Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps.

For photonic crystals (PhCs) and related devices, it is useful to calculate the Dirichlet-to-Neumann (DtN) map of a unit cell, which maps the wave field to its normal derivative on the boundary. The DtN map can be used to avoid further calculations in the interiors of the unit cells and formulate mathematical problems on the cell boundaries. We develop a method to approximate the DtN map for two-dimensional PhCs involving anisotropic media, and we calculate band structures for PhCs involving liquid crystals.

Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps.

An efficient numerical method based on the Dirichlet-to-Neumann (DtN) maps of the unit cells is developed for accurate simulations of two-dimensional photonic crystal (PhC) devices in the frequency domain. The DtN map of a unit cell is an operator that maps the wave field on the boundary of the cell to its normal derivative and it can be approximated by a small matrix. Using the DtN maps of the regular and defect unit cells, we can avoid computations in the interiors of the unit cells and calculate the wave field only on the edges.

A better block partition and ligation strategy for individual haplotyping.

Motivation: Haplotype played an important role in the association studies of disease gene and drug responsivity over the past years, but the low throughput of expensive biological experiments largely limited its application. Alternatively, some efficient statistical methods were developed to deduce haplotypes from genotypes directly. Because these algorithms usually needed to estimate the frequencies of numerous possible haplotypes, the partition and ligation strategy was widely adopted to reduce the time complexity.