Free space mode approximation of radiation modes for weakly guiding planar optical waveguides

The radiation modes of weakly guiding planar optical waveguides have been approximated and simplified as free space modes. The power spectrum of radiation modes has been numerically compared with that of free space modes. Except a very small angle (the angle between radiation direction and the waveguide walls), the approximation is accurate. Applying this approximation for radiation modes to the radiation loss calculation caused by random wall imperfections of a slab waveguide and a grating-assisted directional coupler, we have obtained very simple formulas and hence saved computation time. Our calculated results are close to those using exact radiation modes. Accuracy and limits by using this method have been discussed, Comparisons with other methods have also been made.