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Optics Express

Optics Express

  • Editor: Micha
  • Vol. 13, Iss. 23 — Nov. 14, 2005
  • pp: 9155–9166

Three-dimensional finite element analysis of nonreciprocal phase shifts in magneto-photonic crystal waveguides

Naoya Kono and Masanori Koshiba  »View Author Affiliations


Optics Express, Vol. 13, Issue 23, pp. 9155-9166 (2005)
http://dx.doi.org/10.1364/OPEX.13.009155


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Abstract

This report presents the first three-dimensional characterization of nonreciprocal phase shifts in magneto-photonic crystal (MPC) slab waveguides. We model MPC waveguides using a three-dimensional finite element method with curvilinear tetrahedral edge elements. This study investigates the dependence of nonreciprocal phase shifts on the width and the thickness of the waveguides, and we investigate the dependence of losses on the air hole depth, leading to a guideline for the design of optical isolators. Simulations show that waveguides with reduced width and deep air holes exhibit high nonreciprocal phase shifts and low losses. The study also shows that, compared with two-dimensional calculations, nonreciprocal phase shifts express key similarities, although the frequencies of the guided modes shift.

© 2005 Optical Society of America

OCIS Codes
(130.1750) Integrated optics : Components
(230.3810) Optical devices : Magneto-optic systems
(230.3990) Optical devices : Micro-optical devices
(230.7370) Optical devices : Waveguides

ToC Category:
Research Papers

History
Original Manuscript: September 30, 2005
Revised Manuscript: October 25, 2005
Published: November 14, 2005

Citation
Naoya Kono and Masanori Koshiba, "Three-dimensional finite element analysis of nonreciprocal phase shifts in magneto-photonic crystal waveguides," Opt. Express 13, 9155-9166 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9155


