volume | PIER Journals

Abstract

In this paper a transfer matrix treatment for the reflectivity and transmissivity spectra of electromagnetic waves propagating in a nano sized multilayer periodic structure has been presented. Effect of varying the angle of incidence on the photonic bandgaps is shown. The design of a tunable polarizer by reflection which is more efficient in comparison to that obtained by reflection from a single dielectric slab, has been suggested.

1. Sigalas, M. M., C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic bandgaps," Phys. Rev. B, Vol. 59, 12767-12770, 1999.
doi:10.1103/PhysRevB.59.12767 Google Scholar

2. Johnson, S. G. and J. D. Joannopoulos, "Introduction to photonic crystal: Bloch's theorem, band diagrams and gaps (but no defects)," Photonic Crystal Tutorial, 1-16, 2003, http://ab-initio.mit.edu/photons/tutorial/. Google Scholar

3. Yeh, P., A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory," J. Opt. Soc. Am., Vol. 67, 423-438, 1977. Google Scholar

4. Sakoda, K., Optical Properties of Photonic Crystals, Springer, 2001.

5. Yablonovitch, E., "Inhibited spontaneous emission in solid state physics and electromagnetics," Phys. Rev. Lett., Vol. 58, 2059, 1987.
doi:10.1103/PhysRevLett.58.2059 Google Scholar

6. Mekis, A., M. Meier, A. Dodabalapur, R. E. Slusher, and J. D. Joannopulos, "Lasing mechanism in two-dimensional photonic crystal lasers," Appl. Phy. A: Materials Science and Processing, Vol. 69, 111-114, 1999.
doi:10.1007/s003390050981 Google Scholar

7. Painter, O., R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dappus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science, Vol. 284, 1819-1821, 1999.
doi:10.1126/science.284.5421.1819 Google Scholar

8. Noda, S., M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarisation mode control of two-dimensional photonic crystal laser by unit cell structure design," Science, Vol. 293, 1123-1125, 2001.
doi:10.1126/science.1061738 Google Scholar

9. Knight, J. C., J. Broeng, T. A. Bieks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science, Vol. 282, 1476-1479, 1998.
doi:10.1126/science.282.5393.1476 Google Scholar

10. Ziolkowski, R. W. and M. Tanaka, "FDTD analysis of PBG waveguides, power splitters and switches," Opt. Quant. Electron., Vol. 31, 843-855, 1999.
doi:10.1023/A:1006964830895 Google Scholar

11. Ozbay, E., M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled cavity modes in two-dimensional photonic bandgap structures," IEEE Journal of Quantum Electronics, Vol. 38, 837-843, 2002.
doi:10.1109/JQE.2002.1017595 Google Scholar

12. Zheng, Q. R., Y. Q. Fu, and N. C. Yuan, "Characteristics of planar PBG structures witha cover layer," Journal of Electromagnetic Waves and Applications, Vol. 20, 1439-1453, 2006.
doi:10.1163/156939306779274264 Google Scholar

13. Rojas, J. A. M., J. Alpuente, J. Pineiro, 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 Google Scholar

14. Ozbay, E., B. Temelkuran, and M. Bayinder, "Microwave application of photonic crystals," Progress In Electromagnetics Research, Vol. 41, 185-209, 2003.
doi:10.2528/PIER02010808 Google Scholar

15. Srivastava, R., S. Pati, and S. P. Ojha, "Enhancement of omnidirectional reflection in photonic crystal heterostructures," Progress In Electromagnetics Research B, Vol. 1, 197-208, 2008.
doi:10.2528/PIERB07102903 Google Scholar

16. 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 Google Scholar

17. 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 Google Scholar

18. Singh, S. K., J. P. Pandey, K. B. Thapa, and S. P. Ojha, "Structural parameters in the formation of omnidirectional high reflectors," Progress In Electromagnetics Research, Vol. 70, 53-78, 2007.
doi:10.2528/PIER07010501 Google Scholar

