Fig. 1. TC (a) and LC (b). The second half of the compressor (third and fourth gratings) is absolutely symmetric to the first one, so it is not shown in the figure. The angle of reflection in the diffraction plane is , which explains the minus sign in the figure. The angle of reflection in the plane orthogonal to the diffraction plane is always equal to the angle of incidence .

Fig. 2. Restrictions on maximum beam size at , N = 1050/mm for the TC (a) and for the out-of-plane compressor at (b). Green curve for (Equation (12)) – no beam clipping on the grating; blue curve for (Equations (14) and (16)) – decoupling needed; black square wave (Equation (18)) – range of angles without other diffraction orders (Equation (18)), the first order is possible to the left of the square wave and the minus second order to the right; the red dashed curve combines all restrictions and shows (Equation (19)); the yellow line shows the Littrow angle for clarity.

Fig. 3. Maximum beam size for the TC (a) and for the out-of-plane compressor (b) for  N = 950/mm (blue), N = 1200/mm (green) and N = 1400/mm (red).

Fig. 4. Curves for compressor parameters for XCELS for the TC (a) and the LC (b) with grating length (blue) and (red). Squares and triangles – beam size at optimal angles and ; circles and diamonds – difference between the incidence angle in the diffraction plane and the Littrow angle (a) and the incidence angle in the plane orthogonal to the diffraction plane (b); plus signs and asterisks in (b) – grating height .