Fig. 3: Principle of electrical control of SHG domain contrast and nonreciprocity via the interference of optical transitions.

a Intensity contrast between Domains B (left) and A (right) due to the interference of complex SHG sources shown in (c) and (d), respectively. b Unequal efficiency for the forward (left) and reversed (right) light paths arising from the interferences shown in (d) and (e), respectively. c–e Conceptual illustration of MD, ED, and field-dependent ΔED transitions interfering on the complex plane. Endpoints 1 to 3 provide guidance for vector summation in the interference process. The distance from the origin to Point 3 gives the SH amplitude, whose square leads to SH intensity. Point 3 coincides with Point 2 at \(E=0\). The two labels in (e) denote the same physical process viewed from front and back. Domains A and B interchange upon a \({2}_{b}\)-operation which is equivalent to their observation from opposite sides (front/back), as shown between (a) and (b).