Efficient and spurious-free integral-equation-based optical waveguide mode solver

Optics Express

Volumn 15, Issue 22, 2007, Pages 14431-14453

  Hochman, Amit ^a   Leviatan, Yehuda ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; INTEGRAL EQUATIONS; MICROSTRUCTURE; OPTICAL FIBERS;

MATRIX SINGULARITY; SPURIOUS SOLUTIONS; WAVEGUIDE MODE SOLVER;

OPTICAL WAVEGUIDES;

EID: 35948979723     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.15.014431     Document Type: Article

References (40)

1. K. Hayata, M. Koshiba, M. Eguchi, and M. Suzuki, "Vectorial Finite-Element Method Without Any Spurious Solutions for Dielectric Waveguiding Problems Using Transverse Magnetic-Field Component," IEEE Trans. Microwave Theory Tech. 34, 1120-1124 (1986).
2. B. Rahman, F. Fernandez, and J. Davies, "Review of finite element methods for microwave and optical waveguides," Proc. IEEE 79, 1442-1448 (1991).
3. J. T. Chen, T. W. Lin, K. H. Chen, and S. W. Chyuan, "True and spurious eigensolutions for the problems with the mixed-type boundary conditions using BEMs," Finite Elem. Anal. Des. 40, 1521-1549 (2004).
4. C. Vassallo, "1993-1995 optical mode solvers," Opt. Quantum Electron. 29, 95-114 (1997).
5. Y. Leviatan, A. Boag, and A. Boag, "Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution," IEEE Trans. on Antennas Propag. 36, 1722-1734 (1988).
6. A. Hochman and Y. Leviatan, "Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique," J. Opt. Soc. Am. A 21, 1073-1081 (2004).
7. W. Schroeder and I. Wolff, "The origin of spurious modes in numerical solutions of electromagnetic field eigenvalue problems," IEEE Trans. Microwave Theory Tech. 42, 644-653 (1994).
8. W. Schroeder and I. Wolff, "Full-wave analysis of the influence of conductor shape and structure details on losses in coplanar waveguide," IEEE MTT S International Microwave Symposium Digest 3, 1273-1273 (1995).
9. O. Bucci, G. D'Elia, and M. Santojanni, "Non-redundant implementation of method of auxiliary sources for smooth 2D geometries," Electron. Lett. 41, 22 (2005).
10. B. E. Spielman and R. F. Harrington, "Waveguides of Arbitrary Cross Section by Solution of a Nonlinear Integral Eigenvalue Equation," IEEE Trans. Microwave Theory Tech. 20, 578-585 (1972).
11. V. Labay and J. Bornemann, "Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods," IEEE Microwave Guid. Wave Lett. 2, 49-51 (1992).
12. W. Schroeder and I. Wolff, "A reliable and efficient numerical method for indirect eigenvalue problems arising in waveguide and resonator analysis," Int. J. Numer. Model. 12, 197-208 (1999).
13. N. Don, S. Germani, M. Bozzi, A. Kirilenko, and L. Perregrini, "Determination of the mode spectrum of arbitrarily shaped waveguides using the eigenvalue-tracking method," Microwave Opt. Technol. Lett. 48, 553 (2006).
14. The Source-Model Technique Package (SMTP) may be downloaded at: http://www.ee.technon.ac.il/leviatan/smtp/index.htm.
15. Z. Altman, H. Cory, and Y. Leviatan, "Cutoff frequencies of dielectric waveguides using the multifilament current model," Microwave Opt. Technol. Lett. 3, 294-295 (1990).
16. M. Golberg, Solution Methods for Integral Equations: Theory and Applications (Plenum Press, 1979).
17. C. Müller, Foundations of the Mathematical Theory of Electromagnetic (Springer-Verlag, 1969).
18. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Highly efficient full-vectorial integral equation solution for the bound, leaky, and complex modes of dielectric waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 1225-1232 (1990).
19. H. Cheng, W. Y. Crutchfield, M. Doery, and L. Greengard, "Fast, accurate integral equation methods for the analysis of photonic crystal fibers," Opt. Express. 12, 3791-3805 (2004).
20. D. L. Young, S. P. Hu, C. W. Chen, C. M. Fan, and K. Murugesan, "Analysis of elliptical waveguides by the method of fundamental solutions," Microwave Opt. Technol. Lett. 44, 552-558 (2005).
21. R. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, Philadelphia, 1998).
22. C. F. Van Loan, "Generalizing the singular value decomposition," SIAM J. Numer. Anal. 13, 76-83 (1976).
23. R. Brent, Algorithms for Minimization Without Derivatives (Dover Publications, 2002).
24. B. N. Datta, Numerical Linear Algebra and Applications (Brooks/Cole, Pacific Grove, CA, 1994).
25. C. G. Broyden, "The convergence of a class of double-rank minimization algorithms," J. Inst. Math. Its Appl. 6, 76-90 (1970).
26. G. Golub, C. F. Van Loan, Matrix Computations (Johns Hopkins Univ Pr, 1996).
27. K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
28. M. J. Steel and R. Osgood Jr, "Polarization and dispersive properties of elliptical-hole photoniccrystal fibers," J. Lightwave Technol. 19, 495-503 (2001).
29. P. R. McIsaac, "Symmetry-induced modal characteristics of uniform waveguides-I: Summary of results," IEEE Trans. Microwave Theory and Tech. 23, 421-429 (1975).
30. D. Marcuse, Light Transmition Optics, 2nd ed. (Rober E. Krieger Publishing Company, Malabar, Florida, 1989).
31. J. Kottmann, O. Martin, D. Smith, and S. Schultz, "Plasmon resonances of silver nanowires with a nonregular cross section," Phys. Rev. B 64, 235,402 (2001).
32. J. Krenn and J. Weeber, "Surface plasmon polaritons in metal stripes and wires," Philosophical Transactions: Mathematical, Physical and Engineering Sciences 362, 739-756 (2004).
33. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. Aussenegg, and J. Krenn, "Silver Nanowires as Surface Plasmon Resonators," Phys. Rev. Lett. 95, 257,403 (2005).
34. L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. ESO, 4094-4106 (1994).
35. P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
36. J. Burke, G. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
37. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10,484-10,503 (2000).
38. M. Szpulak, W. Urbanczyk, E. Serebryannikov, A. Zheltikov, A. Hochman, Y. Leviatan, R. Kotynski, and K. Panajotov, "Comparison of different methods for rigorous modeling of photonic crystal fibers," Opt. Express 14, 5699-5714 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5699.
39. A. Webb, F. Poletti, D. Richardson, J. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010,503 (2007).
40. A. Hochman and Y. Leviatan, "Calculation of confinement losses in photonic crystal fibers by use of a source-model technique," J. Opt. Soc. Am. B 22, 474-480 (2005).