volume | PIER Journals

Abstract

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.

1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059

2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486

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.
doi:10.1364/JOSAB.24.003040

4. Joannopoulos, J. D., P. R. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature, Vol. 386, 143-149, 1997.
doi:10.1038/386143a0

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.
doi:10.1163/156939306779274264

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.
doi:10.1126/science.282.5394.1679

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.
doi:10.2528/PIER06042501

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.
doi:10.1007/s003390050849

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.
doi:10.1364/JOSAB.20.001996

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.
doi:10.1109/50.803000

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.
doi:10.1126/science.284.5421.1819

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.
doi:10.1007/s003390050981

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.
doi:10.1126/science.1061738

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.
doi:10.1103/PhysRevLett.77.3787

17. Sondergaard, T. and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B, Vol. 61, 15688-15696, 2000.
doi:10.1103/PhysRevB.61.15688

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.
doi:10.1126/science.282.5393.1476

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.
doi:10.1364/JOSAB.10.000404

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.
doi:10.1063/1.123553

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.
doi:10.1364/OL.21.002017

22. Zandi, O., Z. Atlasbaf, and K. Forooraghi, "Flat multilayer dielectric reflector antennas," Progress In Electromagnetics Research, Vol. 72, 1-19, 2007.
doi:10.2528/PIER07022604

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.
doi:10.2528/PIER05091701

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.
doi:10.1163/156939305775570468

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.
doi:10.1080/09500340600590547

28. Brooks, D. and S. Ruschin, "Integrated electrooptic multielectrode tunable filter," J. Lightwave Technol., Vol. 13, 1508-1513, 1995.
doi:10.1109/50.400719

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.
doi:10.1109/50.548151

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.
doi:10.1109/49.57818

31. Stone, J. and L. W. Stulz, "High-performance fibre Fabry-Perot filters," Electron. Lett., Vol. 27, 2239-2240, 1991.
doi:10.1049/el:19911385

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.
doi:10.1109/68.281812

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.
doi:10.1109/50.554384

35. Sneh, A. and K. M. Johnson, "High-speed tunable liquid crystal filter for WDM networks," J. Lightwave Technol., Vol. 14, 1067-1080, 1996.
doi:10.1109/50.511608

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.
doi:10.1109/68.559390

37. Fujii, Y., "High-isolation polarization-independent optical circulator circulator ," J. Lightwave Technol., Vol. 9, 456-460, 1991.
doi:10.1109/50.76659

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.
doi:10.1109/49.57821

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.
doi:10.2528/PIERB07121003

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.
doi:10.1109/68.60765

41. Morishita, K., "Optical fiber devices using dispersive materials," IEEE J. Lightwave Technol., Vol. 7, 198-201, 1989.
doi:10.1109/50.17754

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.
doi:10.1049/el:19900007

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.
doi:10.1143/JJAP.31.281

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.
doi:10.1109/50.548157

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.
doi:10.1364/JOSAB.23.002566

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).

Dr. Suneet Awasthi

Prof. Sant Ojha