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Annular photonic crystals

Hamza Kurt and D. S. Citrin

Open Access Open Access

Abstract

A new type of two-dimensional photonic-crystal (PC) structure called annular PC composed of a dielectric-rod and a circular-air-hole array in a square or triangular lattice such that a dielectric rod is centered within each air hole is studied. The dielectric rods within the air holes greatly modify the dispersion diagram of the photonic crystal despite the fact that the percentage of volume occupied by the dielectric rods may be small (<12%). Increasing the radius of the inner-dielectric rod, starting from zero to a critical value, reduces the band gap and closes it completely as expected, because of the addition of more dielectric material inside the unit cell. Continuing to increase the radius of the rod above the critical value surprisingly creates another photonic band gap. Comparison of the dispersion diagrams of the new structure and the original lattice (circular air hole square/triangular array in dielectric background) reveals that the photonic band gap is considerably enhanced in size for both square and triangular lattice with the new structure. This approach preserves the symmetry of the structure and provides a complete photonic band gap away from the close-packed condition and at low normalized frequencies.

©2005 Optical Society of America

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Supplementary Material (1)

Media 1: AVI (878 KB)     

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Figures (6)
Fig. 1.
Fig. 1. Schematic diagram of the PC lattice. (a) Square lattice with cylindrical dielectric rods of radius r 2 and permittivity ε r 2 are inserted in the middle of the holes with radius r 1 in dielectric background ε r 1 and r 1 > r 2. The unit cell is a combination of the dielectric rod in the air and hole in dielectric background. (b) Triangular lattice with cylindrical dielectric rods of radius r 2 and permittivity ε r 2 are inserted in the middle of the holes with radius r 1 in dielectric background ε r 1 and r 1 > r 2. The unit cell is a combination of the dielectric rod in the air and hole in dielectric background.

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Fig. 2.
Fig. 2. Complete PBG variation, Δω/ω0 with respect to the changes of inner dielectric rod radius. (a) Square lattice with r 1 from 0.49a to 0.47a and r 2 from zero to 0.20a. (b) Triangular lattice with r 1 from 0.49a to 0.43a and r 2 from zero to 0.20a. After the closure of the first PBG, the second one appears as r 2 increases.

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Fig. 3.
Fig. 3. Dispersion diagram of triangular-array PBG lattice: (a) r 1/r 2 =0.47/0.02 and εr =13 (b) r 1/r 2 =0.47/0.14 and εr =13 . Solid lines represent TM modes and dashed lines represent TE modes. The shaded frequency region corresponds to the PBG.

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Fig. 4.
Fig. 4. Dispersion diagram of square-array photonic-crystal lattice: (a) r 1/r 2 =0.49/0.02 and εr = 13 (b) r 1/r 2 =0.49/0.11 and εr = 13. Solid lines represent TM modes and dashed lines represent TE modes. The shaded frequency region corresponds to the PBG.

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Fig. 5.
Fig. 5. Electric field of TM modes for square array of annular photonic crystal (Movie, 877 KB). The inner rod radius is 0.02a (left) and 0.12a (right).

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Fig. 6.
Fig. 6. (a) PBG to midgap ratio, Δω/ω 0, for square lattice with low dielectric value (εr = 4) for the TE modes with respect to the rod radius r 2 and hole radius r 1. (b) PBG to midgap ratio, Δω/ω 0, of triangular lattice with low dielectric value (εr = 4) for the TM modes with respect to the rod radius r 2 and hole radius r 1.

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