Abstract

We present a numerical study of optical properties of an octagonal quasi-periodic lattice of dielectric rods. We report on a complete photonic bandgap in TM polarization up to extremely low dielectric constants of rods. The first photonic bandgap remains open down to dielectric constant as small as ε=1.6 (n=1.26). The properties of an optical microcavity and waveguides are examined for the system of rods with dielectric constant ε=5.0 (n=2.24) in order to design an add-drop filter. Proposed add-drop filter is numerically characterized and further optimized for efficient operation. The two-dimensional finite difference time domain method was exploited for numerical calculations. We provide a numerical evidence of effective add-drop filter based on low index material, thus opening further opportunities for application of low refractive index materials in photonic bandgap optics.

© 2005 Optical Society of America

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Appl. Phys Lett. (2)

M. Bayindir, E. Ozbay, �??Dropping of electromagnetic waves through localized modes in three-dimensional photonic bandgap structures,�?? Appl. Phys Lett. 81, 4514-4516 (2002).
[CrossRef]

T. Asano, B.S. Song, Y. Tanaka,and S. Noda, "Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab," Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

M. Qiu, B. Jaskorzynska, �??Design of a channel drop filter in a two-dimensional triangular photonic crystal,�?? Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, �??Duplexer using microwave photonic band gap structure,�?? Appl. Phys. Lett. 76, 2301�??2303 (2000).
[CrossRef]

K. Nozaki, T. Baba, �??Quasiperiodic photonic crystal microcavity lasers,�?? Appl. Phys. Lett. 84, 4875-4877 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little, et al., �??Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,�?? IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

J. Lightwave Technol. (2)

D. J. W. Klunder, et al., �??Experimental and numerical study of SiON microresonators with air and polymer cladding,�?? J. Lightwave Technol. 21, 1099-1110 (2003).
[CrossRef]

S. C. Hagness, et al., �??FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,�?? J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

J. Mod. Opt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes," J. Mod. Opt. 47, 1771- 1778 (2000).

J. Mod. Optics (1)

Wang K.; David S.; Chelnokov A.; Lourtioz J.-M., �??Photonic band gaps in quasicrystal-related approximant structures,�?? J. Mod. Optics 50, 2095-2105 (2003)

J. Phys. Cond. Matt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar and R. M. De La Rue, �??Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,�?? J. Phys. Cond. Matt. 13, 10459-10470 (2001).
[CrossRef]

Nature (1)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Opt. Quantum Electr. (1)

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, �??Design and optimization of 2D photonic crystal waveguides based on silicon,�?? Opt. Quantum Electr. 34, 145-159 (2002).
[CrossRef]

Phys. Rev. B (3)

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, �??Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,�?? Phys. Rev. B 68, 165106 (2003).
[CrossRef]

S. S. M. Cheng, L. M. Li, C. T. Chan and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4098 (1999).
[CrossRef]

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, "Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals", Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Phys. Rev. B. (1)

X. Zhang, Z. Q. Zhang and C. T. Chang, "Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, "Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice," Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Y. S. Chan, C. T. Chang and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, �??Tight-binding description of the coupled defect modes in three dimensional photonic crystals,�?? Phys. Rev. Lett. 84, 2140-2143 (2000).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 1995).

J.-B. Suck, M. Schreiber and P. Häussler, eds., Quasicrystals (Springer, Berlin, 2002).

Supplementary Material (4)

» Media 1: GIF (924 KB)     
» Media 2: GIF (786 KB)     
» Media 3: GIF (776 KB)     
» Media 4: GIF (682 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

(Left panel) Sketch of the analyzed 8-fold quasi-periodic structure. Building tiles are depicted in red. (Right panel) The gap map of the first PBG in TM polarization for the PQC versus dielectric constant. The minimum (black line) and maximum (red line) normalized frequencies of the gap as a function of the dielectric constant are shown. The inset shows the gap width to midgap ratio as a function of the dielectric constant (points) together with an interpolation fit (green line).

Fig. 2.
Fig. 2.

(Left panel) Sketch of the microcavity made by removing rods around the central one. (Right panel) Energy density inside the PQC (black dashed line) and inside the cavity (solid blue line). The spectral range of a complete PBG is shown. Three cavity modes are designated by Ω 1, Ω 2 and Ω 3.

Fig. 3.
Fig. 3.

Field patterns of the cavity modes of PQC corresponding to the spectral range of the first PBG. Mode Ω 1 is a quadropole, mode Ω 2 is a hexapole and mode Ω 3 is a dipole. Two degenerated hexapole modes are shown in central panels. Hexapole-0 (Hexapole-90) mode is even with respect to the vertical (horizontal) plane. Colors represent electric field amplitude. Arrows show magnetic field lines. Circles show positions of rods in the structure.

Fig. 4.
Fig. 4.

(Top panel) Sketch of different PQC waveguide configurations. W1, W2 and W3 waveguides are shown. (Bottom panel) Transmission efficiency spectra for W1 (green), W2 (red) and W3 (black) waveguides. Spectral positions of the cavity modes are shown as a vertical blue lines.

Fig. 5.
Fig. 5.

Energy density stored in the cavity by hexapole modes. (Left panel) Two hexapole modes are completely degenerate in square patch of PQC. (Center panel) Degeneracy is lifted, when the symmetry of the system is broken by waveguides. Hexapole-0 and Hexapole-90 modes have different resonant frequencies. (Right panel) The modes overlap is partially restored in the system based on a rectangular patch of PQC. Sketches of considered structures are shown in the top panel above the corresponding energy density spectra.

Fig. 6.
Fig. 6.

Field patterns are shown for the Hexapole-0 (left panel) and Hexapole-90 (center panel) modes and for their superposition (right panel) decaying into the waveguides channels. Colors represent electric field amplitude. Circles show positions of rods in the structure. In the top panel, the sign of the electric field amplitude in waveguide channels in the direct vicinity of the cavity is shown for the appropriate modes.

Fig. 7.
Fig. 7.

(Left panel) Transmission efficiency of the add-drop filter based on a square patch of octagonal PQC. Transmission in the main channel (black line), reflection back at the entrance of the filter (blue line), backward (red line) and forward (green line) transmission in the upper waveguide is shown. Energy density stored in the Hexapole-0 and Hexapole-90 modes are shown for comparison by dashed black and dashed red lines, respectively. Energy density spectra are normalized to their maximum value. Electric field patterns are shown for the resonance (center panel) and out of the resonant (right panel) frequencies. Light is coupled to the add-drop filter at the Input channel and propagates in backward (forward) direction in the Output-2 (Output-1) channel for the resonance (out of the resonant) frequency. Colors represent electric field amplitude. Circles show positions of rods in the structure. (Movies 946 KB, 805 KB)

Fig. 8.
Fig. 8.

(Left panel) Transmission efficiency of the optimized add-drop filter based on a rectangular patch of octagonal PQC. Transmission in the main channel (black line), reflection back at the entrance of the filter (blue line), backward (red line) and forward (green line) transmission in the upper waveguide is shown. Energy density stored in the Hexapole-0 and Hexapole-90 modes are shown for comparison by dashed black and dashed red, respectively. Energy density spectra are normalized to their maximum value. Electric field patterns are shown for the resonance (center panel) and out of the resonant (right panel) frequencies. Light is coupled to the add-drop filter at the Input channel and propagates in backward (forward) direction in the Output-2 (Output-1) channel for the resonant (out of the resonance) frequency. Colors represent electric field amplitude. Circles show positions of rods in the structure. (Movies 794 KB, 699 KB)

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