Novel beam propagation algorithms for tapered optical structures

Novel beam propagation algorithms for tapers have been developed that elimi nate errors caused by staircase approximations, Nonorthogonal coordinate sy stems are introduced that model the effects of beam spreading and obliquene ss while retaining the standard coordinate z to advance the solution forwar d uniformly. Both two- and three-dimensional (2-D) and (3-D) examples are c onsidered to illustrate both the accuracy and utility of the scheme. The ne w method maintains its accuracy with fewer sample points allowing significa nt reduction in calculation time.