OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 6 — Jun. 1, 2014
  • pp: 1360–1376

Solving leaky modes on a dielectric slab waveguide involving materials of arbitrary dielectric anisotropy with a finite-element formulation

Hsuan-Hao Liu and Hung-chun Chang  »View Author Affiliations


JOSA B, Vol. 31, Issue 6, pp. 1360-1376 (2014)
http://dx.doi.org/10.1364/JOSAB.31.001360


View Full Text Article

Enhanced HTML    Acrobat PDF (1322 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A planar optical waveguide mode solver is established based on a finite-element (FE) formulation for determining the guided and leaky modes that exist on waveguides made of anisotropic materials with an arbitrary permittivity tensor, for example, with arbitrary optic-axis orientation in the uniaxially anisotropic material case. Correct numerical determination of the complex effective index, especially its imaginary part that gives the modal leakage, is particularly emphasized referring to available analytical solutions. For the situation when the optic axis changes its direction only in the plane parallel to the waveguide interface planes, analytical characteristic equations for solving purely guided and leaky modes are separately derived in a more systematic manner compared with prior analytical formulae reported more than three decades ago, with the obtained complex effective indices agreeing excellently with FE solutions. It is found that in the FE analysis of leaky modes, the thickness of the perfectly matched layer (PML) and the PML theoretical reflection coefficient should be properly chosen. The FE formulation is based on either the three electric-field components or the three magnetic-field components using quadratic nodal bases, resulting in a quadratic eigenvalue equation that is then solved by the shift-and-invert Arnoldi method.

© 2014 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7390) Optical devices : Waveguides, planar
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

History
Original Manuscript: December 18, 2013
Revised Manuscript: April 4, 2014
Manuscript Accepted: April 4, 2014
Published: May 26, 2014

Citation
Hsuan-Hao Liu and Hung-chun Chang, "Solving leaky modes on a dielectric slab waveguide involving materials of arbitrary dielectric anisotropy with a finite-element formulation," J. Opt. Soc. Am. B 31, 1360-1376 (2014)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-6-1360


