Waveguide discontinuities are frequently encountered in modern photonic structures. It is important to characterize the reflection and transmission that occurs at the discontinuous during the design and analysis process of these structures. Significant effort has been focused upon the development of accurate modelling tools, and a variety of modelling techniques have been applied to solve this kind of problem. Throughout this work, a Transmission matrix based Bidirectional Beam Propagation Method (T-Bi-BPM) is proposed and applied on the uncoated facet and the single coating layer reflection problems, including both normal and angled incident situations. The T-Bi-BPM method is developed on the basis of an overview of Finite Difference Beam Propagation Method (FD-BPM) schemes frequently used in photonic modelling including paraxial FD-BPM, Imaginary Distance (ID) BPM, Wide Angle (WA) BPM and existing Bidirectional (Bi) BPM methods. The T-Bi-BPM establishes the connection between the total fields on either side of the coating layer and the incident field at the input of a single layer coated structure by a matrix system on the basis of a transmission matrix equation used in a transmission line approach. The matrix system can be algebraically preconditioned and then solved by sparse matrix multiplications. The attraction of the T-Bi-BPM method is the potential for more rapid evaluation without iterative approach. The accuracy of the T-Bi-BPM is verified by simulations and the factors that affect the accuracy are investigated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:594646 |
| Date | January 2013 |
| Creators | Liu, Deyun |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/13491/ |
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