Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme

As a simple analysis method to solve eigenmodes of optical waveguides, we present an imaginary distance beam propagation method (BPM) based on finite element scheme. The matrices used in the beam propagation analysis are essentially complex, so lossy optical waveguides can be easily treated. Moreover, employing the transparent boundary condition or perfectly matched layer boundary condition, the validity of a which has been already confirmed in the real distance BPM, we can easily treat not only guided modes but leaky ones. To show the validity and usefulness of this approach, eigenmodes of twoand three-dimensional leaky waveguides, and optical fibers are calculated.