Applications of the finite-difference frequency-domain mode solution method to photonic crystal structures

Electromagnetic Theory and Applications for Photonic Crystals

Volumn , Issue , 2005, Pages 351-400

  Yu, Chin Ping ^a   Chang, Hung Chun ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85129826275     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (73)

1. C.P. Yu and H.C. Chang, Applications of the finite difference mode solution method to photonic crystal structures, Opt. Quantum Electron, 36, 145-163, 2004.
2. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett., 58, 2059-2062, 1987.
3. S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett., 58, 2486-2489, 1987.
4. A. Mekis, J.C. Chen, I. Kurland, S. Fan, P.R. Villeneuve, and J.D. Joannopoulos, High transmission through sharp bends in photonic crystal waveguides, Phys. Rev. Lett., 77, 3787-3790, 1996.
5. T. Baba, N. Fukaya, and J. Yonekura, Observation of light propagation in photonic crystal optical waveguides with bends, Electron. Lett., 35, 654-655, 1999.
6. A. Adibi, Y. Xu, R.K. Lee, A. Yariv, and A. Scherer, Properties of the slab modes in photonic crystal optical waveguides, J. Lightwave Technol, 18, 1554-1564, 2000.
7. J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, All-silica single-mode optical fiber with photonic crystal cladding, Opt. Lett, 21, 1547-1549, 1996.
8. T.A. Birks, J.C. Knight, and P.St.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett., 22, 961-963, 1997.
9. M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett, 35, 63-64, 1999.
10. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite element method, Opt. Fiber Technol, 6, 181-191, 2000.
11. S.E. Barkou, J. Broeng, and A. Bjarklev, Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect, Opt. Lett., 24, 46-48, 1999.
12. A. Ferrando, E. Silvestre, J.J. Miret, P. Andrés, and M.V. Andrés, Full-vector analysis of a realistic photonic crystal fiber, Opt. Lett., 24, 276-278, 1999.
13. H. Benisty, Modal analysis of optical guides with two-dimensional photonic bandgap boundaries, J. Appl. Phys., 79, 7483-7492, 1996.
14. M. Qiu, Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method, Microwave Opt. Technol. Lett, 30, 327-330, 2001.
15. M. Koshiba and K. Saitoh, Numerical verification of degeneracy in hexagonal photonic crystal fibers, IEEE Photon. Technol. Lett., 13, 1313-1315, 2001.
16. K. Yasumoto and H. Jia, Modal analysis of two-dimensional photonic crystal waveguides using lattice sums technique. 3rd International Conference on Microwave and Millimeter Wave Technology Proceedings, 2002, 1063-1066.
17. P. Lüsse, P. Stuwe, J. Schule, and H.G. Unger, Analysis of vectorial mode fields in optical waveguides by a new finite difference method, J. Lightwave Technol., 12, 487-194, 1994.
18. G.R. Hadley and R.E. Smith, Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary conditions, J. Lightwave Technol, 13, 465-169, 1995.
19. C.P. Yu and H.C. Chang, Finite difference modal analysis of photonic crystal fibers, Proceedings of 2001 Progress in Electromagnetics Research Symposium (PIERS 2001), Osaka, Japan, 2001, 432.
20. H.S. Sözüer, J.W. Haus, and R. Inguva, Photonic bands: convergence problems with the plane-wave method, Phys. Rev. B, 45, 13,962-13,972, 1992.
21. M.J. Robertson, S. Ritchie, and P. Dayan, Semiconductor waveguides: analysis of optical propagation in single rib structures and directional couplers, Inst. Elec. Eng. Proc. J, 132, 336-342, 1985.
22. M.S. Stern, Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles, Inst. Elec. Eng. Proc. J., 135, 56-63, 1988.
23. C. Vassallo, Improvement of finite difference methods for step-index optical waveguides, Inst. Elec. Eng. Proc. J., 139, 137-142, 1992.
24. K. Bierwirth, N. Schulz, and F. Arndt, Finite-difference analysis of rectangular dielectric waveguide structures, IEEE Trans. Microwave Theory Tech., 34, 1104-1114, 1986.
