Progress In Electromagnetics Research M
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By S. K. Awasthi and S. P. Ojha

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A band pass filter with a linearly periodic refractive index profile is discussed in analogy with Kroning Penney model in band theory of solids. The suggested filter is a one-dimensional ternary periodic structure and provides better control in dispersion relation as compared to a binary structure because it has two more controlling parameters relative to those of the binary one. Since three layers are involved in the formation of band gaps a much broader range of dispersion control is obtained. Both refractive index modulation and optical thickness modulation are considered. A mathematical analysis is presented to predict allowed and forbidden bands of wavelength with variation of angle of incidence. It is also possible to get desired ranges of the electromagnetic spectrum filtered with this structure by manipulating the value of the lattice parameters.

S. K. Awasthi and S. P. Ojha, "Design of a Tunable Optical Filter by Using a One-Dimensional Ternary Photonic Band Gap Material," Progress In Electromagnetics Research M, Vol. 4, 117-132, 2008.

1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.

2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.

3. Makhan, M. and S. K. Ramchurn, "Polarization-independent omnidirectional defect modes in Bragg gaps of one-dimensional photonic crystals," J. Opt. Soc. Am. B, Vol. 24, 3040-3047, 2007.

4. Joannopoulos, J. D., P. R. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature, Vol. 386, 143-149, 1997.

5. Zheng, Q. R., Y. Q. Fu, and N. C. Yuan, "Characteristics of planar PBG structures with a cover layer," Journal of Electromagnetic Waves andApplic ations, Vol. 20, No. 11, 1439-1453, 2006.

6. Fink, Y., J. N. Winn, S. Fan, C. Chen, and J. Michel, "A dielectric omnidirectional reflector," Science, Vol. 282, No. 5394, 1679-1682, 1998.

7. Rojas, J. A. M., J. Alpuente, J. PiEoeneiro, and R. Sanchez, "Rigorous full vectorial analysis of electromagnetic wave propagation in 1D ," Progress In Electromagnetics Research, Vol. 63, 89-105, 2006.

8. Chigrin, D. N., A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A, Vol. 68, 25-28, 1999.

9. Sakoda, K., Optical Properties of Photonic Crystals, Springer-Verlag, Berlin, 2001.

10. Han, P. and H. Wang, "Extension of omnidirectional reflection range in one-dimensional photonic crystal with a staggered structure," J. Opt. Soc. Am. B, Vol. 20, No. 9, 1996-2001, 2003.

11. Ozbay, E., M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. of Quantum Electronics, Vol. 38, 837-843, 2004.

12. Boroditsky, M., R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, "Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals," J. Lightwave Technol., Vol. 17, 2096-2112, 1999.

13. Painter, O., R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two dimensional photonic bandgap defect mode laser," Science, Vol. 284, 1819-1821, 1999.

14. Mekis, A., M. Meier, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, "Lasing mechanism in two-dimensional photonic crystal lasers," Appl. Phys. A: Materials Science and Processing, Vol. 69, 111-114, 1999.

15. Noda, S., M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science, Vol. 293, 1123-1125, 2001.

16. Mekis, A., 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., Vol. 77, 3787-3790, 1996.

17. Sondergaard, T. and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B, Vol. 61, 15688-15696, 2000.

18. Knight, J. C., J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic bandgap guidance in optical fibers," Science, Vol. 282, 1476-1479, 1998.

19. Brown, E. R., C. D. Parker, and E. Yablonovitch, "Radiation properties of a planar antenna on a photonic-crystal substrate," J. Opt. Soc. Amer. B, Vol. 10, 404-407, 1993.

20. Kosaka, H., T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakamib, "Photonic crystals for micro lightwave circuits using wavelength dependent angular beam steering," Appl. Phys. Lett., Vol. 74, 1370-1372, 1999.

21. Villeneuve, P. R., D. S. Abrams, S. Fan, and J. D. Joannopoulos, "Single-mode waveguide microcavity for fast optical switching," Opt. Lett., Vol. 21, 2017-2019, 1996.

22. Zandi, O., Z. Atlasbaf, and K. Forooraghi, "Flat multilayer dielectric reflector antennas," Progress In Electromagnetics Research, Vol. 72, 1-19, 2007.

23. Aissaoui, M., J. Zaghdoudi, M. Kanzari, and B. Rezig, "Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures," Progress In Electromagnetics Research, Vol. 59, 69-83, 2006.

24. Maka, T., D. N. Chigrin, S. G. Romanov, and C. M. S. Torres, "Three dimensional photonic crystals in the visible regime," Progress In Electromagnetics Research, Vol. 41, 307-335, 2003.

25. Wu, C.-J., "Transmission and reflection in a periodic superconductor/dielectric film multilayer structure," Journal of Electromagnetic Waves andApplic ations, Vol. 19, 1991-1996, 2005.

