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Proceedings Paper

Design of a waveguide grating using Lagrange's integral invariant
Author(s): Joseph J. M. Braat; Michel O. E. Laurijs
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Paper Abstract

In this paper the design of a focusing grating coupler (FGC) is treated in the geometrical optics approximation for a rather general configuration. The guided mode may have an arbitrary phase profile and the free space wave which is generated by the FGC travels through an optical system before the final focal point is generated. This optical system does not need to have symmetry of revolution. The analysis uses the data of the ray fields coming from the free space and from the guided region at the location of a general point of the grating coupler. In this way an effective matching of the two ray fields is obtained without the need for time- consuming iterative ray-tracing. By using Lagrange's integral invariant, the optical pathlength function is obtained over the grating surface. The pathlength function is used to obtain the grating vector distribution when ray-tracing the designed FGC. The pathlength function also serves to construct the diffracted wavefront.

Paper Details

Date Published: 15 April 1993
PDF: 8 pages
Proc. SPIE 1780, Lens and Optical Systems Design, (15 April 1993); doi: 10.1117/12.142823
Show Author Affiliations
Joseph J. M. Braat, Delft Univ. of Technology (Netherlands)
Michel O. E. Laurijs, Delft Univ. of Technology (Netherlands)


Published in SPIE Proceedings Vol. 1780:
Lens and Optical Systems Design

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