Fig. 3.

Analyses of experimental results. a Theoretical and experimental thickness dispersions of the fundamental ordinary (TE₀) and extraordinary (TM₀) waveguide modes in the air–MoS₂–SiO₂ three-layer waveguide, the superstrate air, and the substrate SiO₂ are assumed to be semi-infinite in the calculations. b Theoretical thickness dispersions of the fundamental ordinary (TE₀) and extraordinary (TM₀) waveguide modes in free-standing MoS₂ nanoflakes. c Evolution of mode profiles associated with the fundamental ordinary waveguide mode (TE₀), the inset shows a decreasing coupling factor between the tip-induced hot spot and the waveguide mode with increasing sample thickness. We assume the interval 0 nm ≤ z ≤ 100 nm to be the efficient coupling region since the tip-tapping amplitude is set to 50 nm in the experiments. d Normalized mode profiles of the fundamental ordinary (TE₀) and extraordinary (TM₀) waveguide modes for the 170-nm-thick MoS₂ sample indicate that the extraordinary mode retains stronger electric field at the virtual SiO₂/Si interface and tends to leak out through the SiO₂ layer. The calculations in c and d use the same air–MoS₂–SiO₂ three-layer waveguide model as in a