Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions

Details Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions

2011-03-31

arxiv.org/abs/1104.0562v1

Physics

Optics

Scientific paper

Wannier function expansions are well suited for the description of photonic- crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the efficiency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two- dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based, stochastic methods. Besides the commonly used second moment (SM) locality measure, we introduce a new locality measure, namely the integrated modulus (IM) of the Wannier function. We show numerically that, in contrast to the SM criterion, the IM criterion leads to an optimization problem with a single extremum, thus allowing for fast and efficient construction of maximally localized Wannier functions using local optimization techniques. We also present an analytical formula for the initial choice of Bloch phases, which under certain conditions represents the global maximum of the IM criterion and, thus, further increases the optimization efficiency in the general case.

Affiliated with

Also associated with

No associations

Rating

Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-247174