Vol. 126

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Influence of Fluctuations of the Geometrical Parameters on the Photonic Band Gaps in One-Dimensional Photonic Crystals

By Vladimir A. Tolmachev, Аnna V. Baldycheva, Kevin Berwick, and Tatiana S. Perova
Progress In Electromagnetics Research, Vol. 126, 285-302, 2012


The influence of random fluctuations in the layer thicknesses in high contrast, one-dimensional Photonic Crystals (PCs) on the transmission spectra and Photonic Band Gaps (PBGs) is investigated. The change in the PBGs depends on the magnitude of the fluctuations and increases with an increase in the order of the PBG. Introducing thickness non-uniformity into the PC of up to 0.004 times the value of lattice constant for different types of fluctuation distributions has a negligible effect on either the position or the shape of the 1st and nearest PBGs. The approach suggested here allows the determination of the tolerances required in the geometrical parameters of PCs during fabrication. It also allows the optimisation of PC structures using high order PBGs.


Vladimir A. Tolmachev, Аnna V. Baldycheva, Kevin Berwick, and Tatiana S. Perova, "Influence of Fluctuations of the Geometrical Parameters on the Photonic Band Gaps in One-Dimensional Photonic Crystals," Progress In Electromagnetics Research, Vol. 126, 285-302, 2012.


    1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics ," Phys. Rev. Lett., Vol. 58, No. 20, 2059-2062, 1987.

    2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, No. 23, 2486-2489, 1987.

    3. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd Edition, Chapter 1, 1, Princeton University Press, Princeton, 2008.

    4. Fink, Y., J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science, Vol. 282, No. 5394, 1679-1682, 1998.

    5. Busch, K., S. Lolkes, R. Wehrspohn, and H. Foll, Photonic Crystals. Advances in Design, Fabrication, and Characterization, Chapter 4, 64, Wiley-VCH, Weinheim, 2004.

    6. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys., Vol. 78, No. 3, 1415-1418, 1995.

    7. Maskaly, K. R., G. R. Maskaly, W. C. Carter, and J. L. Maxwell, "Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness," Opt. Lett., Vol. 29, No. 23, 2791-2793, 2004.

    8. Jaksic, Z., M. Maksimovic, O. Jaksic, D. Vasiljevic-Radovic, Z. Djuric, and A. Vujanic, "Fabrication-induced disorder in structures for nanophotonics," Microelectronic Engineering, Vol. 83, No. 4-9, 1792-1797, 2006.

    9. Glushko, O., R. Meisels, F. Kuchar, and R. Danzer, "Numerical and experimental investigations of surface roughness in 1D photonic Crystals ," J. Phys.: Condens. Matter, Vol. 20, No. 45, 454220/1-7, 2008.

    10. Barillaro, G., L. M. Strambini, V. Annovazzi-Lodi, and S. Merlo, "Optical characterization of high-order 1-D silicon photonic crystals," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 15, No. 5, 1359-1367, 2009.

    11. McGurn, A. R., K. T. Christensen, F. M. Mueller, and A. A. Maradudin, "Anderson localization in one-dimensional randomly disordered systems that are periodic on average," Phys. Rev. B, Vol. 47, No. 20, 13120-13125, 1993.

    12. Kaliteevski, M. A., J. Manzanares Martinez, D. Cassagne, and J. P. Albert, "Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap," Phys. Stat. Sol. A, Vol. 195, No. 3, 612-617, 2003.

    13. Kaliteevskii, M. A., V. V. Nikolaev, and R. A. Abram, "Eigenstate statistics and optical properties of one-dimensional disordered photonic crystals," Phys. Solid State, Vol. 47, No. 10, 1948-1957, 2005.

    14. Yeh, P., Optical Waves in Layered Media, Chapter 6, 118, Wiley, New York, 1988.

    15. Lu, X. D., P. D. Han, Y. J. Quan, Q. J. Ran, L. P. Gao, F. P. Zeng, C. H. Zhao, and J. Z. Yu , "Optical response of high-order band gap in one-dimensional photonic crystal applying in-plane integration," Opt. Commun., Vol. 277, 315-321, 2007.

    16. Tolmachev, V. A., V. A. Melnikov, A. V. Baldycheva, K. Berwick, and T. S. Perova, "Electrically tunable fabry-perot resonator based on microstructured Si containing liquid crystal," Progress In Electromagnetic Research, Vol. 122, 293-309, 2012.

    17. Baldycheva, A., V. A. Tolmachev, T. S. Perova, Y. A. Zharova, E. V. Astrova, and K. Berwick, "Silicon photonic crystal filter with ultra-wide pass-band characteristics," Opt. Lett., Vol. 36, No. 10, 1854-1856, 2011.

    18. Tolmachev, V. A., T. S. Perova, J. Ruttle, and E. Khokhlova, "Design of one-dimensional photonic crystals using combination of band diagrams and photonic gap map approaches ," J. Appl. Phys., Vol. 104, No. 3, 033536/1-6, 2008.

    19. Tolmachev, V. A., A. V. Baldycheva, S. A. Dyakov, K. Berwick, and T. S. Perova, "Optical contrast tuning in three-component 1D Photonic Crystals," IEEE Journal of Lightwave Technology, Vol. 28, No. 10, 1521-1529, 2010.

    20. Tolmachev, V. A., T. Perova, and A. Baldycheva, "Transformation of one-dimensional silicon photonic crystal into Fabry-Perot resonator," Proc. SPIE, Vol. 7943, 79430E/1-12, 2011.

    21. Azzam, R. M. A. and N. M. Bashara, Ellipsometry and Polarized Light, Chapter 4, 269, Amsterdam, North-Holland, 1977.

    22. Tolmachev, V., T. Perova, E. Krutkova, and E. Khokhlova, "Elaboration of the gap map method for the design and analysis of one-dimensional photonic crystal structures," Physica E: Low-dimensional Systems and Nanostructures, Vol. 41, No. 6, 1122-1126, 2009.

    23. 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, Vol. 111, 105-117, 2011.

    24. Wu, C.-J., Y.-C. Hsieh, and H.-T. Hsu, "Tunable photonic band gap in a doped semiconductor photonic crystal in near infrared region ," Progress In Electromagnetics Research, Vol. 114, 271-283, 2011.

    25. Banerjee, A., "Enhanced temperature sensing by using one-dimensional ternary photonic band gap structures," Progress In Electromagnetics Research Letters, Vol. 11, 129-137, 2009.

    26. Ni, J., B. Chen, S. L. Zheng, X. M. Zhang, X. F. Jin, and H. Chi, "Ultra-wideband on electrooptic phase modulator and phase-shift fiber Bragg grating," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5-6, 795-802, 2010.

    27. 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.

    28. Khalaj-Amirhosseini, M. and S. M. J. Razavi, "Wide-angle reflection wave polarizers using inhomogeneous planar layers," Progress In Electromagnetics Research M, Vol. 9, 9-20, 2009.

    29. 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.

    30. Hsu, H.-T., M.-H. Lee, T.-J. Yang, Y.-C. Wang, and C.-J. Wu, "A multichanneled filter in a photonic crystal containing coupled defects," Progress In Electromagnetics Research, Vol. 117, 379-392, 2011.