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Point Defects in GaAs Photonic Crystals

Dissanayake S. E., Wijewardena Gamalath K. A. I. L.

International Letters of Chemistry, Physics and Astronomy

2015

Vol. 43

91--102

Applying plane wave expansion method to one dimensional multilayer system formed from alternating layers of GaAs and air, a defect mode was artificially introduced by removing a GaAs layer at the centre of a supercell and the band structures and mode field distributions were obtained. The defect mode normalized frequency was 0.28. The parameters for developing a Febry-Perot filter in the visible frequencies are given. The point defects in a two dimensional square lattice formed from GaAs rods of radius 0.16a in air was created by removing one GaAs rod at the centre of a supercell and also by increasing the centre GaAs rod radius to 0.5a. The removal of the rod folded the band structure 25 times creating a localized evanescent defect mode. The increment of the centre GaAs rod radius led to five defect bands inside the band gap with one degenerate state creating a monopole, two quadrupoles and two hexapoles. Evolution of the defect modes with the variation of the radius of GaAs rod is also presented.

Simulation of two dimensional photonic band gaps

Dissanayake S. E., Wijewardena Gamalath K. A. I. L.

International Letters of Chemistry, Physics and Astronomy

2014

Vol. 5

58--88

The plane wave expansion method was implemented in modelling and simulating the band structures of two dimensional photonic crystals with square, triangular and honeycomb lattices with circular, square and hexagonal dielectric rods and air holes. Complete band gaps were obtained for square lattice of square GaAs rods and honeycomb lattice of circular and hexagonal GaAs rods as well as triangular lattice of circular and hexagonal air holes in GaAs whereas square lattice of square or circular air holes in a dielectric medium ε = 18 gave complete band gaps. The variation of these band gaps with dielectric contrast and filling factor gave the largest gaps for all configurations for a filling fraction around 0.1.The gap maps presented indicated that TM gaps are more favoured by dielectric rods while TE gaps are favoured by air holes. The geometrical gap maps operating at telecommunication wavelength λ = 1.55 m showed that a complete band gap can be achieved for triangular lattice with circular and hexagonal air holes in GaAs and for honeycomb lattice of circular GaAs rods.

Distribution of distances in the Travelling Salesman Problem on a square lattice

Domański Z., Kęsy J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2004

Vol. 3, nr 1

27--30

The Manhattan distance between two points is defined as the sum of the horizontal distance along streets and the vertical distance along avenues. We derive an exact formula for the number of zigzag distances travelled by a salesman on a finite N × N, square lattice. In the limit N → ∞, we obtain the density function of distances on a unit square.