Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals

Optics Express

Volumn 20, Issue 3, 2012, Pages 3015-3033

  Trevino, Jacob ^a   Liew, Seng Fatt ^b   Noh, Heeso ^b   Cao, Hui ^b   Negro, Luca Dal ^a  

^a Boston University   (United States)

^b Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIELECTRIC DEVICES; FRACTALS; LIGHT SOURCES; STRUCTURAL PROPERTIES;

BAND EDGE; DIELECTRIC CYLINDER; DIVERGENCE ANGLE; GEOMETRICAL STRUCTURE; LIGHT-MATTER COUPLING; MULTI FRACTALS; MULTIFRACTAL SPECTRUM; NUMERICAL STUDIES; OPTICAL COUPLER; OPTICAL MODES; PAIR CORRELATION FUNCTIONS; PHOTONIC DENSITY; PHOTONIC MODE DENSITY; RANDOM STRUCTURES; SPATIAL LOCALIZATION; SPIRAL STRUCTURES; STRUCTURAL COMPLEXITY;

PHOTONIC DEVICES;

ARTICLE; COMPUTER SIMULATION; LIGHT; PHOTON; RADIATION SCATTERING; THEORETICAL MODEL;

COMPUTER SIMULATION; LIGHT; MODELS, THEORETICAL; PHOTONS; SCATTERING, RADIATION;

EID: 84856424245     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.20.003015     Document Type: Article

References (43)

1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton U. Press, Princeton, 2008).
2. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, "Novel applications of photonic band gap materials: Low-loss bends and high Q cavities," J. Appl. Phys. 75(9), 4753-4755(1994).
3. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High Transmission through Sharp Bends in Photonic Crystal Waveguides," Phys. Rev. Lett. 77(18), 3787-3790(1996). (Pubitemid 126624383)
4. T. F. Krauss, D. Labilloy, A. Scherer, and R. M. de la Rue, "Photonic Crystals for Light-Emitting Devices," Proc. SPIE 3278, 306-313(1998). (Pubitemid 35018683)
5. 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(12), 123906(2004).
6. Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic Band Gaps in Two Dimensional Photonic Quasicrystals," Phys. Rev. Lett. 80(5), 956-959(1998). (Pubitemid 128622247)
7. L. Dal Negro and S. V. Boriskina, "Deterministic Aperiodic Nanostructures for Photonics and Plasmonics Applications," Laser Photon. Rev. (2011), doi: 10.1002/lpor.201000046.
8. M. E. Pollard and G. J. Parker, "Low-contrast bandgaps of a planar parabolic spiral lattice," Opt. Lett. 34(18), 2805-2807(2009).
9. A. Agrawal, N. Kejalakshmy, J. Chen, B. M. A. Rahman, and K. T. V. Grattan, "Golden spiral photonic crystal fiber: polarization and dispersion properties," Opt. Lett. 33, 2716-2718(2008).
10. J. Trevino, H. Cao, and L. Dal Negro, "Circularly symmetric light scattering from nanoplasmonic spirals," Nano Lett. 11(5), 2008-2016(2011).
11. S. F. Liew, H. Noh, J. Trevino, L. D. Negro, and H. Cao, "Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral," Opt. Express 19(24), 23631-23642(2011).
12. J. A. Adam, A Mathematical Nature Walk (Princeton University Press, 2009).
13. E. Macia, Aperiodic Structures in Condensed Matter: Fundamentals and Applications (CRC Press Taylor & Francis, Boca Raton, 2009).
14. M. Naylor, "Golden, √ 2, and π Flowers: A Spiral Story," Math. Mag. 75, 163-172(2002).
15. G. J. Mitchison, "Phyllotaxis and the fibonacci series," Science 196(4287), 270-275(1977).
16. C. Janot, Quasicrystals: A Primer (Clarendon Press, 1992).
17. C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, "Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticles arrays," Phys. Rev. B 79(8), 085404(2009).
18. C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, "Nanoplasmonics of prime number arrays," Opt. Express 17(26), 24288-24303(2009).
19. A. Baddeley and R. Turner, "Spatstat: an R package for analyzing spatial point patterns," J. Stat. Softw. 12(6), 1-42(2005). (Pubitemid 40218000)
20. B. D. Ripley, "Modelling spatial patterns," J. R. Stat. Soc, B 39, 172-212(1977).
21. J. K. Yang, H. Noh, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, "Lasing modes in polycrystalline and amorphous photonic structures," Phys. Rev. A 84(3), 033820(2011).
22. S. Torquato and F. H. Stillinger, "Local density fluctuations, hyperuniformity, and order metrics," Phys. Rev. e Stat. Nonlin. Soft Matter Phys. 68(4), 041113(2003).
23. J. Illian, A. Penttinen, H. Stoyan, and D. Stoyan, Statistical Analysis and Modeling of Spatial Point Patterns, S. Senn, M. Scott, and V. Barnett, ed. (John Wiley, 2008).
24. http://www.comsol.com.
25. Y. Lai, Z. Zhang, C. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large twodimensional photonic quasicrystals," Phys. Rev. B 76(16), 165132(2007).
26. E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376 (4-5), 225-337(2003). (Pubitemid 36280289)
27. P. K. Thakur and P. Biswas, "Multifractal scaling of electronic transmission resonances in perfect and imperfect Fibonacci d-function potentials," Physica A 265 (1-2), 1-18(1999).
28. J. Feder, Fractals (Plenum Press, 1988).
29. J. Gouyet, Physics and Fractal Structures (Springer, 1996).
30. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Co., 1982).
31. H. E. Stanley and P. Meakin, "Multifractal phenomena in physics and chemistry," Nature 335(6189), 405-409(1988) (Review).
32. B. B. Mandelbrot, "An introduction to multifractal distribution functions," Fluctuations and Pattern Formation, H. E. Stanley, N. Ostrowsky, eds., (Kluwer, 1988).
33. U. Frisch and G. Parisi, "Fully developed turbulence and intermittency," Turbulence and Predictability in Geophysical Fluid Dynamic and Climate Dynamics, M. Ghil, R. Benzi, and G. Parisi, eds. (North Holland, 1985).
34. J. F. Muzy, E. Bacry, and A. Arneodo, "The multifractal formalism revisited with wavelets," Int. J. Bifurcat. Chaos 4(2), 245-302(1994).
35. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, "Fractal measures and their singularities: The characterization of strange sets," Phys. Rev. A 33(2), 1141-1151(1986).
36. A. Chhabra and R. V. Jensen, "Direct determination of the f (α) singularity spectrum," Phys. Rev. Lett. 62(12), 1327-1330(1989).
37. A. Karperien, FracLac for ImageJ, version 2.5. http://rsb.info.nih.gov/ ij/plugins/fraclac/FLHelp/Introduction.htm. (1999-2007).
38. W. S. Rasband and J. Image, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://imagej.nih.gov/ij/, (1997-2011).
39. X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic bandgaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86(20), 201110(2005).
40. S. Mallat, A Wavelet Tour of Signal Processing, 3rd ed., (Elsevier, 2009).
41. J. C. van den Berg, ed., Wavelets in Physics (Cambridge University Press, 2004).
42. J. Buckheit, S. Chen, D. Donoho, I. Johnstone, and J. Scargle, WaveLab850 http://www.stat.stanford.edu/~wavelab Stanford University & NASA-Ames Research Center (2005).
43. Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, "Investigation of random lasers with resonant feedback," Phys. Rev. A 64(6), 063808(2001).