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Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides

Summary: Numerical studies of 2D photonic crystals:
Waveguides, coupling between waveguides
and «lters
R . S T O F F E R , H. J. W. M. H O E K S T R A , R. M. D E R I D D E R
E . V A N G R O E S E N A N D F. P. H. V A N B E C K U M
MESA+ Research Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
(E-mail: r.stoer@el.utwente.nl)
Abstract. In photonic crystals, light propagation is forbidden in a certain wavelength range, the bandgap.
In a two-dimensional crystal composed of parallel high-refractive index rods in a low-index background a
line defect can be formed by removing a row of these rods, which can act as a waveguide for frequencies in
the bandgap of the crystal. In order to get more insight into the main features of such waveguides we have
studied a number of properties, using simulation tools based on the «nite dierence time domain method
and a «nite element Helmholtz solver. We show conceptually simple methods for determining the bandgap
of the crystal as well as the dispersion of a waveguide for wavelengths in this bandgap. For practical
applications, it is also important to know how much light can be coupled into the waveguide. Therefore,
the coupling of light from a dielectric slab waveguide into the photonic crystal waveguide has been
examined, showing that a coupling eciency of up to 83% can be obtained between a silicon oxide slab
and a waveguide in a crystal of silicon rods. Finally, calculations on an ultra-compact «lter based on
re»ectively terminated side-branches of waveguides (similar to tuned stubs in microwave engineering) are
shown and discussed.


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering