The invention relates to determining transmission characteristics of multimode extruded optical waveguides by way of beam tracking (ray tracing).
To calculate the beam propagation in dielectric channel waveguides, in particular light guides, wave-optical analysis methods such as the method of finite elements (FEM) or the ‘Beam Propagation Method’ (BPM) were previously available. However these can then only be used efficiently if only one or a few modes are to be considered and the cross-section of the waveguides, in respect of the optical wave length, is not too large.
By contrast, beam trackings based on geometric optics are efficiently possible for multimodal step index or gradient index waveguides, in which the cross-section is substantially larger than the wavelength of the radiation used.
A plurality of beams is (in the simulation) injected here into the waveguide in a predetermined direction and polarization. This either takes place at the end of the waveguide or is interrupted at a wall of the optical channel, i.e. the boundary area of the index increment. These methods are specified for instance in the publication by Th. Bierhoff, A. Himmler, E. Griese and G. Mrozynski, “3D-rendering technique to model arbitrary shaped board integrated optical step index waveguides using cubic spline interpolation”, Proceedings of 5th International IEEE Workshop on Signal Propagation on Interconnects (SPI'01), Venice (Italy). Detailed representations can also be found in the dissertation by Th. Bierhoff, “Strahlenoptische Analyse der Wellenausbreitung und Modenkopplung in optisch hoch multimodalen Wellenleitern” [Beam-optical analysis of the wave propagation and mode coupling in optically high multimodal waveguides], Shaker publishing company 2006, ISBN 3-8322-5801-9.
The efficient calculation of such beam profiles is needed for the production of development tools, with which the development engineer is able to monitor a project by way of simulation and compare a test piece with the simulation using the facility specified in DE 199 48 378 C1.
The publication DE 103 34 107 A1 specifies an improved method compared with the afore-cited publication, said method enabling beam tracking in continuous multimodular channel waveguides by overlaying analytically describable partial pieces. This method is advantageous in that the very complex three-dimensional structure, as occur at the coupling point of optical guides, can be calculated efficiently. Nevertheless, practice has shown that the calculation for optical waveguides embedded in conductor boards for instance, which are mostly very long proportionately to thickness, is also not possible in an adequately efficient fashion.
The article by D. Israel, R. Baets, M. J. Goodwin, et.al., “Multimode polymeric Y junctions for star couplers in back-plane optical interconnect”, Applied Optics, Vol. 36 No. 21, Jul. 20, 1997 uses beam tracking to determine the performance data of Y junctions. A 2D calculation is used here for approximation.
The object of the invention is to improve efficiency and accuracy when determining the transmission in optical waveguides of the said type, in particular for complex structures such as junctions and reflectors.
The invention achieves this object for waveguides with a rectangular cross-section. With this type of problem, the waveguide can be regarded as a linear extrusion of a base area. The knowledge is utilized such that in this case the projection of each test beam on the base area equates to the profile which, as a two-dimensional problem, listens the reflection rules. The outlay can thus be substantially simplified by the beam profile being calculated for the two-dimensional case in a first step and then being extended to the three-dimensional case. This occurs by a traverse being determined from the enriched projected profile in the first step, said traverse, when folded out, once again representing a two-dimensional channel in which the reflection can be more easily calculated than in the three-dimensional case. In simple cases, only the length of the sample beam and the exit direction is needed (and/or loss due to a total reflection not carried out); in this case the three-dimensional beam profile does not need to be calculated explicitly. Since not only the path length but also the number of reflections are already present at the same time, a weakening can also be considered by way of an incomplete total reflection.
The invention is described on the basis of an exemplary embodiment, in which;
a and 5b show calculated exemplary beam profiles, in the base plane and in the 3D room.
A channel waveguide is outlined spatially by way of example in
Once the base area is determined, the projection in the plane of the base area is determined for a sample beam, which strikes the entrance area, so that this strikes the linear edge E of the base area. After the corresponding refraction on the media transition of the entrance area, a beam appears, the profile of which is calculated according to the rules of the geometric optics, as shown in image 3 for three examples (marking the polylines for clarification). Depending on the angle and position of incidence, an incident beam either reaches the first exit A1 or the second exit A2 or gets lost (beam 3), because the angle of impact on the wall is not sufficient for total reflection. The latter determines the maximum entrance angle, according to which a transmitter can be determined, so that as few losses as possible occur.
Because the projection of the three-dimensional profile of a sample beam is no longer determined in the base area, this polyline is extruded in the same fashion as the base area. This is shown in
Since the polygon sequence is however pulled apart in a manner similar to a fanfold paper and can be transformed into a single rectangle, it is possible to reachieve the beam profile as a simple two-dimensional object. To this end, only the length of the polyline has to be determined in the base plane. To further determine the beam profile, a single rectangle is then used at the height of the waveguide and the calculated length of the sample beam. The start angle is calculated from the projection of the incident beam on the first rectangle of the traverse, said start angle determining the further profile.
a shows two other sample beams, the profile of which was calculated in the base plane. The corresponding spatial profile is shown in
Number | Date | Country | Kind |
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10 2007 031 681.1 | Jul 2007 | DE | national |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/EP08/58052 | 6/25/2008 | WO | 00 | 2/1/2010 |