DOI QR코드

DOI QR Code

Eigenmode of Anisotropic Planar Waveguide

  • 투고 : 2004.03.11
  • 발행 : 2004.09.01

초록

A new method of obtaining the eigenmode of an anisotropic planar waveguide is studied. The planar waveguide can be composed of an arbitrary number of isotropic or uniaxially anisotropic layers, provided all the optical axes arc lying in the incidence plane. Since the equation of motion for the TE mode is not different from that for the TE mode in an isotropic planar waveguide, only the equation of motion for the TM mode is of any concern. For this kind of device structure, the Maxwell's equations can be solved for one component of the electric field and one component of the magnetic field. The resulting coupled set of equations is linear in the propagation constant and the eigenmode can be easily obtained using canned numerical routines.

키워드

참고문헌

  1. T. P. Sosnowski, 'Polarization mode filters for integrated optics,' Opt. Commun., vol. 4, no. 6, pp. 408-412, 1972 https://doi.org/10.1016/0030-4018(72)90112-5
  2. M. Wakaki, Y. Komachi, H. Machida, and H. Kobayashi, 'Fiber-optic polarizer using birefringent crystal as a cladding,' Appl. Opt., vol. 35, no. 15, pp. 2591-2594, 1996 https://doi.org/10.1364/AO.35.002591
  3. G. K. Singh, V. K. Sharma, A. Kapoor, and K. N. Tripathi, 'Four layer polymeric mode polarization filter for integrated optics,' Optics & Laser Technology, vol. 33, pp. 455-459, 2001 https://doi.org/10.1016/S0030-3992(01)00058-5
  4. K. Liu, W. V. Sorin, and H. J. Shaw, 'Single-mode-fiber evanescent polarizer/amplitude modulator using liquid crystals,' Opt. Lett., vol. 11, no. 3, pp. 180-182, 1986 https://doi.org/10.1364/OL.11.000180
  5. R. A. Kashnow and C. R. Stein, 'Total-reflection liquid-crystal electrooptic device,' App. Opt., vol. 12, no. 10, pp. 2309-2311, 1973 https://doi.org/10.1364/AO.12.002309
  6. S. Wang, M. Shar, and J. D. Crow, 'Studies of the use of gyrotropic and anisotropic materials for mode conversion in thin-film optical-waveguide applications,' J. Appl. Phys., vol. 43, no. 4, pp. 1861-1875, 1972 https://doi.org/10.1063/1.1661410
  7. S. Yamamoto, Y. Koyamada, and T. Makimoto, 'Normalmode analysis of anisotropic and gyrotropic thin-film waveguides for integrated optics', J. Appl. Phys., vol. 43, no. 12, pp. 5090-5097, 1972 https://doi.org/10.1063/1.1661077
  8. J. Ctyroky and M. Cada, 'Guided and semileaky modes in anisotropic optical waveguides of the LiNb$O_3$ type,' Opt. Commun., vol. 27, no. 3, pp. 353-357, 1978 https://doi.org/10.1016/0030-4018(78)90397-8
  9. K. Yamanouchi, T. Kamiya, and K. Shibayama, 'New leaky surface waves in anisotropic metal-diffused optical waveguides,' IEEE Trans. Microwave Theory Tech., vol. 26, no. 4, pp. 298-305, 1978 https://doi.org/10.1109/TMTT.1978.1129368
  10. S. K. Sheem, W. K. Burns, and A. F. Milton, 'Leaky-mode propagation in Ti-diffused LiNb$O_3$ and LiTa$O_3$ waveguides,' Opt. Lett., vol. 3, no. 3, pp. 76-78, 1978 https://doi.org/10.1364/OL.3.000076
  11. L. Torner, J. Recolons, and J. P. Torres, 'Guided-to-leaky mode transition in uniaxial optical slab waveguides,' J. Lightwave Technol., vol. 11, no. 10, pp. 1592-1600, 1993 https://doi.org/10.1109/50.249901
  12. D. F. Nelson and J. McKenna, 'Electromagnetic modes of anisotropic dielectric waveguides at p-n junctions,' J. Appl. Phys., vol. 38, no. 10, pp. 4057-4074, 1967 https://doi.org/10.1063/1.1709067
