New Finite Elements for Large-Scale Simulation of Optical Waves

We present a new method to simulate optical waves in large geometries. This method is based on newly developed finite elements, so-called trigonometric finite wave elements (TFWEs). They are constructed by linear elements as well as by trigonometric functions such that the one-dimensional Helmholtz equation is exactly solved under certain conditions. In comparison with the transfer matrix method, the TFWE method offers equally good results, but it can be extended to higher dimensions and applied to time-dynamic problems. The analysis of TFWEs shows that these elements approximate functions with certain oscillation properties more accurately than standard finite elements. Thus, a finite element discretization with TFWEs leads to a smaller system of equations which eases the solving process. Numerical results obtained by applying the TFWE method to the simulation of the optical wave in distributed feedback lasers are presented.