Photonic crystals in biology - NanoTR-VI

PP TOBBPoster Session, Thursday, June 17Theme F686 - N11231Special Slow Light Properties of Photonic Crystal Waveguides11UKadir UstunUP P* and Hamza KurtPUniversity of Economics and Technology, Department of Electrical and Electronics Engineering, Ankara 06560, TurkeyAbstract- The drastic changes on the radii values of the side rows of a linear-defect triangular lattice photonic crystal waveguide results inunique dispersion curves with large constant group index and high bandwidth values. The delay of picosecond optical pulses were realized.Photonic crystals exhibit bandgap property that enables usto use them as cavities and waveguides. The light isconfined in the desired spatial regions by inducing defects inthe periodic structure. In addition to that property, photoniccrystal waveguides show dispersive characteristics so thatthe group velocity is very low in some regions near k-points(0, 0) and (0.5, 0). But at close proximity of these points, thestrong group velocity dispersion (GVD) distorts the pulseshape and information cannot be carried properly. So havinghigh group index ( n g ) values with small GVD and largebandwidth is an important research interest [1-5] because ofthe diverse applications of slow light in opticalcommunications, optical buffers and nonlinear optics [1]. Inthis work, we present a new type of dispersion diagram andcorresponding group index values that can be used for largebandwidth slow light.The photonic crystal used in this paper is a twodimensional photonic crystal with a triangular lattice. Theair holes are located in the dielectric media according to thelattice basis vectors. The waveguide is constructed by fillingthe center holes with dielectric material along the ( )direction as shown. We made investigations to find flatbands which yield constant group index n g , where the groupindex is defined as n g = c / vg, and small GVD as [3-5].We modified the side row circles of the waveguide andchanged the radii of these holes step by step symmetricallyalong the waveguide. This modification method isdemonstrated in Fig. 1(a). The dispersion diagrams andngvs. frequency plots are obtained for different values ofradii of the modified holes by evaluating the dispersiondiagram using PWM [6]. The result is shown in Fig. 1(b) forvarious cases that results in flat bands which produceconstant n region between k 0. 35 and k 0.45. Thegngvalues are ‘U’ shaped and the bottom of this ‘U’ shape isvery appropriate for obtaining high n g values with smallGVD and high bandwidth as it will be shown in a figure thatwill be presented in the conference . By looking at Fig. 1(c),we can say that increasing the radius of the circles decreasesthe constant ngvalues, but there is an increase in bandwidthof the constant group index region as will be presented inadditional figures in the conference.As the group index and bandwidth values are inverselyproportional, we decided to determine a figure of merit suchas delay-bandwidth product (DBP). The DBP versus radiusrelation is depicted in Fig. 1(d). As it is shown, the DBPalso increases as the radius increases. But this increase is notso rapid in spite of the drastic changes in ngand bandwidthvalues.Figure 1. (a) Triangular lattice structure with the inner row of holesmodified. (b) the different dispersion diagrams for different radiusvalues (radius is swept from 0.3625a to 0.450a). (c) Group indexvalues obtained in the linear regions of the dispersion diagrams withrespect to corresponding radii. (d) DBP values with respect tocorresponding radii alteration.frequency domain. The frequency domain calculations showthat ngdecreases and bandwidth increases as the radii of theside rows increases. On the other hand, the DBP increases asthe radii of the side rows are increased. The presented resultsobtained by simple geometrical modifications are promisingin terms of yielding large bandwidth and constant groupindex for slow light applications.The authors gratefully acknowledge the financial support of theScientific and Technological Research Council of Turkey(TUBITAK), Project no: 108T717.*Corresponding author: HTk.ustun@etu.edu.trT[1] T. F. Krauss, Nat. Photonics 2, 448 (2008).[2] M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C.Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).[3] L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I.Borel, Opt. Exp. 14, 9444 (2006).[4] S. Kubo, D. Mori, and T. Baba, Opt. Lett. 32, 2981 (2007).[5] J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F.Krauss, Opt. Express 16, 6227 (2008).[6] S. Johnson and J. Joannopoulos, TOpt. ExpressT 8, 173 (2001).The aim achieved in this study is to find ways of obtainingconstant group index values with large bandwidths in the6th Nanoscience and Nanotechnology Conference, zmir, 2010 635