Photonic crystals in biology - NanoTR-VI

Poster Session, Thursday, June 17Theme F686 - N1123Modal Analysis of Circularly Bent Coupled Optical WaveguidesN. Özlem Ünverdi 1* and N. Aydın Ünverdi 21 Department of Electrical-Electronics Engineering, Yldz Technical University, stanbul 34349, Turkey2 Department of Mechanical Engineering, stanbul Technical University, stanbul 34437, TurkeyAbstract— In this study, a pair of circularly bent, bare, weakly guiding, lossless, multimode and slab optical fibers located inthe same plane was analyzed. The impact of coupling on the modal propagation constant was investigated, and the couplingbetween even TE leaky modes was found to be stronger than the coupling between all other leaky modes.Radiation is tangent to the radiation caustic in circularly bentoptical waveguides. In this study, the interactions ofevanescent fields of optical waveguides are solved byconsidering the problems of determining the behaviour ofincident radiation on a convex surface and modal analysis [1,2].In optics, a beam is an idealized concept of infinitesimallythin light cluster. Light beams are modeled as lines in physicsand optical problems are solved based on geometricalprinciples. In this study, a pair of circularly bent, bare, weaklyguiding, lossless, multimode and slab optical waveguideswhich are surrounded by a simple medium as shown in Figure1, are considered as scattering objects, and the effect of one ofthe waveguide’s radiation on the other waveguide’s behaviouris examined by Geometric Theory of Diffraction (GTD) whichexplains the diffraction of very high frequency waves byasymptotic methods [3-6].utilized by considering the propagation directions of theoptical waveguides. It is obvious that, the coupled bare andslab optical waveguides considered in this study must be in thesame plane.In the analysis, the effective regions of optical waveguides inmutual coupling, which are amongst the important parametersof optical directional couplers, are determined. It is observedthat the effected region of one of the circularly bent coupledoptical waveguides by the other optical waveguide is equal tothe longer arc length between the points of common inner andouter tangents on the radiation caustic. On the other hand, theeffected region of the other waveguide by this waveguide isequal to the shorter arc length. It is concluded that the aboveobservations are independent of the propagation directions, inother words, of the feeding directions of the opticalwaveguides.In this study, in TE and TM leaky modes of opticalwaveguides, the variation in the modal propagation constantbecause of coupling is investigated. As a result of the analysis,it is proved that the coupling between even TE leaky modes ismore efficient than those amongst the other modes. As anatural consequence of coupling mechanism, it is observedthat the coupling amongst the leaky modes and radiationmodes is stronger than those amongst the evanescent fields ofthe guided modes.The authors express their sincere gratitudes to Dr. S. ÖzenÜnverdi for helpful discussions and suggestions.*unverdi@yildiz.edu.trFigure 1. A pair of circularly bent, bare and slab optical waveguides.The path of the light beam on the optical waveguide isdetermined by Fermat principle. In this study, it is assumedthat there are not singular points on the surfaces of theanalyzed optical waveguides, all the surface points areconsidered as regular. In spite of the fact that, according to theGeneral Relativity Theory, the light beams passing nearby theoptical waveguide without hitting it are bent towards thewaveguide, the present coupling analysis neglects this effect.In circularly bent optical waveguides, the radiation is in factinside the beam tube. However, in this study, where the mutualcoupling mechanism of optical waveguides is analyzed andeffective lengths are determined, the aforementioned beamtube is considered as a single beam. In determining theeffected region of an optical waveguide by the radiation of theother waveguide and the effective region of the radiatingoptical waveguide in the coupling phenomena, the “commoninternal tangent” and “common external tangent” concepts are[1] A. W. Snyder and J. D. Love, Optical Waveguide Theory, J. W.Arrowsmith Ltd., Bristol - Great Britain, 1983.[2] N. Ö. Ünverdi, “The Effect of Evanescent Fields of GuidedModes and Leaky Modes on Mutual Coupling of Straight and BentOptical Waveguides”, Ph.D. Thesis, Yıldız Technical University,Istanbul, Turkey, 1998.[3] W. H. Louisell, Coupled Mode Parametric Electronics, JohnWiley & Sons, New York, 1960.[4] C. A. Balanis, Advanced Engineering Electromagnetics, JohnWiley & Sons Inc., New York, 1989.[5] J. M. Senior, Optical Fiber Communications, Second Edition,Prentice-Hall, Cambridge, 1992.[6] M. N. O. Sadiku, Optical and Wireless Communications, CRCPress, New York, 2002.6th Nanoscience and Nanotechnology Conference, zmir, 2010 629