W. P. Huang, L. Han, and J. Mu, “A rigorous circuit model for simulation of large-scale photonic integrated circuits,” IEEE Photon. J. 4, 1622–1638 (2012).

[CrossRef]

Y. Y. Lu and J. Zhu, “Propagating modes in optical waveguides terminated by perfectly matched layers,” IEEE Photon. Technol. Lett. 17, 2601–2603 (2005).

[CrossRef]

L. Knockaert, H. Rogier, and D. De Zutter, “An FFT-based signal identification approach for obtaining the propagation constants of the leaky modes in layered media,” Int. J. Electron. Commun. 59, 230–238 (2005).

[CrossRef]

F. Olyslager, “Discretization of continuous spectra based on perfectly matched layers,” SIAM J. Appl. Math. 64, 1408–1433 (2004).

[CrossRef]

H. Rogier, L. Knockaert, and D. De Zutter, “Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer,” Microw. Opt. Technol. Lett. 37, 167–171 (2003).

[CrossRef]

S. B. Gaal, H. J. W. M. Hoekstra, and P. V. Lambeck, “Determining PML modes in 2-D stratified media,” J. Lightwave Technol. 21, 293–298 (2003).

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microw. Theory Tech. 49, 712–715 (2001).

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quant. Electron. 33, 327–341 (2001).

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

R. Z. L. Ye and D. Yevick, “Noniterative calculation of complex propagation constants in planar waveguides,” J. Opt. Soc. Am. A 18, 2819–2822 (2001).

[CrossRef]

H. Derudder, F. Olyslager, and D. De Zutter, “An efficient series expansion for the 2-D Green’s function of a microstrip substrate using perfectly matched layers,” IEEE Microw. Guided Wave Lett. 9, 505–507 (1999).

[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for 2-dimensional wave-guides: the TM case,” Opt. Quant. Electron. 27, 995–1007 (1995).

[CrossRef]

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

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwells equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive-index steps,” IEEE Photon. Technol. Lett. 5, 554–557 (1993).

[CrossRef]

R. Mittra, Y. L. Hou, and V. Jamnejad, “Analysis of open dielectric wave-guides using mode-matching technique and variational-methods,” IEEE Trans. Microw. Theory Tech. 28, 36–43 (1980).

T. E. Rozzi, “Rigorous analysis of step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microw. Theory Tech. 26, 738–746 (1978).

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quant. Electron. 33, 327–341 (2001).

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for 2-dimensional wave-guides: the TM case,” Opt. Quant. Electron. 27, 995–1007 (1995).

[CrossRef]

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

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quant. Electron. 33, 327–341 (2001).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwells equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

L. Knockaert, H. Rogier, and D. De Zutter, “An FFT-based signal identification approach for obtaining the propagation constants of the leaky modes in layered media,” Int. J. Electron. Commun. 59, 230–238 (2005).

[CrossRef]

H. Rogier, L. Knockaert, and D. De Zutter, “Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer,” Microw. Opt. Technol. Lett. 37, 167–171 (2003).

[CrossRef]

L. F. Knockaert and D. De Zutter, “On the completeness of eigenmodes in a parallel plate waveguide with a perfectly matched layer termination,” IEEE Trans. Antennas Propag. 50, 1650–1653 (2002).

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in optical fibers terminated with a perfectly matched layer,” J. Lightwave Technol. 20, 1141–1148 (2002).

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microw. Theory Tech. 49, 712–715 (2001).

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

H. Derudder, F. Olyslager, and D. De Zutter, “An efficient series expansion for the 2-D Green’s function of a microstrip substrate using perfectly matched layers,” IEEE Microw. Guided Wave Lett. 9, 505–507 (1999).

[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

H. Derudder, F. Olyslager, and D. De Zutter, “An efficient series expansion for the 2-D Green’s function of a microstrip substrate using perfectly matched layers,” IEEE Microw. Guided Wave Lett. 9, 505–507 (1999).

[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for 2-dimensional wave-guides: the TM case,” Opt. Quant. Electron. 27, 995–1007 (1995).

[CrossRef]

W. P. Huang, L. Han, and J. Mu, “A rigorous circuit model for simulation of large-scale photonic integrated circuits,” IEEE Photon. J. 4, 1622–1638 (2012).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

R. Mittra, Y. L. Hou, and V. Jamnejad, “Analysis of open dielectric wave-guides using mode-matching technique and variational-methods,” IEEE Trans. Microw. Theory Tech. 28, 36–43 (1980).

W. P. Huang, L. Han, and J. Mu, “A rigorous circuit model for simulation of large-scale photonic integrated circuits,” IEEE Photon. J. 4, 1622–1638 (2012).

[CrossRef]

W. P. Huang and J. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17, 19134–19152 (2009).

[CrossRef]

J. Mu and W. P. Huang, “Simulation of three-dimensional waveguide discontinuities by a full-vector mode-matching method based on finite-difference schemes,” Opt. Express 16, 18152–18163 (2008).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

R. Mittra, Y. L. Hou, and V. Jamnejad, “Analysis of open dielectric wave-guides using mode-matching technique and variational-methods,” IEEE Trans. Microw. Theory Tech. 28, 36–43 (1980).

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

L. Knockaert, H. Rogier, and D. De Zutter, “An FFT-based signal identification approach for obtaining the propagation constants of the leaky modes in layered media,” Int. J. Electron. Commun. 59, 230–238 (2005).

[CrossRef]

H. Rogier, L. Knockaert, and D. De Zutter, “Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer,” Microw. Opt. Technol. Lett. 37, 167–171 (2003).

