We theoretically investigated optical properties of phase shift defects in onedimensional rugate photonic structures at oblique incidence. Transmission spectra and energy density distributions of such continuous gradient-index structures with phase shift defects were numerically calculated for TE and TM waves using the propagation matrix method. The study shows that when the angle of incidence increases, (1) the wavelength of the defect mode shifts to a shorter wavelength, (2) the full width at half maximum (FWHM) of the defect mode decreases for TE wave but it increases for TM wave, (3) the stop band of the rugate structure moves toward a shorter wavelength region, (4) the bandwidth is enlarged for TE wave, but it is shortened for TM wave, (5) the peak energy density increases and then drops for TE wave, while it always decreases for TM wave. The effect of number of periods of rugate structures on the energy density distribution was also examined.
2. 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.
3. Banerjee, A., "Tunable polarizer using one-dimensional nano sized photonic bandgap structure," Progress In Electromagnetics Research B, Vol. 5, 133-152, 2008.
4. Golmohammadi, S., Y. Rouhani, K. Abbasian, and A. Rostami, "Photonic bandgaps in quasiperiordic multilayer using Fourier transform of the refractive index profile," Progress In Electromagnetics Research B, Vol. 18, 311-325, 2009.
5. 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.
6. Srivastava, R., K. B. Thapa, S. Pati, and S. P. Ojha, "Omni-directional reflection in one-dimensional photonic crystals," Progress In Electromagnetics Research B, Vol. 7, 133-143, 2008.
7. Banerjee, A., "Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures," Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009.
8. 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.
9. Wu, C.-J., Y.-H. Chung, B.-J. Syu, and T.-J. Yang, "Band gap extension in a one-dimensional ternary metal-dielectric photonic crystal," Progress In Electromagnetics Research, Vol. 102, 81-93, 2010.
10. Rahimi, H., A. Namdar, S. Roshan Entezar, and H. Tajalli, "Photonic transmission spectra in one-dimensional fibonacci multilayer structures containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 102, 15-30, 2010.
11. Essadqui, A., J. Ben-Ali, D. Bria, B. Djafari-Rouhani, and A. Nougaoui, "Photonic band structure of 1D periodic composite Photonic band structure of 1D periodic composite system with left handed and right handed materials by green function approach," Progress In Electromagnetics Research B, Vol. 23, 229-249, 2010.
12. Deopura, M., C. K. Ullal, B. Temelkuran, and Y. Fink, "Dielectric omnidirectional visible reflector," Opt. Lett., Vol. 26, 1197-1199, 2001.
13. 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.
14. 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.
15. Van Popta, A. C., M. M. Hawkeye, J. C. Sit, and M. J. Brett, "Gradient-index narrow-bandpass filter fabricated with glancing-angle deposition," Opt. Lett., Vol. 29, 2545-2547, 2004.
16. 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.
17. Hawkeye, M. M., 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.
18. 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.
19. Hawkeye, M. M. and M. J. Brett, "Glancing angle deposition: Fabrication properties, and applications of micro- and nanostructured thin films," J. Vac. Sci. Technol. A, Vol. 25, 1317-1335, 2007.
20. 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.
21. Brett, M. J. and M. M. Hawkeye, "Materials science: New materials at a glance," Science, Vol. 319, 1192-1193, 2008.
22. 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.
23. Southwell, W. H., "Spectral response calculations of rugate filters using coupled-wave theory," J. Opt. Soc. Am. A, Vol. 5, 1558-1564, 1988.
24. Yeh, P., Optical Waves in Layered Media, John Wiley and Sons Ltd., New York, 1988.
25. Bovard, B. G., "Rugate filter theory: An overview," Appl. Opt., Vol. 32, 5427-5442, 1993.
26. 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.
27. Chin, S. A., "Symplectic integrators from composite operator factorizations," Phys. Lett. A, Vol. 226, 344-348, 1997.
28. Chin, S. A. and C. R. Chen, "Gradient symplectic algorithms for solving the Schrodinger equations with time-dependent potentials," J. Chem. Phys., Vol. 117, 1409-1415, 2002.
29. Chin, S. A. and D. W. Kidwell, "Higher-order force gradient symplectic algorithms," Phys. Rev. E, Vol. 62, 8746-8752, 2000.
30. Berreman, D. W., "Optics in stratified and anisotropic media: 4 × 4 matrix formualtion," J. Opt. Soc. Am., Vol. 62, 502-510, 1972.
31. 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.
32. Lu, Z., "Accurate calculation of reflectance spectra for thick one-dimensional inhomogeneous optical structures and media: Stable propagation matrix method," Opt. Lett., Vol. 33, 1948-1950, 2008.
33. Suzuki, M., Quantum Monte Carlo Methods in Condensed Matter Physics, World Scientific Pub. Co. Inc., 1994.
34. Jin, J., The Finite Element Method in Electromagnetics, John Wiley and Sons Ltd., New York, 1993.