Finite element methods for junctions of microwave and optical waveguides

It is noted that the finite-element method is capable of calculating the electromagnetic fields in many microwave and optical components and providing scattering matrices. Two approaches have been used: exciting the device with incident waves and calculating reflected waves; and exciting the device with applied voltages and calculating currents. It is pointed out that 3-D analysis is computationally expensive, but, fortunately, there are important classes of device amenable to analysis in 2-D. Optical components, which are usually unbounded, can be handled with the help of absorbing boundary conditions. Two examples are given: a rectangular-waveguide phase-shifter and a dielectric-waveguide transformer. It is concluded that developments such as automatic mesh generators, absorbing boundary conditions, and efficient sparse matrix techniques have made the finite-element method competitive with integral-equation approaches, and distinctly advantageous when there are several materials or complicated shapes to model.<>