Radiation losses of tapered dielectric slab waveguides

In this paper we calculate radiation losses of a single mode dielectric slab waveguide for TE and TM modes. The theory is based on the determination of the radiation losses of one abrupt step. We obtain the losses of arbitrarily deformed waveguides by regarding the arbitrary deformations as a succession of infinitely many infinitesimal steps. This method yields the same results as a very different method presented earlier. It allows us to calculate the losses of TM modes that were hard to obtain by the earlier method. The radiation losses of single mode slab waveguides with abrupt steps of a 2:1 ratio are surprisingly low and can be kept below 1 percent by dimensioning the guide properly. The loss advantage of linear tapers becomes noticeable only when the tapers are very long. An optimized taper changes more rapidly in its wider portion and becomes more gradual in its narrow part.