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23 January 1997 Applications of standard BPM algorithms
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The beam propagation method (BPM) as a design tool for integrated optics is usually implemented with respect to waveguide configurations. When single interfaces and arbitrary refractive index distributions are used to define the geometry, the remaining limitations are due to the approximation of the Helmholtz-operator and the neglect of reflection. Using wide angle propagation schemes and taking into account he reflection at a single interface the BPM, solving an initial value problem only, can be applied to a variety of microoptic structures. This includes graded index lenses, microprisms, transmission gratings and so on. Thus, a sequence of integrated optical and microoptic components can be modeled within one scheme, inherently operating with the amplitude and the phase of the optical field. In the case of 1D refractive index profiles, finite difference algorithms give very rapid answers. This is profitably used when the BPM is applied to ion exchanged transmission gratings, which is described in more detail. With a Fourier- transform in the plane of the air-glass interface, the reflection can be taken into account using Fresnel's formulae. The results for the diffraction efficiencies into different orders calculated by the BPM are compared with those of a rigorous integral equation method. Because multiple reflections can be neglected, the results of both methods agree well. The calculated phase relations between different diffraction orders, which are of special interest in the filed of interferometry, are found to agree well with experimental results, too.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Christoph A. Waechter, Martin Palme, and Peter Schreiber "Applications of standard BPM algorithms", Proc. SPIE 2997, Integrated Optics Devices: Potential for Commercialization, (23 January 1997);

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