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Berhe AM, As’ham K, Al-Ani I et al. Strong coupling and catenary field enhancement in the hybrid plasmonic metamaterial cavity and TMDC monolayers. Opto-Electron Adv 7, 230181 (2024). doi: 10.29026/oea.2024.230181
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Strong coupling and catenary field enhancement in the hybrid plasmonic metamaterial cavity and TMDC monolayers
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Abstract
Strong coupling between resonantly matched surface plasmons of metals and excitons of quantum emitters results in the formation of new plasmon-exciton hybridized energy states. In plasmon-exciton strong coupling, plasmonic nanocavities play a significant role due to their ability to confine light in an ultrasmall volume. Additionally, two-dimensional transition metal dichalcogenides (TMDCs) have a significant exciton binding energy and remain stable at ambient conditions, making them an excellent alternative for investigating light-matter interactions. As a result, strong plasmon-exciton coupling has been reported by introducing a single metallic cavity. However, single nanoparticles have lower spatial confinement of electromagnetic fields and limited tunability to match the excitonic resonance. Here, we introduce the concept of catenary-shaped optical fields induced by plasmonic metamaterial cavities to scale the strength of plasmon-exciton coupling. The demonstrated plasmon modes of metallic metamaterial cavities offer high confinement and tunability and can match with the excitons of TMDCs to exhibit a strong coupling regime by tuning either the size of the cavity gap or thickness. The calculated Rabi splitting of Au-MoSe2 and Au-WSe2 heterostructures strongly depends on the catenary-like field enhancement induced by the Au cavity, resulting in room-temperature Rabi splitting ranging between 77.86 and 320 meV. These plasmonic metamaterial cavities can pave the way for manipulating excitons in TMDCs and operating active nanophotonic devices at ambient temperature.-
Keywords:
- catenary-shaped field enhancement /
- strong coupling /
- plasmon /
- exciton /
- Rabi splitting
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References
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Supplementary Information
Supplementary information for Strong coupling and catenary field enhancement in the hybrid plasmonic metamaterial cavity and TMDC Monolayers 
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Berhe AM, As’ham K, Al-Ani I et al. Strong coupling and catenary field enhancement in the hybrid plasmonic metamaterial cavity and TMDC monolayers. Opto-Electron Adv 7, 230181 (2024). doi: 10.29026/oea.2024.230181
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Figure 1.
Plasmon resonances and electric field distribution in Au cavity. (a) Schematic drawing of Au nanostructure with design parameters of the structure are as follows: W1 = 39 nm, W2 = 33 nm, h =157 nm, g = 108 nm, α = 307 nm, and t = 60 nm. (b) Absorption mapping of uncoupled Au cavity at a p = 420 nm period. (c) The absorbance of uncoupled Au cavity (red line) and the uncoupled WSe2 monolayers. The Au cavity's resonance wavelength is designed to resonate with the exciton in WSe2. The electric field is generated at a unit cell of the Au cavity, at the planes (d) z = 13 nm and (e) y = 70 nm with a polarization along the y-axis. (f) The retrieved catenary-shaped near-field enhancement at air−gold interfaces. (g) The absorption spectra of the Au cavity at different polarisation angles. The thickness of the Au cavity gap was fixed at 60 nm with cavity gaps of W1 = 39 nm and W2 = 33 nm. The polarization angle of 0° is along the x-axis, and 90° is along the y-axis. (h) Near-field enhancement |E/E0| with increasing polarisation angle from 0° − 90°. (see (e) for the position). (i) The absorption mapping of Au-WSe2 heterostructure at different polarization angles.
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Figure 2.
