Frequency-domain PML layer based on the complex mapping of space boundary condition treatment

Mapping of real space into a complex one is done in order absorb the radiative held, The boundary condition which ensures reflectionless incidence at the vacuum/PML interface is established, The application of this boundary condition results in a modified finite-difference approximation of the second derivative of the field. This approach, which is valid only for frequency-domain methods is applied using the Method of Lines. Comparison of theory and numerical simulation establishes the validity of the approach.