International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Djurdjevic D.  

The application of the Du-Fort Frankel beam propagation method in photonics

     The beam propagation method (BPM) is well known as the most widely used propagation technique for modelling optoelectronic and photonic devices. The finite difference beam propagation method (FD-BPM) is the most commonly employed numerical technique for simulating field propagation in optical components. FD-BPM still offers computational advantages over time domain numerical techniques such as Finite Difference Time Domain (FDTD) method.
      FD-BPM is usually implemented by using implicit schemes such as Crank-Nicolson scheme (CN) due to its stability. However, in the case of modelling three-dimensional (3D) photonic structures the CN scheme uses iterative matrix solvers and thus requires huge computational resources and long run-times. The way out might be the implementation of explicit Du-Fort Frankel (DFF) finite difference schemes. DFF is three-level explicit algorithm, but providing better stability condition than simple explicit schemes and very attractive computational efficiency for modelling realistic waveguide based 3D photonic devices.
      Some examples of FD-BPM field simulation using the DFF scheme are given in this paper. The computational efficiency and stability of DFF FD-BPM formulation and inherent downsides of the method (such as spurious or “ghost” solutions) are compared against standard implicit CN FD-BPM schemes.

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