Novel beam propagation algorithms for tapered optical structures

Novel beam propagation algorithms for tapers have been developed that eliminate errors caused by staircase approximations. Nonorthogonal coordinate systems are introduced that model the effects of beam spreading and obliqueness while retaining the standard coordinate z to advance the solution forward uniformly. Both two- and three-dimensional (2-D) and (3-D) examples are considered to illustrate both the accuracy and utility of the scheme. The new method maintains its accuracy with fewer sample points allowing significant reduction in calculation time.