  13. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, 'Superprism phenomena in photonic crystals: toward microscale lightwave circuits,' J. Lightwave Technol., vol. 17, no. 11, pp. 2032-2038, 1999 https://doi.org/10.1109/50.802991
  14. D. P. Gia Russo and J. H. Harris, 'Wave propagation in anisotropic thin-film optical waveguides,' J. Opt. Soc. Am., vol. 63, no. 2, pp. 138-145, 1973 https://doi.org/10.1364/JOSA.63.000138
  15. M. S. Kharusi, 'Uniaxial and biaxial anisotropy in thin-film optical waveguides,' J. Opt. Soc. Am., vol. 64, no. 1, pp. 27-35, 1974 https://doi.org/10.1364/JOSA.64.000027
  16. W. K. Burns and J. Warner, 'Mode dispersion in uniaxial optical waveguides,' J. Opt. Soc. Am., vol. 64, no. 4, pp. 441-446, 1974 https://doi.org/10.1364/JOSA.64.000441
  17. V. Ramaswamy, 'Propagation in asymmetrical anisotropic film waveguides,' App. Opt., vol. 13, no. 6, pp. 1363-1371, 1974 https://doi.org/10.1364/AO.13.001363
  18. D. Marcuse, 'Modes of a symmetric slab optical waveguide in birefringent media-part I: optical axis not in plane of slab,' IEEE J. Quantum Electron., vol. 14, no. 10, pp. 736-741, 1978 https://doi.org/10.1109/JQE.1978.1069682
  19. 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., vol. 15, no. 2, pp. 92-101. 1979 https://doi.org/10.1109/JQE.1979.1069973
  20. E. A. Kolosovsky, D. V. Petrov, A. V. Tsarev, and I. B. Yakovkin, 'An exact method for analysing light propagation in anisotropic inhomogeneous optical waveguides,' Opt. Commun., vol. 43, no. 1, pp. 21-25, 1982 https://doi.org/10.1016/0030-4018(82)90187-0
  21. A. Knoesen, T. K. Gayload, and M. G. Moharam, 'Hybrid guided modes in uniaxial dielectric planar waveguides,' J. Lightwave Technol., vol. 6, no. 6, pp. 1083-1104, 1988 https://doi.org/10.1109/50.4101
  22. A. D'Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, 'Leaky mode propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configuration,' J. Lightwave Technol., vol. 12, no. 3, pp. 453-462, 1994 https://doi.org/10.1109/50.285328
  23. T. A. Maldonado and T. K. Gayload, 'Hybrid guided modes in biaxial planar waveguides,' J. Lightwave Technol., vol. 14, no. 3, pp. 486-499, 1996 https://doi.org/10.1109/50.485612
  24. D. V. Petrov and E. A. Kolosovsky, 'Radiation modes of an anisotropic optical waveguide with arbitrary refractive index profile,' Opt. Commun., vol. 124, pp. 240-243, 1996 https://doi.org/10.1016/0030-4018(95)00683-4
  25. A. A. Romanenko, 'Features of mode's characteristics of anisotropic planar optical waveguides in the vicinity of degeneration points,' Proc. SPIE, vol. 4358, pp. 203-211, 2001 https://doi.org/10.1117/12.418855
  26. Q. Guo, Z. Shi, and W. Xu, 'Modal fields of symmetric metal-clad planar uniaxial crystal waveguide,' Proc. SPIE, vol. 4603, pp. 30-35, 2001 https://doi.org/10.1117/12.444580
  27. Y. Jeong and B. Lee, 'Theory of electrically controllable long-period gratings built in liquid-crystal fibers', Opt. Eng., vol. 40, no. 7, pp. 1227-1233, 2001 https://doi.org/10.1117/1.1371933
  28. M. O. Vassell, 'Structure of optical guided modes in planar multilayers of optically anisotropic materials,' J. Opt. Soc. Am., vol. 64, no. 2, pp. 166-173, 1974 https://doi.org/10.1364/JOSA.64.000166
  29. P. Yeh, 'Electromagnetic propagation in birefringent layered media,' J. Opt. Soc. Am., vol. 69, no. 5, pp. 742-756, 1979 https://doi.org/10.1364/JOSA.69.000742
  30. L. M. Walpita, 'Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix,' J. Opt. Soc. Am. A, vol. 2, no. 4, pp. 595-602, 1985 https://doi.org/10.1364/JOSAA.2.000595
