An efficient technique for the design of an arrayed-waveguide grating with flat spectral response
The spectral response of the arrayed-waveguide grating (AWG) plays an important role in optical networks. Ideally, the grating should have a rectangular transfer function to reduce the need for accurate wavelength control and achieve low crosstalk. A new technique for designing an AWG with flat spectral response is presented. The problem of the optimization of the transfer function is reduced to that of adjusting the arrayed waveguide lengths and their relative positions on the edge of the free propagating regions in order to minimize a certain error function. As a result, the waveguide lengths and their positions are determined using a rigorous mathematical procedure. The resultant transfer function is flat with low sidelobes.
Abstract Characterizing the spatial variation of allele frequencies in a population has a wide range of applications in population genetics. This article introduces a new nonparametric method, which provides a two-dimensional representation of a structural parameter called the genetical bandwidth, which describes genetic structure around arbitrary spatial locations in a study area. This parameter corresponds to the shortest distance to areas of significant allele variation, and its computation is based on the Womble's systemic function. A simulation study and application to data sets taken from the literature give evidence that the method is particularly demonstrative when the fine-scale structure is stronger than the large-scale structure, and that it is generally able to locate genetic boundaries or clines precisely.