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. V. Schmidt and H. Kogelnik, “Electro-optically switched coupler with stepped Delta β reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976). [CrossRef]
  2. A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar wave-guides,” J. Lightwave Technol. 6, 1083–1104 (1988). [CrossRef]
  3. K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. 26, 298–305 (1978). [CrossRef]
  4. S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3, and LiNbO3, waveguides,” Opt. Lett. 3, 76–78 (1978). [CrossRef]
  5. W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979). [CrossRef]
  6. J. Ctyroky and M. Cada, “Guided and semileaky modes in anisotropic optical waveguides of the LiNbO3 type,” Opt. Commun. 27, 353–357 (1978). [CrossRef]
  7. S. Yamamoto, Y. Koyamada, and T. Makimoto, “Normal-mode analysis of anisotropic and gyrotropic thin-film waveguides for integrated optics,” J. Appl. Phys. 43, 5090–5097 (1972). [CrossRef]
  8. W. K. Burns and J. Warnert, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64, 441–446 (1974). [CrossRef]
  9. Y. Satomura, M. Matsuhara, and N. Kumagai, “Analysis of electromagnetic-wave modes in anisotropic slab waveguide,” IEEE Trans. Microwave Theory Tech. 22, 86–92 (1974). [CrossRef]
  10. E. A. Kolosovskii, D. V. Petrov, A. V. Tsarev, and I. B. Iakovin, “An exact method for analysing light propagation in anisotropic inhomogeneous optical waveguides,” Opt. Commun. 43, 21–25 (1982). [CrossRef]
  11. D. Marcuse, “Electrooptic coupling between TE and TM modes in anisotropic slabs,” IEEE J. Quantum Electron. QE-11, 759–767 (1975). [CrossRef]
  12. D. Marcuse, “Modes of a symmetric slab optical waveguide in birefringent media–Part 1: optical axis not in plane of slab,” IEEE J. Quantum Electron. QE-14, 736–741 (1978). [CrossRef]
  13. S. Yamamoto and Y. Okamoto, “Guided-radiation mode interaction in off-axis propagation in anisotropic optical waveguides with application to direct-intensity modulators,” J. Appl. Phys. 50, 2555–2564 (1979). [CrossRef]
  14. D. Marcuse and I. P. Kaminow, “Modes of a symmetric slab optical waveguide in birefringent media, Part II: slab with coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979). [CrossRef]
  15. D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63, 138–145 (1973). [CrossRef]
  16. M. S. Kharusi, “Uniaxial and biaxial anisotropy in thin-film optical waveguides,” J. Opt. Soc. Am. 64, 27–35 (1974). [CrossRef]
  17. J. Ctyroky and M. Cada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981). [CrossRef]
  18. L. Torner, F. Canal, and J. Hernandez-Marco, “Leaky modes in multilayer uniaxial optical waveguides,” Appl. Opt. 29, 2805–2814 (1990). [CrossRef]
  19. M. Lu and M. M. Fejer, “Anisotropic dielectric waveguides,” J. Opt. Soc. Am. A 10, 246–261 (1993). [CrossRef]
  20. A. B. Yakovle, G. W. Hanson, and R. L. Byer, “Fundamental modal phenomena on isotropic and anisotropic planar slab dielectric waveguides,” IEEE Trans. Antennas Propag. 51, 888–897 (2003). [CrossRef]
  21. M. A. Boroujeni and M. Shahabadi, “Modal analysis of multilayer planar lossy anisotropic optical waveguides,” J. Opt. A 8, 856–863 (2006). [CrossRef]
  22. T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996). [CrossRef]
  23. L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993). [CrossRef]
  24. F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998). [CrossRef]
  25. 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, 618–623 (2000). [CrossRef]
  26. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371 (2001). [CrossRef]
  27. M. Koshiba and M. Suzuki, “Numerical-analysis of planar arbitrarily anisotropic diffused optical waveguides using finite-element method,” Electron. Lett. 18, 579–581 (1982). [CrossRef]
  28. M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrarily anisotropic diffused optical waveguides,” J. Lightwave Technol. 3, 773–778 (1985). [CrossRef]
  29. M. Koshiba, H. Kumagami, and M. Suzuki, “Correction to finite-element solution of planar arbitrarily anisotropic diffused optical waveguides,” J. Lightwave Technol. 4, 100 (1986). [CrossRef]
  30. A. P. Zhao and S. R. Cvetkovic, “Finite-element analysis of hybrid modes in uniaxial planar waveguides by a simple iterative method,” Opt. Lett. 20, 139–141 (1995). [CrossRef]
  31. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  32. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19, 405–413 (2001). [CrossRef]
  33. C. H. Lai and H. C. Chang, “Effect of perfectly matched layer reflection coefficient on modal analysis of leaky waveguide modes,” Opt. Express 19, 562–569 (2011). [CrossRef]
  34. O. C. Zienkiewitz, The Finite Element Method (McGraw-Hill, 1977).
  35. J. F. Lee, D. K. Sun, and Z. J. Cendes, “Full-wave analysis of dielectric waveguides using tangential vector finite elements,” IEEE Trans. Microwave Theory Tech. 39, 1262–1271 (1991). [CrossRef]
  36. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equation and the Schrödinger Equation (Wiley, 2001).
  37. C. M. Krowne, “Theoretical considerations for finding anisotropic permittivity in layered ferroelectric/ferromagnetic structures from full-wave electromagnetic simulations,” Microw. Opt. Technol. Lett. 28, 63–69 (2001). [CrossRef]
  38. R. B. Lehoucq and D. C. Sorensen, “Deflation techniques for an implicitly restarted Arnoldi iteration,” SIAM J. Matrix Anal. Appl. 17, 789–821 (1996). [CrossRef]
  39. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, 1998).
  40. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000). [CrossRef]
  41. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. 1, 58–106 (2009). [CrossRef]
  42. R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express 17, 24112–24129 (2009). [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