19. Pandey, P. C., A. Mishra, and S. P. Ojha, "Modal dispersion characteristics of a single mode dielectric optical waveguide with a guiding region cross-section bounded by two involuted spirals," Progress In Electromagnetics Research, Vol. 73, 1-13, 2007.
doi:10.2528/PIER07022702 Google Scholar

20. Osipov, A. V., I. T. Iakubov, A. N. Lagarkov, S. A. Maklakov, D. A. Petrov, K. N. Rozanov, and I. A. Ryzhikov, "Multi-layered Fe films for microwave applications," PIERS Online, Vol. 3, 1303-1306, 2007.
doi:10.2529/PIERS070320070112 Google Scholar

21. Shi, S. and D. W. Prather, "Lasing dynamics of a novel silicon photonic crystal cavity," PIERS Online, Vol. 3, 746-750, 2007.
doi:10.2529/PIERS060907132027 Google Scholar

22. Yatsyk, V., "Effects of the resonant scattering of intensive fields by weakly nonlinear dielectric layer," PIERS Online, Vol. 3, 524-527, 2006.
doi:10.2529/PIERS050909054039 Google Scholar

23. Brongersma, M. L., R. Zia, and J. Schuler, "Plasmonics — The missing link between nanoelectronics and microphotonics," PIERS Online, Vol. 3, 360-362, 2007.
doi:10.2529/PIERS060907171131 Google Scholar

24. Hou, S. and C. Hu, "Influence of electro-optic effecton waveguide efficiency of optical fiber withcladding made of uniaxial crystal materials," PIERS Online, Vol. 2, 614-618, 2006.
doi:10.2529/PIERS060829092541 Google Scholar

25. Li, L., C.-H. Liang, and C. H. Chan, "Waveguide end slot phased array antenna integrated with electromagnetic bandgap structures," Journal Electromagnetic Waves and Applications, Vol. 21, 161-174, 2007.
doi:10.1163/156939307779378826 Google Scholar

26. Kokkorakis, G. C., "Calculating the electric field in nanostructures," Journal Electromagnetic Waves and Applications, Vol. 21, 1433-1443, 2007. Google Scholar

27. Li, L. and J. A. Dobrowolski, "Visible broadband, wide-angle, thin-film multilayer polarizing beam splitter," Appl. Opt., Vol. 35, 2221-2225, 1996. Google Scholar

28. Hecht, E., Optics, 4th Ed., 349, Addison Wesley, 2002.

29. Yeh, P., "Optics of periodic layered media," Optical Waves in Layered Media, 118-142, 1998. Google Scholar

30. Born, M. and E. Wolf, "Basic properties of the electromagnetic field," Principles of Optics, 1-70, 1980. Google Scholar

31. Dowling, J. P. and C. M. Bowden, "Anomalous index of refraction in photonic band gap materials," J. Mod. Optics, Vol. 41, 345-351, 1994.
doi:10.1080/09500349414550371 Google Scholar

32. John, S. and J. Wang, "Quantum optics of localized light in a photonic band gap," Phys. Rev. B, Vol. 43, 12772-12789, 1991.
doi:10.1103/PhysRevB.43.12772 Google Scholar

33. Liu, N.-H., "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B, Vol. 55, 3543-3547, 1997.
doi:10.1103/PhysRevB.55.3543 Google Scholar

34. Liu, N.-H., "Defect modes of stratified dielectric media," Phys. Rev. B, Vol. 55, 4097-4100, 1997.
doi:10.1103/PhysRevB.55.4097 Google Scholar

35. Born, M. and E. Wolf, "Basic properties of the electromagnetic field," Principles of Optics, Vol. 60, 1980. Google Scholar

36. Born, M. and E. Wolf, "Basic properties of the electromagnetic field," Principles of Optics, Vol. 44, 1980. Google Scholar

Dr. Suneet Awasthi

Dr. Usha Malaviya

Prof. Sant Ojha

Mr. Nishakant K. Mishra

Dr. Bachau Singh