Quasiconformal maps in transformation optics and their electrostatic analogs

Quasiconformal maps have been utilized for generating transformation optical devices with a range of applications including invisibility cloaks, waveguide benders, couplers, surface-conformal lenses and antennas. Here, we discuss their generation by numerically solving the Poisson's equation where the analytic solution of a typical electrostatic problem in the virtual space acts as a seed in numerically generating a quasiconformal map with a transformed shape of boundary. Two examples about capacitor under external voltage and a point charge in a cavity are given.