Abstract

Leaky boundary conditions are implemented in a meshless numerical method to solve vectorial mode fields in optical waveguides which allow for the solution of both guided and leaky modes. The modes are found using an approximating solution, the Finite Cloud Method (FCM), to the coupled field equations of the transverse components of the magnetic field. In this paper we extend the method by implementing two absorbing boundary conditions, Transparent Boundary Conditions (TBC) and Perfectly Matched Layers (PML), to solve the leaky modes for several microstructured air hole waveguides. Presented are methods to further refine the boundary conditions and to stabilize the solutions. A comparison between these methods and previously published results show close agreement. Finally, we conclude that the TBC boundary condition is the superior method due to its robustness and lack of fitting parameters.

© 2013 IEEE

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  1. P. Lusse, P. Stuwe, J. Schule, H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by a new finite difference method," J.Lightw. Technol. 12, 487-494 (1994).
  2. H. Uranus, H. Hoekstra, "Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Exp. 12, 2795-2809 (2004).
  3. D. R. Burke, T. J. Smy, "Optical mode solving for complex waveguides using a finite cloud method," Opt. Exp. 20, 17783-17796 (2012).
  4. N. Aluru, G. Li, "Finite cloud method: A true meshless technique based on a fixed reproducing kernel approximation," Int. J. Numer. Meth. Eng. 50, 2373-2410 (2001).
  5. D. Burke, T. Smy, "A meshless based solution to vectorial mode fields in optical microstructured waveguides," Opt. Exp. 20, 17783-17796 (2012).
  6. R. B. Lehoucq, D. C. Sorensen, C. Yang, “Arpack Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods,” (1997).
  7. MathWorks. http://www.mathworks.com/products/matlab/ (2011).
  8. GNU Octave. http://www.gnu.org/s/octave/ (2011).
  9. M. Panju, “Iterative Methods for Computing Eigenvalues and Eigenvectors,” arXiv:1105.1185 (2011).
  10. Y. Y. Lu, J. Zhu, "Perfectly matched layer for acoustic waveguide modelling—Benchmark calculations and perturbation analysis," Comp. Model. Eng. Sci. 22, 235-247 (2007).
  11. C.-P. Yu, H.-C. Chang, "Yee-mesh-based finite difference eigenmode solver with pml absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).
  12. C.-H. Lai, H. C. Chang, "Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes," Opt. Exp. 19, 562-569 (2011).
  13. D. Burke, S. Moslemi-Tabrizi, T. Smy, "Simulation of inhomogeneous models using the finite cloud method," Mat.-wiss. u. Werkstofftech. 41, 336-340 (2010).

2012 (2)

D. R. Burke, T. J. Smy, "Optical mode solving for complex waveguides using a finite cloud method," Opt. Exp. 20, 17783-17796 (2012).

D. Burke, T. Smy, "A meshless based solution to vectorial mode fields in optical microstructured waveguides," Opt. Exp. 20, 17783-17796 (2012).

2011 (1)

C.-H. Lai, H. C. Chang, "Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes," Opt. Exp. 19, 562-569 (2011).

2010 (1)

D. Burke, S. Moslemi-Tabrizi, T. Smy, "Simulation of inhomogeneous models using the finite cloud method," Mat.-wiss. u. Werkstofftech. 41, 336-340 (2010).

2007 (1)

Y. Y. Lu, J. Zhu, "Perfectly matched layer for acoustic waveguide modelling—Benchmark calculations and perturbation analysis," Comp. Model. Eng. Sci. 22, 235-247 (2007).

2004 (2)

C.-P. Yu, H.-C. Chang, "Yee-mesh-based finite difference eigenmode solver with pml absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).

H. Uranus, H. Hoekstra, "Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Exp. 12, 2795-2809 (2004).

2001 (1)

N. Aluru, G. Li, "Finite cloud method: A true meshless technique based on a fixed reproducing kernel approximation," Int. J. Numer. Meth. Eng. 50, 2373-2410 (2001).

1994 (1)

P. Lusse, P. Stuwe, J. Schule, H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by a new finite difference method," J.Lightw. Technol. 12, 487-494 (1994).

Comp. Model. Eng. Sci. (1)

Y. Y. Lu, J. Zhu, "Perfectly matched layer for acoustic waveguide modelling—Benchmark calculations and perturbation analysis," Comp. Model. Eng. Sci. 22, 235-247 (2007).

Int. J. Numer. Meth. Eng. (1)

N. Aluru, G. Li, "Finite cloud method: A true meshless technique based on a fixed reproducing kernel approximation," Int. J. Numer. Meth. Eng. 50, 2373-2410 (2001).

J.Lightw. Technol. (1)

P. Lusse, P. Stuwe, J. Schule, H.-G. Unger, "Analysis of vectorial mode fields in optical waveguides by a new finite difference method," J.Lightw. Technol. 12, 487-494 (1994).

Mat.-wiss. u. Werkstofftech. (1)

D. Burke, S. Moslemi-Tabrizi, T. Smy, "Simulation of inhomogeneous models using the finite cloud method," Mat.-wiss. u. Werkstofftech. 41, 336-340 (2010).

Opt. Exp. (1)

D. R. Burke, T. J. Smy, "Optical mode solving for complex waveguides using a finite cloud method," Opt. Exp. 20, 17783-17796 (2012).

Opt. Exp. (4)

H. Uranus, H. Hoekstra, "Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Exp. 12, 2795-2809 (2004).

C.-P. Yu, H.-C. Chang, "Yee-mesh-based finite difference eigenmode solver with pml absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).

C.-H. Lai, H. C. Chang, "Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes," Opt. Exp. 19, 562-569 (2011).

D. Burke, T. Smy, "A meshless based solution to vectorial mode fields in optical microstructured waveguides," Opt. Exp. 20, 17783-17796 (2012).

Other (4)

R. B. Lehoucq, D. C. Sorensen, C. Yang, “Arpack Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods,” (1997).

MathWorks. http://www.mathworks.com/products/matlab/ (2011).

GNU Octave. http://www.gnu.org/s/octave/ (2011).

M. Panju, “Iterative Methods for Computing Eigenvalues and Eigenvectors,” arXiv:1105.1185 (2011).

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