volume | PIER Journals

Abstract

Fractal structures have been widely used in many fields of science, such as biology, physics and chemistry. In this article, we analyze the basic properties of a fractal-like square lattice of air holes, with most of the holes having a lattice constant of Λ while others are repeated with a lattice constant of 2Λ. We change the radii of these holes and analyze their effects on the bandgap regions and transmission properties. The analysis conducted here is based upon band diagrams and 2D Finite difference time-domain (FDTD) solution of the full-wave Maxwell's equations. We show that this structure provides flexibility in tuning the bandgap of the photonic crystal structure and we show the appearance of mini-bandgap regions along certain directions.

1. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Physical Review Letters, Vol. 58, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486 Google Scholar

2. Knight, J. C., T. A. Birks, P. St J. Russell, and D. M. Atkins, "Pure silica single-mode fiber with hexagonal photonic crystal," Optics Letters, Vol. 21, 1547-1549, 1996.
doi:10.1364/OL.21.001547 Google Scholar

3. Schneider, V. M. and H. T. Hattori, "Dispersion characteristics of segmented optical fibers," Applied Optics, Vol. 44, 2391-2391, 2005.
doi:10.1364/AO.44.002391 Google Scholar

4. Franco, M. A. R., E. C. S. Barreto, V. A. Serrao, F. Sircilli, and H. T. Hattori, "Analysis of highly birefringent photonic crystal fibers with squeezed rectangular lattices," Microwave and Optical Technology Letters, Vol. 50, 1083-1086, 2008.
doi:10.1002/mop.23297 Google Scholar

5. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Channel drop filters in photonic crystals," Optics Express, Vol. 3, 4-11, 1998. Google Scholar

6. Matsumoto, T. and T. Baba, "Photonic crystal k-vector super-prism," Journal of Lightwave Technology, Vol. 22, 917-922, 2004.
doi:10.1109/JLT.2004.824537 Google Scholar

7. Chen, C., B. Miao, and D. Prather, "Tunable photonic crystal based on SOI," PIERS Online , Vol. 2, 574-578, 2007.
doi:10.2529/PIERS060907215746 Google Scholar

8. Fan, S., S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, "Waveguide branches in photonic crystals," Journal of the Optical Society of America B, Vol. 18, 162-165, 2001.
doi:10.1364/JOSAB.18.000162 Google Scholar

9. Tayeboun, F., R. Naoum, H. M. Tayeboun, H. T. Hattori, and F. Salah-Belkhodja, "Improved transmission waveguide bends in photonic crystal," Journal of Electromagnetic Waves and Applications, Vol. 19, 615-628, 2005.
doi:10.1163/1569393053305099 Google Scholar

10. Dimitriev, V., "2D magnetic photonic crystals with square latticegroup theoretical standpoint," Progress In Electromagnetics, Vol. 68, 71-100, 2006.
doi:10.2528/PIER05061701 Google Scholar

11. Hattori, H. T., V. M. Schneider, R. M. Cazo, and C. L. Barbosa, "Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures," Applied Optics, Vol. 44, 3069-3076, 2005.
doi:10.1364/AO.44.003069 Google Scholar

12. Hattori, H. T., I. Mc Kerracher, H. H. Tan, and C. Jagadish, "Inplane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides ," IEEE Journal of Quantum Electronics, Vol. 43, 279-286, 2007.
doi:10.1109/JQE.2006.890402 Google Scholar

13. Painter, O., R. K. Lee, A. Scherrer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science, Vol. 284, 1819-1821, 1999.
doi:10.1126/science.284.5421.1819 Google Scholar

14. Ohnishi, D., T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser," Optics Express, Vol. 12, 1562-1568, 2004.
doi:10.1364/OPEX.12.001562 Google Scholar

15. Barnsley, M., Fractals Everywhere, Academic, 1988.

16. Hattori, H. T., V. M. Schneider, C. L. Barbosa, and R. M. Cazo, "“Reflectivity spectra evolution in grating structures with fractionally organized gaps," Microwave and Optical Technology Letters, Vol. 29, 42-45, 2001.
doi:10.1002/mop.1077 Google Scholar

17. Barbosa, C. L., R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave and Optical Technology Letters, Vol. 31, 223-229, 2001.
doi:10.1002/mop.1403 Google Scholar

18. Hattori, H. T., V. M. Schneider, and C. L. Barbosa, "Analysis of distributed-feedback lasers with fractionally organized gaps," Applied Optics, Vol. 46, 1283-1289, 2007.
doi:10.1364/AO.46.001283 Google Scholar

19. Hattori, H. T., H. H. Tan, and C. Jagadish, "Analysis of optically pumped compact laterally coupled distributed feedback lasers with three symmetric defect regions," Journal of Applied Physics, Vol. 102, 083109 1-8, 2007. Google Scholar

20. Biswas, B. N., R. Ghatak, R. K. Mishra, and D. R. Poddar, "Characterization of a self-complementary Sierpinski Gasket microstrip antennas," PIERS Online , Vol. 2, 698-701, 2006.
doi:10.2529/PIERS060901153618 Google Scholar

21. BandSolve 2.0 RSOFT design group, 1999.

22. Fullwave 7.0 RSOFT design group, 2007.

Dr. Haroldo Hattori