| PIER | |
| Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |
Home > Vol. 112 > pp. 257-272
PHASE SHIFT DEFECT MODES IN ONE-DIMENSIONAL ASYMMETRICAL PHOTONIC STRUCTURES CONSISTING OF TWO RUGATE SEGMENTS WITH DIFFERENT PERIODICITIESBy Y. Liu and Z. LuAbstract: A theoretical study of optical properties of phase shift defects in one-dimensional asymmetrical photonic structures consisting of two rugate segments with different periodicities at both normal and oblique incidence is presented. Using the propagation matrix method we numerically calculated transmittance spectra, defect wavelengths, energy density distributions, and group velocities for TE and TM waves, respectively. Our study shows that by adjusting the periodicity of one rugate segment, the defect wavelengths can be shifted toward either a shorter wavelength or a longer wavelength. The differences of the energy density distributions of TE and TM waves at different angles of incidence are explained with the help of group velocity. Effects of the change of the period of one rugate segment on the peak energy densities of defect modes and minimum group velocities at different angles of incidence are also investigated.
Citation:
References:
2. Hawkeye, M. M. and M. J. Brett, "Narrow bandpass optical optical filters fabricated with one-dimensionally periodic inhomogeneous thin films ," J. Appl. Phys., Vol. 100, 044322, 2006. . Hawkeye, M. M. and M. J. Brett, "Glancing angle deposition: Fabrication properites, and applications of micro- and nanostructured thin films," J. Vac. Sci. Technol. A, Vol. 25, 1317-1335, 2007. 4. Tabunshchyk, K. V., M. M. Hawkeye, A. Kovalenko, and M. J. Brett, "Three-dimensional simulation of periodically structured thin films with uniaxial symmetry," J. Phys. D: Appl. Phys., Vol. 40, 4936-4942, 2007. 5. Brett, M. J. and M. M. Hawkeye, "Materials science. New materials at a glance," Science, Vol. 319, 1192-1193, 2008. 6. Hawkeye, M. J., R. Joseph, J. C. Sit, and M. J. Brett, "Coupled defects in one-dimensional photonic crystal films fabricated with glancing angle deposition," Opt. Express, Vol. 18, 13220-13226, 2010. 7. Liu, Y. and Z. Lu, "Properties of phase shift defects in one-dimensional rugate photonic structures," Progress In Electromagnetics Research, Vol. 111, 213-228, 2011. 8. Estevez, J. O., J. Arriaga, A. Mendez Blas, and V. Agarwal, "Omnidirectional photonic bandgaps in porous silicon based mirrors with a Gaussian profile refractive index," Appl. Phys. Lett., Vol. 93, 191915, 2008. 9. Estevez, J. O., J. Arriaga, A. Mendez Blas, and V. Agarwal, "Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index," Appl. Phys. Lett., Vol. 94, 061914, 2009. 10. De Stefano, L., L. Moretti, A. Lamberti, O. Longo, M. Rocchia, A. M. Rossi, P. Arcari, and I. Rendina, "Optical sensors for vapors, liquids, and biological molecules based on porous silicon technology," IEEE Trans. Nanotechnol., Vol. 543, 49-54, 2004. 11. Imenes, A. G. and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: A review," Sol. Energy Mater. Sol. Cells, Vol. 84, 19-69, 2004. 12. Imenes, A. G., D. Buie, and D. R. Mckenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells, Vol. 90, 1579-1606, 2006. 13. Imenes, A. G. and D. R. McKenzie, "Flat-topped broadband rugate filters," Applied Optics, 7841-7850, 2006. 14. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modling the Flow of Light, 2nd Ed., Princeton University Press, 2008.
15. Yariv, A. and P. Yeh, Photonics, Oxford University Press, New York, 2007.
16. Deopura, M., C. K. Ullal, T. Temelkuran, and Y. Fink, Dielectric omnidirectional visible reflector, Vol. 26, 1197-1199, Opt. Lett., 2001.
17. 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. 18. Winn, J. N., Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett., Vol. 23, 1573-1575, 1998. 19. Srivastava, R., S. Pati, and S. P. Ojha, "Enhancement of omnidirectional reflection in photonic crystals heterostructures," Progress In Electromagnetics Research B, Vol. 1, 197-208, 2008. 20. Srivastava, R., K. B. Thapa, S. Pati, and S. P. Ojha, "Omnidirection reflection in one-dimensional photonic crystal," Progress In Electromagnetics Research B, Vol. 7, 133-143, 2008. . Awasthi, S. K., U. Malaviya, S. P. Ojha, N. K. Mishra, and B. Singh, "Design of a tunable polarizer using a one-dimensional nano sized photonic bandgap structure," Progress In Electromagnetics Research B, Vol. 5, 133-152, 2008. 22. Srivastava, R., K. B. Thapa, S. Pati, and S. P. Ojha, "Design of photonic band gap filter," Progress In Electromagnetics Research, Vol. 81, 225-235, 2008. 23. Awasthi, S. K., U. Malaviya, S. P. Ojha, N. K. Mishra, and B. Singh, "Design of a tunable polarizer using a one-dimensional nano sized photonic bandgap structure," Progress In Electromagnetics Research B, Vol. 5, 133-152, 2008. 24. Banerjee, A., "Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures," Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009. 25. Wu, C.-J., B.-H. Chu, and M.-H. Weng, "Analysis of optical reflection in a chirped distributed Bragg reflector," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 129-138, 2009. 26. Wu, C.-J., B.-H. Chu, M.-T. Weng, and H.-L. Lee, "Enhancement of bandwidth in a chirped quarter-wave dielectric mirror," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 4, 437-447, 2009. 27. Wu, C.-J., J.-J. Liao, and T.-W. Chang, "Tunable multilayer Fabry-Perot resonator using electro-optical defect layer," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 4, 531-542, 2010.
