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We report the simulation results for impact of nonlinear Kerr effect on band structures of a ‎two dimensional photonic crystal (2D-PhC) with no defect, a PhC based W1-waveguide ‎‎(W1W), and also Coupled-Cavity Waveguides (CCWs). All PhC structres are assumed to a ‎square lattice of constant a made of GaAs rods of radius r=0.2a, in an air background. The ‎numerical simulation was performed using the nonlinear finite difference time domain ‎‎(NFDTD) technique. To study the impact of Kerr effect on the photonic band structures, E-‎polarized lights of peak input intensities 0.5 GW-cm−2≤I≤25 GW-cm−2 have been used. The ‎numerical results have shown that as the input light intensity increases, the band edges for all ‎PhC waveguide structures considered experience red shifts. These numerical results for CCWs ‎also show that the larger the light input intensity, the smaller is the corresponding maximum ‎light group velocity.‎

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. We experimentally study the performance of the most common construction algorithms for points in the Euclidean plane. In a previous paper [10] we considered the properties of the produced graphs from five common algorithms. We consider several additional algorithms and focus on the running times. This is the first time an extensive comparison has been made between the running times of construction algorithms of t-spanners.

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. In this paper we perform the first extensive experimental study of the properties of t-spanners. The main aim is to examine the quality of the produced spanners in the plane. We implemented the most common t-spanner algorithms and tested them on a number of different point sets. The experiments are discussed and compared to the theoretical results and in several cases we suggest modifications that are implemented and evaluated. The quality measurements that we consider are the number of edges, the weight, the maximum degree, the diameter and the number of crossings.

Let (S,d) be a finite metric space, where each element p¿¿¿S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function d w , where d w (p,q) is w(p)¿+¿d(p,q)¿+¿wq if p¿¿¿q and 0 otherwise. We present a general method for turning spanners with respect to the d-metric into spanners with respect to the d w -metric. For any given e>¿0, we can apply our method to obtain (5¿+¿e)-spanners with a linear number of edges for three cases: points in Euclidean space R d , points in spaces of bounded doubling dimension, and points on the boundary of a convex body in R d where d is the geodesic distance function. We also describe an alternative method that leads to (2¿+¿e)-spanners for points in R d and for points on the boundary of a convex body in R d . The number of edges in these spanners is O(nlogn). This bound on the stretch factor is nearly optimal: in any finite metric space and for any e>¿0, it is possible to assign weights to the elements such that any non-complete graph has stretch factor larger than 2¿-¿e.