Design of a waveguide grating using Lagrange's integral invariant

Joseph Braat; Michel Laurijs

doi:10.1117/12.142823

15 April 1993 Design of a waveguide grating using Lagrange's integral invariant

Joseph Braat, Michel Laurijs

Proceedings Volume 1780, Lens and Optical Systems Design; 17800T (1993) https://doi.org/10.1117/12.142823
Event: Optical Systems Design '92, 1992, Berlin, Germany

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.

Citation Download Citation

Joseph Braat and Michel Laurijs "Design of a waveguide grating using Lagrange's integral invariant", Proc. SPIE 1780, Lens and Optical Systems Design, 17800T (15 April 1993); https://doi.org/10.1117/12.142823

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