Bidirectional Beam Propagation Method

Abstract

In this chapter, the formulation of the finite-element solution for optical waveguide discontinuity problems is presented [1]. The validity and the numerical precision of the proposed method are evaluated through the analysis of three discontinuity problems, including a junction between two different waveguide sections, a laser-air interface and a laser angled facet. In addition, a numerically efficient scalar analysis of optical fibre facet problems based on the finite-element scheme is included [2] and the simulation results of dealing with various numerical uncoated and coated optical fibre facet problems will be detailed. Optical Waveguide Discontinuity ProblemOptical waveguide discontinuities play a very important role in the design of optical communication systems, and are quite often faced in situations such as butt-coupled waveguides, waveguide ends, laser facets and antireflection coatings [3][4][5]. Therefore, an accurate and efficient method for the solution of optical waveguide discontinuities is highly desirable. There are a number of methods proposed in the literature for the analysis of optical waveguide discontinuity problems. These methods can be classified, according to their solution strategy, into two groups. In the first group, the total field on either side of the discontinuity is made up as a weighted summation of all guided and radiation modes. Then, the continuity of the tangential electric and magnetic fields at the discontinuity plane is enforced using, for example, the least squares boundary residual (LSBR) [6], a combination of the finite elements and method of lines (FE-MoL) [7], the finite-element method (FEM) with analytical Computational PhotonicsSalah Obayya