25. C.L. Xu, W.P. Huang, M.S. Stern, and S.K. Chaudhuri, Full-vectorial mode calculations by finite difference method, Inst. Elec. Eng. Proc. J, 141, 281-286, 1994.
26. W.P. Huang, C.L. Xu, S.T. Chu, and S.K. Chaudhuri, The finite-difference vector beam propagation method: analysis and assessment, J. Lightwave Technol., 10, 295-305, 1992.
27. C.L. Xu, W.P. Huang, and S.K. Chaudhuri, Efficient and accurate vector mode calculations by beam propagation method, J. Lightwave Technol, 11, 1209-1215, 1993.
28. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propagat, AP-14, 302-307, 1966.
29. T. Ando, H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface, J. Lightwave Technol., 20, 1627-1634, 2002.
30. Z. Zhu and T.G. Brown, Full-vectorial finite-difference analysis of microstructured optical fibers, Opt. Express, 10, 853-864, 2002.
31. H.C. Chang and C.P. Yu, Yee-mesh-based finite difference eigenmode analysis algorithms for optical waveguides and photonic crystals, OSA Integrated Photonics Research Digest, San Francisco, 2004, paper IFE4.
32. 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, 6165-6177, 2004.
33. T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, and M.J. Steel, Confinement losses in microstructured optical fibers, Opt. Lett., 26, 1660-1662, 2001.
34. J.P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185-200, 1994.
35. W.C. Chew and W.H. Weedon, A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates, Microwave Opt. Technol. Lett., 7, 599-604, 1994.
36. Ü. Pekel and R. Mittra, An application of the perfectly matched layer (PML) concept to the finite element method frequency domain analysis of scattering problem, IEEE Microwave Guided Wave Lett., 5, 258-260, 1995.
37. C.M. Rappaport, Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space, IEEE Microwave Guided Wave Lett., 5, 90-92, 1995.
38. Y.P. Chiou, Y.C. Chiang, and H.C. Chang, Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices, J. Lightwave Technol., 18, 243-251, 2000.
39. Y.C. Chiang, Y.P. Chiou, and H.C. Chang, Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles, J. Lightwave Technol., 20, 1609-1618, 2002.
40. G.R. Hadley, High-accuracy finite-difference equations for dielectric waveguide analysis I: uniform regions and dielectric interfaces, J. Lightwave Technol, 20, 1210-1218, 2002.
41. G.R. Hadley, High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners, J. Lightwave Technol., 20, 1219-1231, 2002.
42. A. Ditkowski, J.S. Hesthaven, and C.H. Teng, Modeling dielectric interfaces in the FDTD-method: a comparative study, 2000 Progress in Electromagnetics Research Proceedings (PIERS 2000), Cambridge, MA, 2000.
43. R.D. Meade, K.D. Brommer, A.M. Rappe, and J.D. Joannopoulos, Existence of a photonic band gap in two dimensions, Appl. Phys. Lett, 61, 495-497, 1992.
44. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystal: Modeling the Flow of Light, Princeton University Press, Princeton, NJ, 1995.
45. C.T. Chan, Q.L. Yu, and K.M. Ho, Order-N spectral method for electromagnetic waves, Phys. Rev. B., 51, 16,635-16,642, 1995.
46. M. Qiu and S. He, A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metalic inclusions, J. Appl. Phys., 87, 8268-8275, 2000.
47. H.Y.D. Yang, Finite difference analysis of 2-D photonic crystals, IEEE Trans. Microwave Theory Tech., 44, 2688-2695, 1996.
48. L. Shen, S. He, and S. Xiao, A finite-difference eigenvalue algorithm for calculating the band structure of a photonic crystal, Comp. Phys. Commun., 143, 213-221, 2002.
49. C.P. Yu and H.C. Chang, Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals, Opt. Express, 12, 1397-1408, 2004.
50. J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, Photonic band gap guidance in optical fibers, Science, 282, 1476-1478, 1998.
51. D.S. Katz, E.T. Thiele, and A. Taflove, Validation and extension to three dimensionals of the Berenger PML absorbing boundary condition for FD-TD meshes, IEEE Microwave Guided Wave Lett, 4, 268-270, 1994.
