OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 562–569

Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes

Chih-Hsien Lai and Hung-chun Chang  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 562-569 (2011)
http://dx.doi.org/10.1364/OE.19.000562


View Full Text Article

Enhanced HTML    Acrobat PDF (1055 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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.

© 2011 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.7370) Optical devices : Waveguides
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Optical Devices

History
Original Manuscript: October 21, 2010
Revised Manuscript: December 22, 2010
Manuscript Accepted: December 22, 2010
Published: January 4, 2011

Citation
Chih-Hsien Lai and Hung-chun Chang, "Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes," Opt. Express 19, 562-569 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-562


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. R. Hadley, “Transparent boundary condition for beam propagation,” Opt. Lett. 16(9), 624–626 (1991). [CrossRef] [PubMed]
  2. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]
  3. 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]
  4. 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]
  5. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  6. 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]
  7. Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18(4), 618–623 (2000). [CrossRef]
  8. C.-P. Yu and H.-C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express 12(25), 6165–6177 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-25-6165 . [CrossRef] [PubMed]
  9. W.-P. Huang and J. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17(21), 19134–19152 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-17-21-19134 . [CrossRef]
  10. 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]
  11. 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]
  12. 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]
  13. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002). [CrossRef]
  14. C.-H. Lai, Y.-C. Hsueh, H.-W. Chen, Y.-J. Huang, H.-C. Chang, and C.-K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009). [CrossRef] [PubMed]
  15. T.-H. Her, X. Ao, and L. W. Casperson, “Gain saturation in gain-guided slab waveguides with large-index antiguiding,” Opt. Lett. 34(16), 2411–2413 (2009). [CrossRef] [PubMed]
  16. H. Cheng, W. Y. Crutchfield, M. Doery, and L. Greengard, “Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: Theory,” Opt. Express 12(16), 3791–3805 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-16-3791 . [CrossRef] [PubMed]
  17. 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]
  18. 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]
  19. 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]
  20. A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A 20(8), 1617–1628 (2003). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited