This example studies the interface between two different materials in a section of a wave guide. The change in material causes the waves to travel at different speeds. This changing diffraction pattern of the planar time harmonic waves can be investigated by using the Helmholtz equation for the amplitude of the waves A
$$ -( \frac{\partial^2 A}{\partial x^2} + \frac{\partial^2 A}{\partial y^2} ) - k^2 A = 0 $$
This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Electromagnetics > Two Material Wave Guide Interface from the File menu. Or alternatively, follow the linked step-by-step instructions.