26. Delano, E. and R. J. Pegis, Progress in Optics, E. Wolf (ed.), Chap. 7, Vol. 69, North-Holland, Amsterdam, 1969.

27. Banerjee, A., S. K. Awasthi, U. Malaviya, and S. P. Ojha, "Design of a nano-layered tunable optical filter," Journal of Modern Optics, Vol. 53, No. 12, 1739-1752, 2006.

28. Brooks, D. and S. Ruschin, "Integrated electrooptic multielectrode tunable filter," J. Lightwave Technol., Vol. 13, 1508-1513, 1995.

29. Wooten, E. L., R. L. Stone, E. W. Miles, and E. M. Bradely, "Rapidly tunable narrowband wavelength filter using LiNbO3," J. Lightwave Technol., Vol. 14, 2530-2536, 1996.

30. Oda, K., N. Yakato, T. Kominato, and H. Toba, "A 16-channel frequency selection switch for optical FDM distribution systems," IEEE J. Sel. Areas Commun., Vol. 8, 1132-1140, 1990.

31. Stone, J. and L. W. Stulz, "High-performance fibre Fabry-Perot filters," Electron. Lett., Vol. 27, 2239-2240, 1991.

32. Born, M. and E. Wolf, "Basic properties of the electromagnetic field," Principles of Optics, Cambridge University Press, U.K., 1980.

33. Zirngibl, M., C. H. Joyner, and B. Glance, "Digitally tunable channel-dropping filter/equalizer based on waveguide grating router and optical amplifier integration ," IEEE Photonics Technol. Lett., Vol. 6, 513-515, 1994.

34. Ishida, O., H. Takahashi, and Y. Inoue, "Digitally tunable optical filters using arrayed-waveguide grating (AWG) multiplexers and optical switches," J. Light Wave Technol., Vol. 15, 321-327, 1997.

35. Sneh, A. and K. M. Johnson, "High-speed tunable liquid crystal filter for WDM networks," J. Lightwave Technol., Vol. 14, 1067-1080, 1996.

36. Chen, P. L., K. C. Lin, W. C. Chuang, Y. C. Tzeng, K. Y. Lee, and W. Y. Lee, "Analysis of a liquid crystal Fabry-Perot etalon filter: A novel model," IEEE Photonics Technol. Lett., Vol. 9, 467-469, 1997.

37. Fujii, Y., "High-isolation polarization-independent optical circulator circulator ," J. Lightwave Technol., Vol. 9, 456-460, 1991.

38. Smith, D. A., J. E. Baran, J. J. Johnson, and K. W. Cheung, "Integrated-optic acoustically tunable filters for WDM networks," IEEE J. Sel. Areas Commun., Vol. 8, 1151-1159, 1990.

39. Zhao, L. P., X. Zhai, B. Wu, T. Su, W. Xue, and C.-H. Liang, "Novel design of dual-mode bandpass filter using rectangle structure," Progress In Electromagnetics Research B, Vol. 3, 131-141, 2008.

40. Jopson, R. M., J. Jtone, and L. W. Stulz, "Nonreciprocal transmission in a fiber Fabry-Perot resonator containing a magneto optic material," Photonics Tech. Lett., Vol. 2, 702-704, 1990.

41. Morishita, K., "Optical fiber devices using dispersive materials," IEEE J. Lightwave Technol., Vol. 7, 198-201, 1989.

42. Reid, D. C. J., C. M. Rogdale, I. Robbins, D. J. Robbins, J. Buus, and W. J. Stewart, "Phase-shifted Moire grating fibre resonators," Electron. Lett., Vol. 26, 10-12, 1990.

43. Ojha, S. P., P. K. Chaudhary, P. Khastgir, and O. N. Singh, "Operating characteristics of an optical filter with a linearly periodic refractive index pattern in the filter material ," Jpn. J. Appl. Phys., Vol. 31, 281-285, 1992.

44. Chen, J. C., A. Haus, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Optical filters from photonic band gap air bridges ," IEEE J. Lightwave Technol., Vol. 14, 2575-2580, 1996.

45. D'Orazio, A., M. de Sario, V. Petruzzelli, and F. Prudenzano, "Photonic band gap filter for wavelength division multiplexer," Opt. Exp., Vol. 11, No. 3, 230-239, 2003.

46. DelVillar, I., I. R. Matias, F. J. Arregui, and R. O. Claus, "Analysis of one-dimensional photonic bandgap structures with a liquid crystal defect toward development of fiber-optic tunable wavelength filters ," Opt. Exp., Vol. 11, No. 5, 430-436, 2003.

47. Awasthi, S. K., U. Malaviya, and S. P. Ojha, "Enhancement of omnidirectional total reflection wavelength range by using onedimensional onedimensional," J. Opt. Soc. Am. B, Vol. 23, 2566-2571, 2006.

48. Born, M. and E. Wolf, "Basic properties of the electromagnetic field," Principles of Optics, 1-70, Cambridge University Press, U.K., 1980.

49. Orfanidis, S. J., "Multilayer film applications," Electromagnetic Waves and Antennas, 193-194, (www.ece.rutgers.edu/∼orfanidi/ewa).

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