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Institute of Commu nications and Rad i o-Freque cy Eng neering, Vienna University f Technology, Gusshausstrasse 25/389, A-1040 Wien, Austria, Email: walter.leeb@tuwien.ac.at ABSTRACT We apply a numerical method for calculating the field distribution in the region immediately behind the input facet of a dielectric step-index single-mode slab waveguide. The input waves considered are focused plane waves and Gaussian beams of various diameters, with and without misalignment. The figures obtained show the formation of radiation modes and the development of the fundamental guided mode and thus give hints on how to design pieces of single-mode fibers that are to be used as modal filters, e.g., in astronomical interferometers with excessive nulling requirements. 1. INTRODUCTION Optical single-mode waveguides constitute a key device in instruments for astronomical interferometry aiming at the investigation of extra-solar planets. To give an example: In ESA's DARWIN mission, the optical fields collected by telescopes will be propagated through a piece of single-mode fiber. Only then they will exhibit the highly identical amplitude distribution and phase distribution required for destructive interference of the (unwanted) radiation originating from the star whose planet is under investigation. Propagating the light through an ideal single-mode waveguide achieves just this. One attempt to analytically estimate the minimum length (as required to achieve proper background suppression by modal filtering) of an otherwise ideal fiber waveguide is found in [1]. This approach, however, could not take into account many of the real-world aspects occurring in fibers. Here we demonstrate the usefulness of a numerical method in calculating – and visualizing – the distribu-tion of the optical field in the input coupling region of a single-mode waveguide. Examining a 2-dimensional single-mode waveguide in a first step already gives an excellent insight into the power flow immediately after the input facet, shows how a steady state intensity distribution in the vicinity of the core is eventually reached, and also yields the coupling efficiency into the waveguides’ fundamental mode. Eventually this method will allow taking into account a non-perfect core-cladding geometry, a finite cladding thickness, an absorbing coating, an input taper, etc. After explaining the system model in Sect. 2 we shortly describe the numerical method applied (Sect. 3) before presenting results for cases where the input radiation is either a focused plane wave (Sect. 4) or a focused Gaussian beam (Sect. 5). We visualize the power flow, show how the fundamental mode develops, and obtain the coupling efficiency as a by-product. Section 6 summa-rizes the findings. 2. SYSTEM MODEL Fig. 1 shows the system model used. The step-index slab waveguide consists of a core of thickness 2d (index of refraction n |
