Fig. 12

Scheme of 2D EPE. a Schematic of 2D EPE based on a pair of cross out-coupling gratings. b Corresponding normalized \(k\)-vector diagram of the 2D EPE scheme, where \({\bar{G}}_{in}, {\bar{G}}_{c1} \; \text{and}\; {\bar{G}}_{c2}\) represent the normalized \(k\)-vectors of the in-coupling grating, cross out-coupling grating 1 and cross out-coupling grating 2 in a, respectively. c Schematic of butterfly 2D EPE. d Corresponding normalized \(k\)-vector diagram of the butterfly 2D EPE scheme, where \({\bar{G}}_{in1}, {\bar{G}}_{in2},{\bar{G}}_{f1}, {\bar{G}}_{f2} \;\text{and}\; {\bar{G}}_{out}\) represent the normalized \(k\)-vectors of the in-coupling grating 1, in-coupling grating 2, folding grating 1, folding grating 2, and out-coupling grating in c, respectively. The coral regions in b and d correspond to all normalized \(k\)-vector within the system FoV. Black dashed arrows in b and d indicate the normalized grating vectors