Absorbance enhancement of monolayer ${\mathrm{MoS}}_2$ in a perfect absorbing system

We reveal numerically and experimentally that dielectric resonances can enhance the absorbance and emission of monolayer ${\mathrm{MoS}}_2$. By quantifying the absorbance of the Si disk resonators and the monolayer ${\mathrm{MoS}}_2$ separately, a model taking into account the absorbance as well as quantum efficiency modifications by the dielectric disk resonators successfully explains the observed emission enhancement under normal light incidence. It is demonstrated that the experimentally observed emission enhancement at different pump wavelength results from the absorbance enhancement, which compensates the emission quenching by the disk resonators. In order to further maximize the absorbance value of monolayer ${\mathrm{MoS}}_2$, a perfect absorbing structure is proposed. By placing a Au mirror beneath the Si nanodisks, the incident electromagnetic power is fully absorbed by the hybrid monolayer-${\mathrm{MoS}}_2$–disk system. It is demonstrated that the electromagnetic power is redistributed within the hybrid structure and 53% of the total power is absorbed by the monolayer ${\mathrm{MoS}}_2$ at the perfect absorbing wavelength.

Figure 1

(a) Schematic of the hybrid Si nanodisk metasurface and monolayer ${\mathrm{MoS}}_2$ on ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate. A normally incident plane wave propagates along the $z$ direction and is polarised along the $x$ direction, ${\mathbf{E}}_{\mathrm{inc}}=E_0{e}^{i(k_{0}z-\omega t)}\widehat{\mathbf{x}}$. (b) The real and imaginary (Imag) components of the dielectric permittivity of monolayer ${\mathrm{MoS}}_2$.

Figure 2

(a) Scanning electron microscope images (top) and Raman (bottom left) and PL (bottom right) maps of the fabricated hybrid ${\mathrm{MoS}}_2$–Si-nanodisk sample on ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate for radius $r=160\mathrm{nm}$. (b) and (c) Experimentally measured PL spectra of monolayer ${\mathrm{MoS}}_2$, on disk and off disk, with the excitation wavelengths of ${\lambda }_{\mathrm{ex}}=405\mathrm{nm}$ (b) and ${\lambda }_{\mathrm{ex}}=532\mathrm{nm}$ (c), denoted as vertical dashed lines in (d). (d) At top, with $y$-axis values shown on the right: the calculated absorbance $\alpha$ of monolayer ${\mathrm{MoS}}_2$ on a ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate (sub) and that hybridized with Si disks on a ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate. At bottom, with $y$-axis values shown on the left: the experimentally measured and calculated PL enhancement $\eta$.

Figure 3

The separate ${\mathrm{MoS}}_2$ monolayer and the hybrid ${\mathrm{MoS}}_2$-monolayer–disk structures are examined for three cases: (a) in air, (b) on ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate, and (c) on ${\mathrm{SiO}}_2/\mathrm{Au}$ substrate, respectively. The disk has radius $r=150\mathrm{nm}$, height $h=45\mathrm{nm}$, and spacer thickness $s=100\mathrm{nm}$. Top panels: the absorbance of the ${\mathrm{MoS}}_2$ monolayer in the alone and hybrid cases. Bottom panels: the reflectance $R$, transmittance $T$, and absorbance $A$ of the total structure.

Figure 4

(a)–(c) Top panels: the simulated amplitude ratio of the electric field, $|\mathbf{E}/{\mathbf{E}}_0|$, in the $x-z$ plane at $y=0$ at the inspected absorbance wavelength of 646 nm. The disk has radius $r=150\mathrm{nm}$, height $h=45\mathrm{nm}$, and spacer thickness $s=100\mathrm{nm}$. The black dashed line illustrates where the ${\mathrm{MoS}}_2$ monolayer is, and the incident light propagates along the $+z$ direction. Bottom panels: the amplitude of the multipolar modes for reflectance and transmittance coefficients, including the electric dipole $\mathbf{P}$, electric toroidal dipole $\mathbf{Te}$, magnetic dipole $\mathbf{m}$, electric quadrupole $\mathbf{Q}$, and magnetic quadrupole $\mathbf{M}$.

Figure 5

(a) Comparison of the absorbance $A$ of the structures on ${\mathrm{SiO}}_2/\mathrm{Au}$ substrate for disk radius $r=150\mathrm{nm}$, height $h=45\mathrm{nm}$, and spacer thickness $s=100\mathrm{nm}$, including the disk only, the monolayer ${\mathrm{MoS}}_2$ only, and the hybrid monolayer ${\mathrm{MoS}}_2$–disk. (b) The absorbance $\alpha$ of the Si nanodisk only on ${\mathrm{SiO}}_2/\mathrm{Au}$ substrate as well as the Si nanodisk in the hybrid monolayer ${\mathrm{MoS}}_2$–disk on ${\mathrm{SiO}}_2/\mathrm{Au}$ substrate.