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References

  1. M. Inoue, K. Arai, T. Fujii, and M. Abe, �??One-dimensional magnetophotonic crystals,�?? J. Appl. Phys. 85, 5768-5770 (1999). [CrossRef]
  2. A. Sakaguchi and N. Sugimoto, �??Transmisson properties of multilayer films composed of magneto-optical and dielectric materials,�?? J. Lightwave Technol. 17, 1087-1092 (1999). [CrossRef]
  3. A. Figotin and I. Vitebsky, �??Nonreciprocal magnetic photonic crystals,�?? Phys. Rev. E 63, 066609 (2001). [CrossRef]
  4. M. J. Steel, M. Levy, and R. M. Osgood Jr., �??Photonic bandgaps with defects and the enhancement of Faraday rotation,�?? J. Lightwave Technol. 18, 1297-1308 (2000). [CrossRef]
  5. A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida, and M. Inoue, �??Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals,�?? J. Magn. Magn. Mater. 282, 256-269 (2004). [CrossRef]
  6. H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, �??Effect of optical losses on optical and magneto-optical properties of one-dimensional magnetophotonic crystals for use in optical isolator devices,�?? Opt. Commun. 219, 271-276 (2003). [CrossRef]
  7. Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, �??Preparation of two-dimensional magneto-photonic crystals of bismuth substitute yttrium iron garnet materials,�?? J. Magn. Magn. Mater. 272-276, 1690-1691, (2004). [CrossRef]
  8. A. K. Zvezdin and V. I. Belotelov, �??Magnetooptical properties of two dimensional photonic crystals,�?? Eur. Phys. J. B 37, 479-487 (2004). [CrossRef]
  9. S. K. Mondal and B. J. H. Stadler, �??Novel designs for integrating YIG/air photonic crystal slab polarizers with waveguide Faraday rotators,�?? IEEE Photonics Technol. Lett. 17, 127-129 (2005). [CrossRef]
  10. A. A. Jalali and A. T. Friberg, �??Faraday rotation in a two-dimensional photonic crystal with a magnetooptic defect,' Opt. Lett. 30, 1213-1215 (2005). [CrossRef] [PubMed]
  11. A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, �??Two-dimensional magnetophotonic crystal: Exactly solvable model,�?? Phys. Rev. B 72, 035123 (2005). [CrossRef]
  12. A. A. Jalali and A. T. Friberg, �??Faraday rotation in two-dimensional magneto-optic photonic crystal,�?? Opt. Commun. 253, 145-150 (2005). [CrossRef]
  13. N. Kono and Y. Tsuji, �??A novel finite-element method for nonreciprocal magneto-photonic crystal waveguides,�?? J. Lightwave Technol. 22, 1741-1747 (2004). [CrossRef]
  14. N. Kono and M. Koshiba, �??General finite-element modeling of 2-D magnetophotonic crystal waveguides,�?? IEEE Photonics Technol. Lett. 17, 1432-1434 (2005). [CrossRef]
  15. Z. Wang and S. Fan, �??Optical circulators in two-dimensional magneto-optical photonic crystals,�?? Opt. Lett. 1989-1991 (2005). [CrossRef] [PubMed]
  16. T. Søndergaard, J. Arentoft, and M. Kristensen, �??Theoretical analysis of finite-height semiconductor-oninsulator- based planar photonic crystal waveguides,�?? J. Lightwave Technol. 20, 1619-1625 (2002). [CrossRef]
  17. M. Lon�?ar, T. Doll, J. Vu�?kovi�?, and A. Scherer, �??Design and fabrication of silicon photonic crystal optical waveguides,�?? J. Lightwave Technol. 18, 1402-1411 (2000). [CrossRef]
  18. T. Ochiai and K. Sakoda, �??Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,�?? Phys. Rev. B 63, 125107 (2001). [CrossRef]
  19. Y. Tanaka, T Asano, R. Hatsuta, and S. Noda, �??Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-crystal slab,�?? J. Lightwave Technol. 22, 2787-2792 (2004). [CrossRef]
  20. Y. Okamura, T. Negami, and S. Yamamoto, �??Integrated optical isolator and circulator using nonreciprocal phase shifters: a proposal,�?? Appl. Opt. 23, 1886-1889 (1984). [CrossRef] [PubMed]
  21. M. Levy, �??The on-chip integration of magnetooptic waveguide isolators,�?? IEEE J. Sel. Top. Quantum Electron. 8, 1300-1306 (2001).
  22. M. Takenaka and Y. Nakano, �??Proposal of a Novel Semiconductor Optical Waveguide Isolator,�?? in Proceedings of IEEE Eleventh International Conference on Indium Phosphide and Related Materials (Institute of Electrical and Electronics Engineers, Davos, Switzerland, 1999), pp. 289-292.
  23. W. Zaets and K. Ando, �??Optical waveguide isolator based on nonreciprocal loss/gain of amplifier covered by ferromagnetic layer,�?? IEEE Photonics Technol. Lett. 11, 1012-1014 (1999). [CrossRef]
  24. C. Kim, W. J. Kim, A. Stapleton, J. R. Cao, J. D. O'Brien, and P. D. Dapkus, �??Quality factors in single-defect photonic-crystal lasers with asymmetric cladding layers,�?? J. Opt. Soc. Am. B 19, 1777-1781 (2002). [CrossRef]
  25. W. J. Kim and J. D. O'Brien, �??Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite-element method,�?? J. Opt. Soc. Am. B 21, 289-295 (2004). [CrossRef]
  26. J. P. Krumme and P. Hansen, �??A new type of magnetic domain wall in nearly compensated Ga-substituted YIG,�?? Appl. Phys. Lett. 22, 312-314 (1973). [CrossRef]
  27. L. Wilkens. D. Trager, H. Dötsch, A. F. Popkov, and A. M. Alekseev, �??Nonreciprocal phase shift of TE modes induced by compensation wall in a magneto-optic rib waveguide,�?? Appl. Phys. Lett. 79, 4292-4294 (2001). [CrossRef]
  28. N. Bahlmann, M. Lohmeyer, H. Dötch, and P. Hertel, �??Finite-element analysis of nonreciprocal phase shift for TE modes in magnetooptic rib waveguides with a compensation wall,�?? J. Quantum Electron. 35, 250- 253 (1999). [CrossRef]
  29. 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]
  30. J. S. Wang and N. Ida, �??Curvilinear and higher order 'edge' finite elements in electromagnetic field computation,�?? IEEE Trans. Magn. 29, 1491-1494 (1993). [CrossRef]
  31. J. F. Lee, D. K. Sun, and Z. J. Cendes, �??Tangential vector finite elements for electromagnetic field,�?? IEEE Trans. Magn. 27, 4032-4035 (1991). [CrossRef]
  32. O. Schenk, and K. Gärtner, �??Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO,�?? J. Fut. Gen. Comput. Syst. 20, 475-487 (2004). [CrossRef]
  33. G. Karypis and V. Kumar, �??A fast and high quality multilevel scheme for partitioning irregular graphs,�?? SIAM J. Scient. Comput. 1, 359-392 (1998). [CrossRef]
  34. L. C. Andreani and M. Agio, �??Intrinsic diffraction losses in photonic crystal waveguides with line defects,�?? Appl. Phys. Lett. 82, 2011-2013 (2003). [CrossRef]
  35. K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, �??Nature of lossy Bloch states in polaritonic photonic crystals,�?? Phys. Rev. B 69, 195111 (2004). [CrossRef]
  36. N. Bahlmann, M. Lohmeyer, O. Zhuromskyy, H. Dötsch, and P. Hertel, �??Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM-modes,�?? Opt. Commun. 161, 330-337 (1999). [CrossRef]
  37. M. Notomi, A. Shinya, K. Yamada, J. Tahashi, C. Takahashi, and I. Yokohama, �??Structural tuning of guideing modes of line-defect waveguides of silicon-on insulator photonic crystal slabs,�?? IEEE J. Quantum Electron. 38, 736-742 (2002). [CrossRef]
  38. J. Fujita, M. Levy, R. M. Osgood Jr., L. Wilkens, and H. Dötsch, �??Waveguide optical isolator based on Mach-Zehnder interferometer,�?? Appl. Phys. Lett. 76, 2158-2160 (2000). [CrossRef]
  39. W. Bogaerts, P. Bienstman, and R. Baets, �??Scattering at sidewall roughness in photonic crystal slabs,�?? Opt. Lett. 28, 689-691 (2003). [CrossRef] [PubMed]
  40. D. Gerace and L. C. Andreani, �??Disorder-induced losses in photonic crystal waveguides with line defects,�?? Opt. Lett. 29, 1897-1899 (2004). [CrossRef] [PubMed]
  41. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, �??Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,�?? Phys. Rev. Lett. 94, 033903 (2005). [CrossRef] [PubMed]
  42. M. Skorobogatiy, G. Bégin, and A. Talneau, �??Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,�?? Opt. Express 13, 2487-2502 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2487">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2487</a>. [CrossRef] [PubMed]
  43. D. Gerace and L. C. Andreani, �??Low-loss guided modes in photonic crystal waveguides,�?? Opt. Express. 13, 4939-4951 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4939">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4939</a>. [CrossRef] [PubMed]
  44. S. G. Johnson, M. L. Povinelli, M. Solja�?i�?, A. Karalis, S. Jacobs, and J. D. Joannopoulos, �??Roughness losses and volume-current methods in photonic-crystal waveguides,�?? Appl. Phys. B 81, 283-293 (2005). [CrossRef]

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