Fig. 1: Principle of loss-assisted giant phase shift of π arising from a monolayer MoS₂ sheet.

a Schematic illustration of the phase shifts (∆∅) of the reflected light between a MoS₂ sheet (\(\emptyset _{{\mathrm{MoS}}_2}\)) and a Si substrate (ϕ_sub) coated by a uniform dielectric film with different refractive indices (n) and film thicknesses (t). b Simulation results of the loss-assisted phase modulation dependence on the thickness (t) and refractive index (n) of the dielectric layer. c Zoom-in view of the blue dashed region in (b). White dashed lines are the iso-phase contours. The singular point of the iso-phase contours marked by the blue star represents the critical coupling point at which the system transfers between the over-coupling and under-coupling states, thus leading to an abrupt phase change in the reflected light. d Phasor diagrams of the complex reflection coefficient for the cases with (colourful circle) and without (olive green circle) a 0.67 nm-thick MoS₂ sheet on the ZnO-Si substrate when sweeping the thickness of the ZnO sheet from 0 to 130 nm. A π phase difference can be reached at the optimal ZnO film thickness of 65 nm.