Abstract

The reflection coefficient is one important parameter of the perfectly matched layer (PML). Here we investigate its effect on the modal analysis of leaky waveguide modes by examining three different leaky waveguide structures, i.e., the holey fiber, the air-core terahertz pipe waveguide, and the gain-guided and index-antiguided slab waveguide. Numerical results reveal that the typical values 10−8 ~10−12 are inadequate for obtaining the imaginary part of the complex propagation constant, and the suggested reflection coefficient would be much smaller, for example, 10−50 or 10−100. With such a small coefficient, both the computational window size and the PML thickness can be significantly reduced without loss of stability. Moreover, in some cases, the modal field profiles can only be accurately obtained with such a small coefficient.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (2)

P.-J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. 22(12), 908–910 (2010).
[CrossRef]

C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-18-1-309 .
[CrossRef] [PubMed]

2009 (3)

2006 (1)

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

2004 (2)

2003 (2)

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A 20(8), 1617–1628 (2003).
[CrossRef]

P. L. Ho and Y. Y. Lu, “A mode-preserving perfectly matched layer for optical waveguides,” IEEE Photon. Technol. Lett. 15(9), 1234–1236 (2003).
[CrossRef]

2002 (1)

2000 (1)

1996 (1)

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

1995 (2)

C. M. Rappaport, ““Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space,”IEEE Microw. Guid. Wave Lett. 5(3), 90–92 (1995).
[CrossRef]

B. Chen, D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 5(11), 399–401 (1995).
[CrossRef]

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equation with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[CrossRef]

1991 (1)

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

Andreani, L. C.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Ao, X.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Bienstman, P.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Botten, L. C.

Casperson, L. W.

Chang, H.-C.

Chen, B.

B. Chen, D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 5(11), 399–401 (1995).
[CrossRef]

Chen, H.-W.

Cheng, H.

Chew, W. C.

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equation with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[CrossRef]

Chiang, P.-J.

P.-J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. 22(12), 908–910 (2010).
[CrossRef]

Chiang, Y.-C.

P.-J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. 22(12), 908–910 (2010).
[CrossRef]

Costa, R.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Crutchfield, W. Y.

de Sterke, C. M.

Dems, M.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Doery, M.

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

Fang, D. G.

B. Chen, D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 5(11), 399–401 (1995).
[CrossRef]

Greengard, L.

Hadley, G. R.

Her, T.-H.

Ho, P. L.

P. L. Ho and Y. Y. Lu, “A mode-preserving perfectly matched layer for optical waveguides,” IEEE Photon. Technol. Lett. 15(9), 1234–1236 (2003).
[CrossRef]

Hopman, W. C. L.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Hsueh, Y.-C.

Huang, W. P.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

Huang, W.-P.

Huang, Y.-J.

Hugonin, J. P.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

Kokubun, Y.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

Koshiba, M.

Kuhlmey, B. T.

Lai, C.-H.

Lalanne, P.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Liu, T.-A.

Lu, J.-Y.

Lu,, Y. Y.

P. L. Ho and Y. Y. Lu, “A mode-preserving perfectly matched layer for optical waveguides,” IEEE Photon. Technol. Lett. 15(9), 1234–1236 (2003).
[CrossRef]

Lui, W.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

Maystre, D.

McPhedran, R. C.

Melloni, A.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Mu, J.

Obayya, S. S. A.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Panajotov, K.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Peng, J.-L.

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

Pinto, D.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Rappaport, C. M.

C. M. Rappaport, ““Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space,”IEEE Microw. Guid. Wave Lett. 5(3), 90–92 (1995).
[CrossRef]

Renversez, G.

Rosa, L.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Selleri, S.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Siegman, A. E.

Sun, C.-K.

Tsuji, Y.

Uranus, H. P.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equation with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[CrossRef]

White, T. P.

Xu, C. L.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

Yokoyama, K.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

You, B.

Yu, C.-P.

Zhou, B. H.

B. Chen, D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 5(11), 399–401 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (2)

C. M. Rappaport, ““Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space,”IEEE Microw. Guid. Wave Lett. 5(3), 90–92 (1995).
[CrossRef]

B. Chen, D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 5(11), 399–401 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

P.-J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. 22(12), 908–910 (2010).
[CrossRef]

P. L. Ho and Y. Y. Lu, “A mode-preserving perfectly matched layer for optical waveguides,” IEEE Photon. Technol. Lett. 15(9), 1234–1236 (2003).
[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations,” IEEE Photon. Technol. Lett. 8(5), 652–654 (1996).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Lightwave Technol. (1)

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

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

Microw. Opt. Technol. Lett. (1)

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equation with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: a mode solver comparison,” Opt. Quantum Electron. 38(9−11), 731–759 (2006).
[CrossRef]

Other (1)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (9)

Fig. 1
Fig. 1

Structure of the six-hole holey fiber.

Fig. 2
Fig. 2

Calculated effective index neff of the holey fiber as a function of W with d=1 μm. (a) Real part. (b) Imaginary part.

Fig. 3
Fig. 3

Calculated effective index neff of the holey fiber as a function of d with W=24 μm. (a) Real part. (b) Imaginary part.

Fig. 4
Fig. 4

Im(neff ) of the holey fiber as a function of R with W=24 μm and d=1 μm.

Fig. 5
Fig. 5

Structure of the air-core pipe waveguide.

Fig. 6
Fig. 6

(a) Im(neff ) of the pipe waveguide as a function of W with d=0.4 mm. (b) Im(neff ) of the pipe waveguide as a function of d with W=14 mm.

Fig. 7
Fig. 7

Im(neff ) of the pipe waveguide as a function of R with W=15.6 mm and d=0.4 mm.

Fig. 8
Fig. 8

Im(neff ) of the gain-guided and index-antiguided slab waveguide as a function of R. (a) g=0 (IAG case). (b) g=1 cm−1 (GG + IAG case).

Fig. 9
Fig. 9

Fundamental TE modal field profiles of the gain-guided and index-antiguided slab waveguide. (a) g=0 (IAG case). (b) g=1 cm−1 (GG + IAG case).

Equations (2)

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α 1 s α ,
s = 1 j ( m + 1 ) λ 4 π n d ( ρ d ) m ln 1 R ,

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