Calculation of dispersion in arrayed waveguide grating demultiplexers by a shifting-image method

It is shown that, as a first approximation, chromatic dispersion in demultiplexers based on arrayed waveguide gratings (AWGs) is proportional to the local spatial curvature of the wavefronts of the field at the output of the input guide, whose image shifts across the output guide as frequency changes. More accurate results can be obtained by convolving the input field with the AWG impulse response and the output guide mode. This approach to the calculation of dispersion provides physical insights from the field of imaging, not available with the commonly used method which relies on a Fourier series approach. Spherical wavefronts lead to constant dispersion. The use of a parabolic taper at the end of the input guide can lead to large amounts of dispersion, varying across the filter passband; this case is treated in detail. The method can also be adapted for use with demultiplexers based on reflective echelle gratings.