Third Day Poster Session, 17 June 2010 - NanoTR-VI

Poster Session, Thursday, June 17
Theme F686 - N1123
Modal Analysis of Circularly Bent Coupled Optical Waveguides
N. Özlem Ünverdi 1* and N. Aydın Ünverdi 2
1 Department of Electrical-Electronics Engineering, Yldz Technical University, stanbul 34349, Turkey
2 Department of Mechanical Engineering, stanbul Technical University, stanbul 34437, Turkey
Abstract— In this study, a pair of circularly bent, bare, weakly guiding, lossless, multimode and slab optical fibers located in
the same plane was analyzed. The impact of coupling on the modal propagation constant was investigated, and the coupling
between 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 bent
optical waveguides. In this study, the interactions of
evanescent fields of optical waveguides are solved by
considering the problems of determining the behaviour of
incident radiation on a convex surface and modal analysis [1,
2].
In optics, a beam is an idealized concept of infinitesimally
thin light cluster. Light beams are modeled as lines in physics
and optical problems are solved based on geometrical
principles. In this study, a pair of circularly bent, bare, weakly
guiding, lossless, multimode and slab optical waveguides
which are surrounded by a simple medium as shown in Figure
1, are considered as scattering objects, and the effect of one of
the waveguide’s radiation on the other waveguide’s behaviour
is examined by Geometric Theory of Diffraction (GTD) which
explains the diffraction of very high frequency waves by
asymptotic methods [3-6].
utilized by considering the propagation directions of the
optical waveguides. It is obvious that, the coupled bare and
slab optical waveguides considered in this study must be in the
same plane.
In the analysis, the effective regions of optical waveguides in
mutual coupling, which are amongst the important parameters
of optical directional couplers, are determined. It is observed
that the effected region of one of the circularly bent coupled
optical waveguides by the other optical waveguide is equal to
the longer arc length between the points of common inner and
outer tangents on the radiation caustic. On the other hand, the
effected region of the other waveguide by this waveguide is
equal to the shorter arc length. It is concluded that the above
observations are independent of the propagation directions, in
other words, of the feeding directions of the optical
waveguides.
In this study, in TE and TM leaky modes of optical
waveguides, the variation in the modal propagation constant
because of coupling is investigated. As a result of the analysis,
it is proved that the coupling between even TE leaky modes is
more efficient than those amongst the other modes. As a
natural consequence of coupling mechanism, it is observed
that the coupling amongst the leaky modes and radiation
modes is stronger than those amongst the evanescent fields of
the guided modes.
The authors express their sincere gratitudes to Dr. S. Özen
Ünverdi for helpful discussions and suggestions.
*unverdi@yildiz.edu.tr
Figure 1. A pair of circularly bent, bare and slab optical waveguides.
The path of the light beam on the optical waveguide is
determined by Fermat principle. In this study, it is assumed
that there are not singular points on the surfaces of the
analyzed optical waveguides, all the surface points are
considered as regular. In spite of the fact that, according to the
General Relativity Theory, the light beams passing nearby the
optical waveguide without hitting it are bent towards the
waveguide, the present coupling analysis neglects this effect.
In circularly bent optical waveguides, the radiation is in fact
inside the beam tube. However, in this study, where the mutual
coupling mechanism of optical waveguides is analyzed and
effective lengths are determined, the aforementioned beam
tube is considered as a single beam. In determining the
effected region of an optical waveguide by the radiation of the
other waveguide and the effective region of the radiating
optical waveguide in the coupling phenomena, the “common
internal 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 Guided
Modes and Leaky Modes on Mutual Coupling of Straight and Bent
Optical Waveguides”, Ph.D. Thesis, Yıldız Technical University,
Istanbul, Turkey, 1998.
[3] W. H. Louisell, Coupled Mode Parametric Electronics, John
Wiley & Sons, New York, 1960.
[4] C. A. Balanis, Advanced Engineering Electromagnetics, John
Wiley & 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, CRC
Press, New York, 2002.
6th Nanoscience and Nanotechnology Conference, zmir, 2010 629