Catenary field enhancement and strong coupling in the Au-MoSe2 and Au-WSe2 heterostructure. (a) Schematic illustration of monolayer MoSe2 on top of Au cavity at normal incidence. (b) Absorption spectrum mapping of Au-MoSe2 as a function of the Au thickness varied from 20 to 120 nm while keeping other parameters constant (W1 = 39 nm, W2 = 33 nm, and period = 450 nm). Light is incident through TMDCs monolayers with polarisation along the y-axis. (c) The absorption spectrum of Au-MoSe2 corresponds to (b) with a gold thickness of t = 36.6 nm. Two different hybridized modes, as the UPB (E+), and LPB (E−) are observed in absorption spectra. The demonstrated energy resonances were taken from the point of matching between excitons in MoSe2 and the plasmon mode of the uncoupled Au cavity. (d) Schematic illustration of monolayer WSe2 on top of Au cavity at normal incidence. (e) Absorption mapping of Au-WSe2 heterostructures by tuning the thickness of Au nanostructure with a fixed value of W1 = 39 nm, W2 = 33 nm, h =157 nm, g = 108 nm, α = 307 nm, and p = 420 nm. (f) The absorption spectrum of Au-WSe2 corresponds to (e) with a gold thickness of t = 60 nm. Electric field distribution at a unit cell of Au-WSe2 nanostructure at the planes (g) y-plane and (h) z-plane using an excitation wavelength of 758 nm. (i) Catenary-shaped symmetric electric field profile of Au-WSe2 with a cavity gap distance of W1 = 39 nm. The magnitude of the electric field intensity distributions obtained by numerical simulations matched with the rigorous catenary model, where a = 7.626×10−9, b = −1.2529, k = 133.949, and c = 9.638 (see Eq. 3).
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Figure 3.
Anticrossing behaviour of the strong plasmon-exciton coupling of Au−MoSe2 and Au−WSe2 heterostructures. (a) Dispersion curve of Au−MoSe2 heterostructure, where the solid black line, solid pink line, blue dash line, and olive dash line represent the UPB, LPB, uncoupled plasmon resonances, and uncoupled exciton resonances, respectively. (b) Hopfield coefficients for MoSe2 exciton and plasmon contributions to UPB and LPB as a function of Au thickness. (c) Dispersion curve of Au−WSe2 heterostructure, where the solid blue line, solid green line, black dash line, and red dash line represent the UPB, LPB, uncoupled plasmon resonances, and uncoupled WSe2 exciton resonances. (d) Hopfield coefficients for WSe2 exciton and plasmon contributions to UPB and LPB as a function of Au thickness.
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Figure 4.
Size and cavity gap−dependent electric field enhancement and Rabi splitting. (a) Calculated electric field enhancement by increasing the size of the Au nanostructure from 20 to 120 nm. (b) Calculated near-field enhancements of the uncoupled Au cavity as a function of cavity gap distance with a fixed thickness of t = 50 nm and 90 nm. The calculated near-field enhancement distributions |E/E0| of the Au cavity are size-dependent. (c) Calculated near-field enhancements of the Au-WSe2 heterostructure as a function of cavity gap with a thickness of t = 50 nm. Compared to the uncoupled Au cavity with a thickness of t = 50 nm and a cavity gap of W1 = 22 nm, the Au-WSe2 heterostructure demonstrates higher near-field enhancement. Their calculated electric field profile and its corresponding catenary-shaped near-field enhancement revealed that the narrower cavity gap has higher field confinement (see
Fig. S5 in the Supplementary information). (d) Size-dependent Rabi splitting of Au-WSe2 while the period and cavity gap are fixed at 420 nm, W1 = 39 nm, and W2 = 33 nm. (e) Cavity gap-dependent Rabi splitting of Au-WSe2 while the period and thickness of Au cavity are fixed at 420 nm and 90 nm, respectively. (f) Plasmon resonance of uncoupled Au cavity corresponds to t = 80 nm at cavity gap of W1 = 39 nm and t = 90 nm at cavity gap of W1 = 42 nm, respectively. Their corresponding plasmon resonance frequency is 426.08 THz, and 423.1 THz, respectively. -
Figure 5.
Effect of Cavity gap on strong coupling of Au-WSe2 and Au-MoSe2 on the substrate. Schematic drawing of (a) Au-WSe2, and (b) Au-MoSe2 nanostructures on SiO2 substrate. (c) Quality factors (Q) as a function of period and cavity gap of gold nanostructure at a thickness of 90 nm. (d) Normal-incidence absorption spectra of the WSe2 monolayer directly embedded in the Au cavity with different cavity gaps. Strong coupling of (e) Au-WSe2, and (f) Au-MoSe2 on SiO2 substrate as a function of Au cavity gap. Here, the diameter of the Au cavity is 90 nm, while the cavity gap varies from 22 nm to 58 nm. The purple and black dash lines represent the excitons of WSe2 and MoSe2, respectively.
