The invariance of the direction of a given order diffracted by a grating used in conical diffraction (i.e., in off-plane mounting) when the grating is rotated about a suitable direction is established. The extension of this property to crossed gratings (2-D gratings) is demonstrated. An explanation of this amazing property is given in terms of Fermat’s principle and applies to any reflecting surface.
D. Maystre, M. Neviere, and W. R. Hunter, "Geometrical invariance property of gratings," Appl. Opt. 24, 215-216 (1985)