28. Wu, C.-J. and Z.-H. Wang, "Properties of defect modes in one-dimensional photonic crystals," Progress In Electromagnetics Research, Vol. 103, 169-184, 2010. 29. Wu, C.-J., Y.-N. Rau, and W.-H. Han, "Enhancement of photonic band gap in a disordered quarter-wave dielectric photonic crystal," Progress In Electromagnetics Research, Vol. 100, 27-36, 2010. 30. Hsu, H. T., T. W. Chang, T. J. Yang, B. H. Chu, and C. J. Wu, "Analysis of wave properties in photonic crystal narrowband filters with left-handed defect," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 16, 2285-2298, 2010. 31. Dai, G. L. and M. Y. Xia, "An investigation of quarter-wavelength square-spiral resonator and its applications to miniaturized bandpass filters," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 10, 1303-1313, 2010. 33. Archuleta-Garcia, R., D. Moctezuma-Enriquez, and J. Manzanares-Martinez, "Enlargement of photonic band gap in porous silicon dielectric mirrors," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 2--3, 351-361, 2010. 33. Manzanares-Martinez, J., R. Archuleta-Garcia, P. Castro-Garay, D. Moctezuma-Enriquez, and E. Urrutia-Banuelos, "One-dimensional photonic heterostructure with broadband omnidirectional reflection," Progress In Electromagnetics Research, 105-117, 2011. 34. Southwell, W., "Using apodization functions to reduce sidelobes in rugate filters," Applied Optics, Vol. 28, 5091-5094, 1989. 35. Abu-Safia, H., A. Al-Sharif, and I. Abu-Aljarayesh, "Rugate filter sidelobe suppression using half-apodization," Applied Optics, Vol. 32, 4831-4835, 1993. 36. Kennedy, S. and M. M. Brett, "Porous broadband antireflection coating by glancing angle deposition," Applied Optics, Vol. 42, 4573-4579, 2003. 37. Vernhes, R., O. Zabeida, J. Klemberg-Spaieha, and L. Martinu, "Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride," Applies Optics, Vol. 43, 97-103, 2004. 38. Berreman, D. W., "Optics in stratified and anisotropic media: 4 × 4 matrix formulations," J. Opt. Soc. Am., Vol. 62, 502-510, 1972. 39. Abdulhalim, I., "Analytical propagtion matrix method for linear optics of arbitrary biaxial layered media," J. Opt. A: Pure Appl. Opt., Vol. 1, 646-653, 1999. 40. Lu, Z., "Accurate and efficient calculation of light propagation in one-dimensional inhomogeneous anisotropic media through extrapolation," J. Opt. Soc. Am. A, Vol. 24, 236-242, 2007. 41. Lu, Z., "Accurate calculation of reflectance spectra for thick onedimensional inhomogeneous optical structures and media: Stable propagation matrix method," Opt. Lett., Vol. 33, 1948-1950, 2008. 42. Lu, Z., "Efficient 4 × 4 propagation matrix method using a fourth-order symplectic integrator for the optics of one-dimensional continuous inhomogeneous materials," Progress In Electromagnetics Research Letters, Vol. 14, 1-9, 2010. 43. Bendickson, J. M. and J. P. Dowling, "Analytical expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E., Vol. 53, 4107-4121, 1996. 44. Cheng, J.-Y. and L.-W. Cheng, "Polarization-dependent filters based on chiral photonic structures with defects," J. Opt. A: Pure and Applied Optics, Vol. 7, 558-566, 2005. 45. Southwell, W. H., "Spectral response calculations of rugate filters using coupled-wave theory," J. Opt. Soc. Am. A,, Vol. 5, 1558-1564, 1988. 46. Biot, M. A., "General theorems on the equivalence of group velocity and energy transport," Phys. Rev., Vol. 105, No. 4, 1129-1137, 1957. 47. Gerasik, V. and M. Stastna, "Complex group velocity and energy transport in absorbing media," Phys. Rev. E., Vol. 81, 056602, 2010. |