[CrossRef]

L. F. Knockaert and D. De Zutter, “On the completeness of eigenmodes in a parallel plate waveguide with a perfectly matched layer termination,” IEEE Trans. Antennas Propag. 50, 1650–1653 (2002).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

R. Mittra, Y. L. Hou, and V. Jamnejad, “Analysis of open dielectric wave-guides using mode-matching technique and variational-methods,” IEEE Trans. Microw. Theory Tech. 28, 36–43 (1980).

W. P. Huang, L. Han, and J. Mu, “A rigorous circuit model for simulation of large-scale photonic integrated circuits,” IEEE Photon. J. 4, 1622–1638 (2012).

[CrossRef]

W. P. Huang and J. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17, 19134–19152 (2009).

[CrossRef]

J. Mu and W. P. Huang, “Simulation of three-dimensional waveguide discontinuities by a full-vector mode-matching method based on finite-difference schemes,” Opt. Express 16, 18152–18163 (2008).

[CrossRef]

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive-index steps,” IEEE Photon. Technol. Lett. 5, 554–557 (1993).

[CrossRef]

F. Olyslager, “Discretization of continuous spectra based on perfectly matched layers,” SIAM J. Appl. Math. 64, 1408–1433 (2004).

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

H. Derudder, F. Olyslager, and D. De Zutter, “An efficient series expansion for the 2-D Green’s function of a microstrip substrate using perfectly matched layers,” IEEE Microw. Guided Wave Lett. 9, 505–507 (1999).

[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).

[CrossRef]

L. Knockaert, H. Rogier, and D. De Zutter, “An FFT-based signal identification approach for obtaining the propagation constants of the leaky modes in layered media,” Int. J. Electron. Commun. 59, 230–238 (2005).

[CrossRef]

H. Rogier, L. Knockaert, and D. De Zutter, “Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer,” Microw. Opt. Technol. Lett. 37, 167–171 (2003).

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in optical fibers terminated with a perfectly matched layer,” J. Lightwave Technol. 20, 1141–1148 (2002).

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microw. Theory Tech. 49, 712–715 (2001).

T. E. Rozzi, “Rigorous analysis of step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microw. Theory Tech. 26, 738–746 (1978).

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive-index steps,” IEEE Photon. Technol. Lett. 5, 554–557 (1993).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwells equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for 2-dimensional wave-guides: the TM case,” Opt. Quant. Electron. 27, 995–1007 (1995).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).

[CrossRef]

H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).

[CrossRef]

H. Derudder, F. Olyslager, and D. De Zutter, “An efficient series expansion for the 2-D Green’s function of a microstrip substrate using perfectly matched layers,” IEEE Microw. Guided Wave Lett. 9, 505–507 (1999).

[CrossRef]

W. P. Huang, L. Han, and J. Mu, “A rigorous circuit model for simulation of large-scale photonic integrated circuits,” IEEE Photon. J. 4, 1622–1638 (2012).

[CrossRef]

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8, 649–651 (1996).

[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, 652–654 (1996).

[CrossRef]

Y. Y. Lu and J. Zhu, “Propagating modes in optical waveguides terminated by perfectly matched layers,” IEEE Photon. Technol. Lett. 17, 2601–2603 (2005).

[CrossRef]

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive-index steps,” IEEE Photon. Technol. Lett. 5, 554–557 (1993).

[CrossRef]

L. F. Knockaert and D. De Zutter, “On the completeness of eigenmodes in a parallel plate waveguide with a perfectly matched layer termination,” IEEE Trans. Antennas Propag. 50, 1650–1653 (2002).

[CrossRef]

P. Bienstman, H. Derudder, R. Baets, F. Olyslager, and D. De Zutter, “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers,” IEEE Trans. Microw. Theory Tech. 49, 349–354 (2001).

H. Rogier and D. De Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microw. Theory Tech. 49, 712–715 (2001).

T. E. Rozzi, “Rigorous analysis of step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microw. Theory Tech. 26, 738–746 (1978).

R. Mittra, Y. L. Hou, and V. Jamnejad, “Analysis of open dielectric wave-guides using mode-matching technique and variational-methods,” IEEE Trans. Microw. Theory Tech. 28, 36–43 (1980).

L. Knockaert, H. Rogier, and D. De Zutter, “An FFT-based signal identification approach for obtaining the propagation constants of the leaky modes in layered media,” Int. J. Electron. Commun. 59, 230–238 (2005).

[CrossRef]

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

[CrossRef]

H. Rogier and D. De Zutter, “Berenger and leaky modes in optical fibers terminated with a perfectly matched layer,” J. Lightwave Technol. 20, 1141–1148 (2002).

[CrossRef]

S. B. Gaal, H. J. W. M. Hoekstra, and P. V. Lambeck, “Determining PML modes in 2-D stratified media,” J. Lightwave Technol. 21, 293–298 (2003).

[CrossRef]

J. Zhu and Y. Y. Lu, “Leaky modes of slab waveguides—asymptotic solutions,” J. Lightwave Technol. 24, 1619–1623 (2006).

[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwells equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).

[CrossRef]

H. Rogier, L. Knockaert, and D. De Zutter, “Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer,” Microw. Opt. Technol. Lett. 37, 167–171 (2003).

[CrossRef]

J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for 2-dimensional wave-guides: the TM case,” Opt. Quant. Electron. 27, 995–1007 (1995).

[CrossRef]

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quant. Electron. 33, 327–341 (2001).

[CrossRef]

F. Olyslager, “Discretization of continuous spectra based on perfectly matched layers,” SIAM J. Appl. Math. 64, 1408–1433 (2004).

[CrossRef]