Perfect Absorption by an Atomically Thin Crystal

Optical absorption is one of the most fundamental processes in light-matter interactions. The ability to achieve and control high absorption is crucial for a broad range of modern photonic technologies. In nanomaterials of length scales much smaller than a wavelength, optical absorption is typically a weak perturbation. To achieve high absorption, exquisite techniques and structures have been developed, such as coherent interference of multiple laser beams and plasmonic metasurfaces. Here, we show that a robust critical-coupling condition exists to allow perfect absorption of light by a subnanometer-thick two-dimensional semiconductor, when the radiative-decay rate of the exciton resonance balances with its loss rate. We measure an absorption up to $99.6\mathrm{\%}$ in a monomolecular ${\mathrm{Mo}\mathrm{Se}}_2$ crystal placed in front of a flat mirror. We furthermore demonstrate control of the perfect absorption by tuning the exciton-phonon, exciton-exciton, and exciton-photon interactions with temperature, pulsed laser excitation, and a movable mirror, respectively. Our work suggests a mechanism to achieve and control critical coupling in two-dimensional excitonic systems, enabling photonic applications including ultrafast low-power light modulators and sensitive optical sensing.

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Figure 1

The absorption mechanism in an excitonic system. (a) The microscopic mechanism of excitonic absorption. After excitation by absorbing a photon, the exciton polarization decays through either radiative recombination or scattering to other states, with rates ${\mathrm{\Gamma }}_{\mathrm{rad}}$ and ${\mathrm{\Gamma }}_{\mathrm{sca}}$, respectively. Only ${\mathrm{\Gamma }}_{\mathrm{sca}}$ causes energy loss and induces optical absorption. (b),(c) The absorption spectra of a free-standing 2D film (b) and a 2D film in front of a mirror (c), with varying scattering rates. In the free-standing 2D cases, the total absorption decreases as the scattering processes are suppressed. The maximum absorption can reach $50\mathrm{\%}$ and $100\mathrm{\%}$ in cases (b) and (c), respectively, when the integrated area is decreased to half. (d) An analogy to a ring resonator for the case in (c). The critical-coupling effect between free-space photons and excitons can occur in TMD monolayers. The photon channel is coupled with the exciton channel, with an input coupling efficiency of ${\mathrm{\Gamma }}_{\mathrm{rad}}$. While the energy is transferred to the exciton channel, scattering processes can create loss with rate ${\mathrm{\Gamma }}_{\mathrm{sca}}$. The critical-coupling condition is reached if ${\mathrm{\Gamma }}_{\mathrm{sca}}={\mathrm{\Gamma }}_{\mathrm{rad}}$ and the absorption approaches $100\mathrm{\%}$.

Figure 2

The sample structure and local field enhancement from a distributed Bragg reflector (DBR). (a) An optical-microscope image of the sample. The red lines encircle the ${\mathrm{Mo}\mathrm{Se}}_2$ monolayer area. The orange dot labels the location of the measurements. (b) A schematic of the sample structure. The sample is designed such that the ${\mathrm{Mo}\mathrm{Se}}_2$ monolayer is $\lambda /4$ away from the DBR mirror to ensure the largest absorption and radiative enhancement. (c) A simulation of the position-dependent squared electric field for photon energy 1.650 eV, showing that the ${\mathrm{Mo}\mathrm{Se}}_2$ monolayer is close to the antinode of the standing light wave.

Figure 3

The reduced optical absorption in the coherent limit. (a) Measured reflection spectra near the $A$-exciton resonance of the ${\mathrm{Mo}\mathrm{Se}}_2$ monolayer at different temperatures. The spectra are offset for clarity. (b) The temperature-dependent exciton resonance energy is shown in olive squares. The simulated $|E_{\mathrm{local}}{|}^2$ at the ${\mathrm{Mo}\mathrm{Se}}_2$ position for the corresponding exciton wavelength at each temperature is plotted in orange squares. The absorption enhancement factor varies within $14\mathrm{\%}$ over the whole temperature range. The error bar originates from the uncertainty of the refractive indices. (c) Measured exciton line widths versus the temperature. The shaded areas show line-width contributions from radiative (green) and scattering (yellow) broadenings. (d) The measured (blue squares) and fitted (violet curve) integrated absorption as a function of the temperature. The gray line shows the prediction from the perturbative theory, taking into account the wavelength-dependent absorption enhancement. A remarkable $67\mathrm{\%}$ reduction in integrated absorption is observed experimentally, indicating that coherent absorption dominates.

Figure 4

Observation of the critical-coupling phenomenon between an exciton and a free-space photon. (a)–(c) Measured absorption spectra (lower panels) with the temperature (a), laser intensity (b), and mirror distance (c) as tuning parameters. All three methods show a clear critical-coupling effect with nearly $100\mathrm{\%}$ maximum absorption of $94.6\mathrm{\%}$, $99.6\mathrm{\%}$, and $98.9\mathrm{\%}$, respectively. The extracted $\hslash {\mathrm{\Gamma }}_{\mathrm{rad}}$ and $\hslash {\mathrm{\Gamma }}_{\mathrm{sca}}$ are plotted in the corresponding upper panels. The critical-coupling condition occurs when the temperature, laser intensity, and mirror distance are tuned such that ${\mathrm{\Gamma }}_{\mathrm{rad}}={\mathrm{\Gamma }}_{\mathrm{rad}}$.