Low-contrast bandgaps of a planar parabolic spiral lattice.

We show that a planar aperiodic lattice, mimicking the appearance of a sunflower, supports photonic bandgaps for weak dielectric contrast. The pattern's high orientational order and spatially uniform modal pitch yields an isotropic Fourier space. A 2D structure of cylinders (=2) in air possesses a wide 21% TM bandgap, versus 5.6% for a sixfold lattice or 14% for a 12-fold fractal tiling. The isotropic gap frequencies imply flat bands, and thus application in nonlinear optics and low threshold lasers, where a reduced group velocity in all directions may be desired.

[1]  Arti Agrawal,et al.  Golden spiral photonic crystal fiber: polarization and dispersion properties. , 2008, Optics letters.

[2]  S. Torquato,et al.  Optimized structures for photonic quasicrystals. , 2008, Physical review letters.

[3]  Walter Steurer,et al.  Photonic and phononic quasicrystals , 2007 .

[4]  Nicolae Strungaru,et al.  Circular Symmetry of Pinwheel Diffraction , 2006 .

[5]  J. Baumberg,et al.  Highly engineered mesoporous structures for optical processing , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  S. Mingaleev,et al.  Arbitrary angle waveguiding applications of two-dimensional curvilinear-lattice photonic crystals , 2004 .

[7]  J. D. Joannopoulos,et al.  Enhancement of nonlinear effects using photonic crystals , 2004, Nature materials.

[8]  Jean-Michel Lourtioz,et al.  Photonic band gaps in quasicrystal-related approximant structures , 2003 .

[9]  Simon J. Cox,et al.  Photonic band gaps in 12-fold symmetric quasicrystals , 2003 .

[10]  Zhaolin Li,et al.  Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region , 2000 .

[11]  M. C. Netti,et al.  Complete photonic bandgaps in 12-fold symmetric quasicrystals , 2000, Nature.

[12]  Zhaolin Li,et al.  Band gap and wave guiding effect in a quasiperiodic photonic crystal , 1999 .

[13]  B. Guizal,et al.  A remarkable diffractive property of photonic quasi-crystals , 1998 .

[14]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[15]  H. Vogel.  A better way to construct the sunflower head , 1979 .