  31. J. F. Offersgaard, 'Waveguides formed by multiple layers of dielectric, semiconductor, or metallic media with optical loss and anisotropy,' J. Opt. Soc. Am. A, vol. 12, no. 10, pp. 2122-2128, 1995 https://doi.org/10.1364/JOSAA.12.002122
  32. I. Hodgkinson, S. Kassam, J. Hazel, S. Cloughley, and Q. Wu, 'Modal contours for biaxial thin-film waveguides,' Appl. Opt., vol. 35, no. 28, pp. 5569-5572, 1996 https://doi.org/10.1364/AO.35.005569
  33. L. Thylen and D. Yevick, 'Beam propagation method in anisotropic media,' Appl. Opt., vol. 21, no. 15, pp. 2751-2754, 1982 https://doi.org/10.1364/AO.21.002751
  34. J. A. Fleck, Jr. and M. D. Feit, 'Beam propagation method in uniaxial anisotropic media,' J. Opt. Soc. Am., vol. 73, no. 7, pp. 920-926, 1983 https://doi.org/10.1364/JOSA.73.000920
  35. G. R. Hadley, 'Wide-angle beam propagation using Pade approximant operators,' Opt. Lett., vol. 17, no. 20, pp. 1426-1428, 1992 https://doi.org/10.1364/OL.17.001426
  36. C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, 'A full-vectorial beam propagation method for anisotropic waveguides,' J. Lightwave Technol., vol. 12, no. 11, pp. 1926-1931, 1994 https://doi.org/10.1109/50.336056
  37. S. V. Polstyanko and J. Lee, '$H_1$ (curl) tangential vector finite element method for modeling anisotropic optical fibers,' J. Lightwave Technol., vol. 13, no. 11, pp. 2290-2295, 1995 https://doi.org/10.1109/50.482050
  38. Y. Tsuji, M. Koshiba, and N. Takimoto, 'Finite element beam propagation method for anisotropic optical waveguides,' J. Lightwave Technol., vol. 17, no. 4, pp. 723-728, 1999 https://doi.org/10.1109/50.754805
  39. K. Saitoh and M. Koshiba, 'Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,' J. Lightwave Technol., vol. 19, no. 3, pp. 405-413, 2001 https://doi.org/10.1109/50.918895
  40. K. Saitoh and M. Koshiba, 'Approximate scalar finite-element beam-propagation method with perfectly matched layers for anisotropic optical waveguides,' J. Lightwave Technol., vol.19, no. 5, pp. 786-792, 2001 https://doi.org/10.1109/50.923493
  41. A. Ciattoni, B. Crosignani, and P. Di Porto, 'Vectorial theory of propagation in uniaxially anisotropic media,' J. Opt. Soc. Am. A, vol. 18, no. 7, pp. 1656-1661, 2001 https://doi.org/10.1364/JOSAA.18.001656
  42. G. Kweon, S. Hwang-bo, and C. Kim, 'Eigenmode of anisotropic planar waveguide,' in Frontiers in Optics/ Laser Science XIX Conference, Optical Society of America, Tucson, Arizona, USA, MT62, 2003
  43. D. W. Berreman, 'Optics in stratified and anisotropic media: 4$\times$4-matrix formulation,' J. Opt. Soc. Am., vol. 62, no. 4, pp. 502-510, 1972 https://doi.org/10.1364/JOSA.62.000502
  44. P. J. Lin-Chung and S. Teitler, '4$\times$4 matrix formalisms for optics in stratified anisotropic media,' J. Opt. Soc. Am. A, vol. 1, no. 7, pp. 703-705, 1984 https://doi.org/10.1364/JOSAA.1.000703
  45. T. Tamir, Guided-Wave Optoelectronics, 2nd ed. (Springer-Verlag, Berlin, 1990), Chap. 2
  46. G. Kweon, S. Hwang-bo, and C. Kim, 'Eigenmode of planar magnetooptical waveguide,' in The 3rd International Conference on Advanced Materials and Devices, Korean Physical Society, Jeju, Korea, DEV-P22, 2003
  47. G. Kweon, S. Hwang-bo, and C. Kim, 'Eigenmode of magnetooptical planar waveguide,' J. Korean Phys. Soc., vol. 45, no. 1, pp. 211-216, 2004
  48. J. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comput. Phys., vol. 114, pp. 185-200, 1994 https://doi.org/10.1006/jcph.1994.1159