volume | PIER Journals

Abstract

In this paper we have theoretically studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructures. Three structures of Na₃AlF₆/Ge multilayer have been studied. The thickness of the two layers of the first and second structure is differing from each other and the third photonic structure is the combination of first and second structures. Using the Transfer Matrix Method (TMM) and the Bloch theorem, the reflectivity of one dimensional periodic structure for TE- and TM-modes at different angles of incidence is calculated. From the analysis it is found that the proposed structure has very wide range of omnidirectional total frequency bands for both polarizations.

1. Pendry, J., "Photonic band structure," J. Mod. Opt., Vol. 41, 209-229, 1994.
doi:10.1080/09500349414550281

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

3. Noda, S., A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature, Vol. 407, 608-610, 2000.
doi:10.1038/35036532

4. Jonopoulos, J. D., R. D. Meade, and J. N. E. Yablonovitch, "Photonic crystals," J. Mod. Opt., Vol. 41, 173-194, 1994.
doi:10.1080/09500349414550261

5. Winn, J. N., Photonic Crystals: Molding the Flow of Light, Princeton University Press, 1995.

6. 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

7. 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

8. Chen, K. M., A. W. Sparks, H. C. Luan, K. Wada, and L. C. Kimerling, "SiO2/TiO2 omnidirectional reflector and microcavity resonator via sol gel method," Appl. Phys. Lett., Vol. 75, 3805-3807, 1999.
doi:10.1063/1.125462

9. Temelkuran, B. and E. Ozbay, "Experimental demonstration of photonic crystal based waveguides," Appl. Phys. Lett., Vol. 74, 486-488, 1999.
doi:10.1063/1.123163

10. Scalora, M., J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulse in nonlinear photonic band gap materials," Phys. Rev. Lett., Vol. 73, 1368-1371, 1994.
doi:10.1103/PhysRevLett.73.1368

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

12. 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

13. 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

14. Srivastava, S. K. and S. P. Ojha, "Operating characteristics of an optical filter in metallic photonic band gap materials," Microwave Opt. Technol. Lett., Vol. 35, 68-71, 2002.
doi:10.1002/mop.10518

15. Winn, J. N., Y. Fink, J. N. Winn, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett., Vol. 23, 1573-1575, 1998.
doi:10.1364/OL.23.001573

16. Fink, Y., J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science, Vol. 282, 1679-1682, 1998.
doi:10.1126/science.282.5394.1679

17. Dowling, J. P., "Mirror on the wall: You're omnidirectional after all?," Science, Vol. 282, 1841-1842, 1998.
doi:10.1126/science.282.5395.1841

18. Yablonovitch, E., "Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters," Opt. Lett., Vol. 23, 1648-1649, 1998.
doi:10.1364/OL.23.001648

19. 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: Mater. Sci. Process., Vol. 68, 25-28, 1999.
doi:10.1007/s003390050849

20. Southwell, W. H., "Omnidirectional mirror design with quarter-wave dielectric stacks," Appl. Opt., Vol. 38, 5464-5467, 1999.
doi:10.1364/AO.38.005464

21. Russell, P. St. J., S. Tredwell, and P. J. Roberts, "Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures," Opt. Commun., Vol. 160, 66-71, 1999.
doi:10.1016/S0030-4018(98)00659-2

22. Chigrin, D. N., A. V. Larinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol., Vol. 17, 2018-2024, 1999.
doi:10.1109/50.802989

23. Abdulhalim, I., "Reflective phase-only modulationusing one-dimensional photonic crystals," J. Opt. A: Pure Appl. Opt., Vol. 2, 9-11, 2000.
doi:10.1088/1464-4258/2/2/101

24. Lekner, J., "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A: Pure Appl. Opt., Vol. 2, 349-352, 2000.
doi:10.1088/1464-4258/2/5/301

25. Lusk, D., I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun., Vol. 198, 273-279, 2001.
doi:10.1016/S0030-4018(01)01531-0

26. 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

27. 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

28. Srivastava, S. K. and S. P. Ojha, "Omnidirectional reflection bands in one-dimensional photonic crystal structure using fullerence films," Progress In Electromagnetics Research, Vol. 74, 181-194, 2007.
doi:10.2528/PIER07050202

29. Srivastava, S. K. and S. P. Ojha, "Omnidirectional reflection bands in one-dimensional photonic crystals with left-handed materials," Progress In Electromagnetics Research, Vol. 68, 91-111, 2007.
doi:10.2528/PIER06061602

30. Ibanescu, M., Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science, Vol. 289, 415-419, 2000.
doi:10.1126/science.289.5478.415

31. Deopura, M., C. K. Ullal, B. Temelkuran, and Y. Fink, "Dielectric omnidirectional visible reflector," Optics Letters, Vol. 26, 1197-1199, 2001.
doi:10.1364/OL.26.001197

32. Li, H., H. Chen, and X. Qiu, "Band-gap extension of disordered 1D binary photonic crystals," Physica B, Vol. 279, 164-167, 2000.
doi:10.1016/S0921-4526(99)00716-4

33. Zi, J., J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett., Vol. 73, 2084-2086, 1998.
doi:10.1063/1.122385

34. Wang, X., X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, "Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures," Appl. Phys. Lett., Vol. 80, 4291-4293, 2002.
doi:10.1063/1.1484547

35. Guida, G., "Numerical studies of disordered photonic crystals," Progress In Electromagnetics Research, Vol. 41, 107-131, 2003.
doi:10.2528/PIER02010805

36. Singh, S. K., K. B. Thapa, and S. P. Ojha, "Large frequency range of omnidirectional reflection in Si-based one-dimensional photonic crystals," International Journal of Microwave and Optical Technology, Vol. 1, 686-690, 2006.

37. Mohamed, S. H., M. M. Wakkad, A. M. Ahmed, and A. K. Diab, "Structural and optical properties of Ge-As-Te thin films," Eur. Phys. J. Appl. Phys., Vol. 34, 165-171, 2006.
doi:10.1051/epjap:2006061

38. Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, 1988.

39. Born, M. and E. Wolf, "Principles of Optics," Cambridge University Press, 1998.

Dr. Ragini Srivastava

Dr. Shyam Pati

Prof. Sant Ojha