Series solutions to the arbitrary profile 1-D waveguide and quantum-well problems.

The 1-D waveguide of arbitrary dielectric profile is solved for TE and TM modes by a method based on series solutions. It is a guess-propagate-iterate scheme. The profile is approximated by small segments of either constant or linearly changing dielectric constant. The method is accurate, generally significantly faster than other methods, copes happily with modes near cutoff, and with lossy or gain-guided modes. Series solutions are also given to solve the 1-D Schrödinger equation.