Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure
Volume 2, Issue 5, October 2013, Pages: 51-60
Received: Aug. 6, 2013;
Published: Sep. 20, 2013
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Scott Ronald. Newman, Dept. of Electronics, Carleton University, Ottawa, Ontario Canada K1S 5B6
Robert Claude. Gauthier, Dept. of Electronics, Carleton University, Ottawa, Ontario Canada K1S 5B6
A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the Fourier-Bessel technique is highly suited for extracting the localized modes as it can be tuned to solve for a particular mode order. The possibility of using the circular structure as the defect region of a hexagonal array is also examined by studying the localized states obtained in a heterostructure configuration.
Scott Ronald. Newman,
Robert Claude. Gauthier,
Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure, Optics.
Vol. 2, No. 5,
2013, pp. 51-60.
R. D. Meade, A. M. Rappe, K. D. Brommer and J. D. Joannopoulus, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B. 10, 328-332 (1993).
M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. Dela Rue and P. Millar, "Two-dimensional Penrose-tiles photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
A. Massaro, R. Cingolani, M. Vittorio and A. Passaseo, "Artificial anisotropy in circular photonic crystals andapplications," IEEE Transc. On Nanotech. 9, 157-169 (2010).
W. Zhong and X. Zhang, "Localized modes in defect-free two-dimensional circular photonic crystal," Phys. Rev. A81, 013805 (2010).
N. Horiuchi, Y. Segawa, T. Nozokido, K. Mizuno and H. Miyazaki, "Isotropic photonic gaps in circular photonic crystal," Opt. Let. 29, 1084-1086 (2003).
A. Massaro, V. Tasco, M. Todaro, T. Stomeo, R. Cingolani, M. Vittorio and A. Passaseo, "FEM design and modeling of (2) second-harmonig enhancement in circular photonic crystal," J. Lightwave Technol. 27, 4262-4268 (2009).
J. Omero-Vivas, D. N. Chirgrin, A. V. Lavrinenko and C. M. Sotomayor Torres, "Resonant add-drop filter based on a photonic quasicrystal," Opt. Exp. 13, 826-835 (2005).
P. Lee, T. Lu, M. Yu and C. Tseng, "Photonic crystal circular-shaped microcavity and its uniform cavity-waveguide coupling property due to presence of whispering gallery mode," Opt. Exp. 15, 9450-9457 (2007).
P. Lee, T. Lu, J. Fan and F. Tsai, "High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect," Appl. Phys. Let. 90, 151125 (2007).
J. Zarbakhsh, A. Mohtashami and K. Hingerl, "Geometrical freedom for constructing variable size photonic bandgap structures," Opt. and Quant. Electron., 39, 395-405, (2007).
J. Chaloupka, J. Zarbakhsh and K. Hingerl, "Local density of states and modes of circular photonic crystal cavities," Phys. Rev. B 72, 085122 (2005).
P. Lee, T. Wu., F. Tsai and T. Lu, "Investigation of whispering gallery mode dependence on cavity geometry of quasiperiodic photonic crystal microcavity lasers," Appl. Phys. Let. 89, 231111 (2006).
K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B. 75 195122 (2007).
W. Steurer and D. Sutter-Widmer, "Photonic and phononicquasicrystals," J. Phys. D 40, R229-R247 (2007).
M Rechtsman, H. Jeong, P. Chaikin, S. Torquato and P. Steinhardt, "Optimized structures for photonic quasicrystals," Phys. Rev. Lett. 101, 073902, (2008).
R. Gauthier, "Perfect periodic photonic quasi-crystals," Proc. SPIE 6901, 69011F (2008).
D. Chang, J. Scheuer and A. Yariv, "Optimization of circular photonic crystal cavities – beyond coupled mode theory," Opt. Exp. 13, 9272-9279 (2005).
J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quant. Electron. 39, 1555-1562 (2003).
J. Scheuer and A. Yariv, "Circular photonic crystal resonator," Phys. Rev. E 70 036603 (2004).
S. R. Newman and R. C. Gauthier, "Representation of photonic crystals and their localized modes through the use of Fourier-Bessel expansions," J. IEEE Photon. 3, 1133-1141 (2011).
J. D. Joannopoulos, R.C. Meade, J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, 1995).
S. R. Newman and R. C. Gauthier, "Fourier-Bessel analysis of localized states and photonic bandgaps in 12-fold photonic quasi-crystals," J. Opt. Soc. Am. A 29, 2344-2349 (2012).
R. Gauthier, K. Mnaymneh, S. Newman, K. Medri and C. Raum, "Hexagonal array photonic crystal with photonic quasi-crystal defect inclusion," Opt. Materials 31, 51-57 (2008).
S. Newman and R. Gauthier, "FDTD sources for localized state excitation in photonic crystals and photonic quasi-crystals," Proc. SPIE 7223, 7940G (2009).