol. 17, 2078–2081 (1999).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

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]

Botten, L. C.

Boyer, P.

P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A: Pure Appl. Opt. 9, 728–740 (2007).
[CrossRef]

Broderick, N. G. R.

Brown, T. G.

Campbell, S.

Chang, H. C.

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).
[CrossRef]

Chao, C.-H.

T.-L. Wu and C.-H. Chao, “Photonic crystal fiber analysis through the vector boundary-element method: Effect of elliptical air hole,” IEEE Photonics Technol. Lett. 16, 126–128 (2004).
[CrossRef]

Cregan, R. F.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

de Sandro, J.-P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

de Sterke, C. M.

Ferrando, A.

Fogli, F.

Guan, N.

Habu, S.

Himeno, K.

Hochman, A.

Hoekstra, H.

Huttunen, A.

Issa, N. A.

Knight, J. C.

W. H. Reeves, J. C. Knight, P. Russell, and P. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002).
[PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

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]

Koshiba, M.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23, 3580–3580 (2005).
[CrossRef]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[CrossRef]

Kotynski, R.

Kuhlmey, B. T.

Leviatan, Y.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 2000).

Martijn de Sterke, C.

Maystre, D.

McPhedran, R. C.

Miret, J. J.

Mogilevtsev, D.

Monro, T. M.

Nevière, M.

P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A: Pure Appl. Opt. 9, 728–740 (2007).
[CrossRef]

Ortigosa-Blanch, A.

E. Silvestre, T. Pinheiro-Ortega, P. Andrés, J. J. Miret, and A. Ortigosa-Blanch, “Analytical evaluation of chromatic dispersion in photonic crystal fibers,” Opt. Lett. 30, 453–455 (2005).
[CrossRef] [PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

Panajotov, K.

Pinheiro-Ortega, T.

Poladian, L.

Popov, E.

P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A: Pure Appl. Opt. 9, 728–740 (2007).
[CrossRef]

Qiu, M.

M. Qiu, “Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,” Microw. Opt. Tech. Lett. 30, 327–330 (2001).
[CrossRef]

Reeves, W. H.

Renversez, G.

Richardson, D. J.

Roberts, P.

Russell, P.

Russell, P. S. J.

Russell, P. St. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

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]

Saccomandi, L.

Saitoh, K.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23, 3580–3580 (2005).
[CrossRef]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[CrossRef]

Serebryannikov, E.

Silvester, E.

Silvestre, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 2000).

Szpulak, M.

Takenaga, K.

Törmä, P.

Torres, P.

Trillo, S.

Uranus, H.

Urbanczyk, W.

Vélez, F. J.

Wada, A.

Wadsworth, W. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

White, T. P.

Wu, T.-L.

T.-L. Wu and C.-H. Chao, “Photonic crystal fiber analysis through the vector boundary-element method: Effect of elliptical air hole,” IEEE Photonics Technol. Lett. 16, 126–128 (2004).
[CrossRef]

Yu, C. P.

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).
[CrossRef]

Zheltikov, A.

Zhu, Z.

Electron. Lett.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

IEEE J. Quantum Electron.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[CrossRef]

IEEE Photonics Technol. Lett.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonics Technol. Lett. 12, 807–809 (2000).
[CrossRef]

T.-L. Wu and C.-H. Chao, “Photonic crystal fiber analysis through the vector boundary-element method: Effect of elliptical air hole,” IEEE Photonics Technol. Lett. 16, 126–128 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. A: Pure Appl. Opt.

P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A: Pure Appl. Opt. 9, 728–740 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Microw. Opt. Tech. Lett.

M. Qiu, “Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,” Microw. Opt. Tech. Lett. 30, 327–330 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

C. P. Yu and H. C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36, 145–163 (2004).
[CrossRef]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 2000).

ARPACK Numerical Library, http://www.netlib.org/arpack.

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Figures (3)

Fig. 1
Fig. 1

Cross section of the three annular-shaped holes PCF.

Fig. 2
Fig. 2

Field intensity profiles with polarization maps calculated from an x-polarized potential vector for (a) HE 11 -, (b) TE 01 -, (c) TM 01 -, and (d) HE 21 -like modes at λ = 1.55 μm .

Fig. 3
Fig. 3

Considered mode effective index of the three annular-shaped holes’ fiber calculated with the corrected scalar scheme discussed in the text. Comparison with vector results reported in [27].

Tables (1)

Tables Icon

Table 1 Calculated Mode Effective Indices a of the Structure with Three Annular-Shaped Holes at λ = 1.55 μm

Equations (16)

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

μ 0 H = × A ,
E = i ω A ψ ,
2 A + ω 2 μ 0 ϵ A ( · A + i ω μ 0 ϵ ψ ) = ϵ ϵ i ω μ 0 ϵ ψ .
· A = i ω μ 0 ϵ ψ ,
2 A + ω 2 μ 0 ϵ A = ϵ ϵ · A .
( t 2 + k 0 2 n 2 β 2 ) A t = t ϵ ϵ t · A t ,
A t = Φ x ^ or A t = Φ y ^ ,
{ t 2 + k 0 2 n 2 β ˜ 2 } Φ = 0 ,
E = i c 2 ω 2 n 2 [ ( ω 2 n 2 c 2 Φ + 2 Φ x 2 ) x ^ + 2 Φ x y y ^ i β Φ x z ^ ] ,
t 2 A + ( k 0 2 n 2 β 2 ) A = ϵ ϵ · A
t 2 A ˜ + ( k 0 2 n 2 β ˜ 2 ) A ˜ = 0 .
V ( A ˜ * · t 2 A A · t 2 A ˜ * ) d V = ( β 2 β ˜ 2 ) V A · A ˜ * d V + V A ˜ * · ( ϵ ϵ · A ) d V .
V ( A ˜ * · t 2 A A · t 2 A ˜ * ) d V = S ( A ˜ * · t A A · t A ˜ * ) d S .
δ β 2 = β 2 β ˜ 2 = V A ˜ * · ( ϵ ϵ · A ) d V V A · A ˜ * d V .
β i 2 β ˜ i 2 = s Φ * 1 n 2 n 2 x i Φ x i d s s | Φ | 2 d s ,
[ B ] { a } = β ˜ 2 [ C ] { a } ,

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