Analysis of the focal pattern distortion of a cylindrical concave micro-grating in a slab waveguide and the mechanism of spatial resolution recovery

With modern lithographic technology, a compact spectrometer is designed to include a blazed micro-grating with cylindrical concave grating profile. In order to restrict the sagittal beam divergence and to reduce the size of the spectrometer, the micro-grating is embedded inside a pair of planar mirrors used as a slab waveguide. In the simulations for the effect of the waveguide, we discover that the focal pattern distortion introduced by the waveguide causes a blunted and side-tailed peak in the spectrum. The distortion can be managed by allowing some gap between the edge of the waveguide and the image sensor. Such a configuration has greatly improved the resolving power of the micro-grating in this compact system.