52. Y.F. Li, K. Iizuka, and J.W.Y. Lit, Equivalent-layer method for optical waveguides with a multiple-quantum-well structure, Opt. Lett., 17, 273-275, 1992.
53. S. Ohke, T. Umeda, and Y. Cho, Equivalent-layer method for optical waveguides with a multiple-quantum-well structure: comment, Opt. Lett., 18, 1870, 1993.
54. M. Saini and E.K. Sharma, Equivalent refractive index of MQW waveguides, IEEE J. Quantum Electron., 32, 1383-1390, 1996.
55. K.H. Dridi, J.S. Hesthaven, and A. Ditkowski, Staircase-free finite-difference time-domain formulation for general materials in complex geometries, IEEE Trans Antennas Propagat, 49, 749-756, 2001.
56. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, Single-mode photonic band gap guidance of light in air, Science, 285, 1537-1539, 1999.
57. T.M. Monro, D.J. Richardson, N.G.R. Broderick, and P.J. Bennett, Holey optical fibers: an efficient modal model, J. Lightwave Technol, 17, 1093-1102, 1999.
58. J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, Photonic crystal fibers: a new class of optical waveguides, Opt. Fiber Technol, 5, 305-330, 1999.
59. D. Mogilevtsev, T.A. Birks, and P.St.J. Russell, Localized function method for modeling defect modes in 2-D photonic crystals, J. Lightwave Technol., 17, 2078-2081, 1999.
60. M.J. Steel, T.P. White, C. Martijn de Sterke, R.C. McPhedran, and L.C. Botten, Symmetry and degeneracy in microstructured optical fibers, Opt. Lett., 26, 488-490, 2001.
61. I.H. Malitson, Interspecimen comparison of the refractive index of fused silica, J. Opt. Soc. Amer, 55, 1205-1209, 1965.
62. B. Brixner, Refractive-index interpolation for fused silica, J. Opt. Soc. Amer., 57, 674-676, 1967.
63. K. Saitoh and M. Koshiba, Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers, IEEE J. Quantum Electron., 38, 927-933, 2002.
64. A. Yariv, Optical Electronics in Modern Communications, 5th ed., Oxford University Press, New York, 1997.
65. B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, and A.H. Greenaway, Experimental study of dual-core photonic crystal fibre, Electron. Lett., 36, 1358-1359, 2000.
66. D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, Leakage properties of photonic crystal fibers, Opt. Express, 10, 1314-1319, 2002.
67. C.M. Smith, N. Venkataraman, M.T. Gallagher, D. Müller, J.A. West, N.F. Borrelli, D.C. Allan, and K.W. Koch, Low-loss hollow-core silica/air photonic bandgap fibre, Nature, 424, 657-659, 2003.
68. B.J. Mangan, L. Farr, A. Langford, P.J. Roberts, D.P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, Low loss (1.7 dB/km) hollow core photonic bandgap fiber, 2004 Optical Fiber Communication (OFC' 04), Los Angeles, CA, 2004, postdeadline paper PDP24.
69. G. Humbert, J.C. Knight, G. Bouwmans, P.St.J. Russell, D.P. Williams, P.J. Roberts, and B.J. Mangan, Hollow core photonic crystal fibers for beam delivery, Opt. Express, 12, 1477-1484, 2004.
70. K. Saitoh, N.A. Mortensen, and M. Koshiba, Air-core photonic band-gap fibers: the impact of surface modes. Opt. Express, 12, 394-400, 2004.
71. J.A. West, C.M. Smith, N.F. Borrelli, D.C. Allan, and K.W. Koch, Surface modes in air-core photonic band-gap fibers, Opt. Express, 12 1485-1496, 2004.
72. H.K. Kim, J. Shin, S. Fan, M.J.F. Digonnet, and G.S. Kino, Designing air-core photonic-bandgap fibers free of surface modes, IEEE J. Quantum Electron., 40, 551-556, 2004.
73. S.G. Johnson and J.D. Joannopoulos, Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis, Opt. Express, 8, 173-190, 2001.