Confinement of Polariton Condensates in quasi-Flatband BICs in Plasmonic and Dielectric Metasurfaces

TL;DR

Addresses confinement and control of exciton-polariton condensates in metasurface lattices hosting symmetry-protected BICs at $k=0$ with $Q_{xy}$ and $m_z$ characters. Uses dielectric Si and plasmonic Ag nanos disks coated with dye-doped PMMA, performing Fourier-space and real-space imaging along with multipolar modeling to reveal hybridization in Ag into $(m_z \pm i \tilde{Q}_{xy})$. Finds that Si condenses into the $Q_{xy}$ BIC producing a donut-shaped far-field in $k$-space, while Ag forms two orthogonally polarized hybrid modes with a quasi-flatband, yielding a double-cross far-field and strong real-space confinement along the polarization axis. The results establish a confinement mechanism that can be tuned via material choice and mode hybridization, with potential applications in quantum computing and polaritonic circuitry.

Abstract

We investigate exciton-polariton condensation in square arrays, composed of either dielectric silicon (Si) or plasmonic silver (Ag) nanodisks, covered with a dye-doped layer. Both arrays support symmetry-protected bound states in the continuum (BICs) at normal incidence, featuring electric quadrupolar ($( Q_{xy} $)) and magnetic dipolar ($( m_z $)) characters. Due to differences in mode coupling, these BICs are split by $(\sim 10$) meV in the Si array, whereas they remain nearly degenerate in the Ag array. Simulations reveal that interference in the Ag array results in hybrid modes, $((m_z + i\tilde{Q}_{xy})$) and $((m_z - i\tilde{Q}_{xy})$), which are polarized along orthogonal directions. Interestingly, this results in similar lasing thresholds in both Si and Ag arrays, regardless of the inherent non-radiative losses of Ag, and also a confinement of the polariton condensates in the Ag array. While condensation in the Si array occurs in the $( Q_{xy} $) BIC, producing a characteristic donut-shaped far-field emission in k-space, condensation in the Ag array populates the hybrid modes, leading to a double-cross emission pattern extending over a broad range of wave vectors due to the quasi-flatband nature of this mode. As a result, the Ag array also exhibits a strong confinement along the polarization axis in real space. However, for unpolarized emission, there is a similar spatial confinement in both Si and Ag arrays. This control over the confinement of condensates could also be exploited to control interactions. Our results highlight a novel mechanism for condensate confinement with potential applications in quantum computing and polaritonic circuitry.

Figures (5)

• Figure 1: a) Schematic geometry of the samples. Nanodisks from either Ag or Si are fabricated on a quartz substrate using e-beam lithography in a square array. The nanodisks are covered with a layer of PMMA with a thickness of 220 nm doped with perylene dye molecules at a concentration of 30 wt%. (b) Extinction (light-gray-dashed curve), emission (solid-black curve), and amplified spontaneous emission (dark-gray-dash-dotted curve) of the bare molecules. (c) SEM image of the Si and (d) Ag nanoparticle arrays. (e) and (f) Dispersion obtained by extinction measurements of the Si and Ag metasurfaces, respectively. Both systems are in the strong coupling regime, evidenced by the anti-crossing of the metasurface mode with the exciton resonance energy at 2.24 eV (indicated with the horizontal white-dashed line). (g) and (h) Close-ups of the photoluminescence (PL) from the strongly coupled metasurfaces near k$_x$=0. Both, the Si and Ag metasurfaces show a BIC at normal incidence.
• Figure 2: (a) Condensation threshold curves for the Si (red curve) and Ag (blue curve) metasurfaces. (b) Linewidths of the emission from the condensates at k$_x=0.05 \upmu$m$^{-1}$ as a function of pump fluence for Si (blue curve) and Ag (red curve). (c)-(d) Emission dispersion at threshold (P=P$_{th}$) for the Si and Ag metasurfaces, respectively. (e)-(f) Emission dispersion at P$\sim$1.3P$_{th}$ on a logarithmic color scale. The dispersions are plotted as a function of k$_x$ with k$_y$=0.
• Figure 3: The dispersion of the Si array (a) and Ag array (b) with the peak maxima of the (quasi) BICs indicated with the white circles. The white curves are a smoothed curve through the data used to calculate the derivative. (c) Group velocity of the magnetic dipolar and electric quadrupolar modes in the Si array represented by the blue solid and dashed curves, respectively, and the group velocity of the hybrid modes ($(m_z + i\tilde{Q}_{xy})$ and $(m_z - i\tilde{Q}_{xy})$) in the Ag array by the red solid and dashed curves, respectively.
• Figure 4: To fully investigate the condensation mode of the Ag and Si arrays, we map the condensate in both real space (red plots) and reciprocal space (green/blue plots) using different orientations of the polarizer in the detection. (a) and (b) show the area of emission below threshold. (c-f) show the emission from the condensate without a polarizer. (g-j) show the vertical polarized fraction of the emission. The emission for the other polarizations are plotted in the SI, Figure S11. The cross sections of the real-space dimensions of the condensate (along the white dashed lines) are plotted in (k-n) and the resulting widths corresponding to the confinement of the condensates are given in Table \ref{['tab:condensate_sizes']}
• Figure 5: (a) Multipolar decomposition of the BIC in the Ag array, showing two contributions of a magnetic dipole along the z-axis, $m_z$ (blue curves), and an electric quadrupole in the $xy-$plane, $\tilde{Q}_{xy}$ (red curves). The modes are mixed, and the decomposition is not appropriate. (b) and (c) Multipolar decomposition of the BIC in the Ag array using the {$(m_z + i\tilde{Q}_{xy})$, $(m_z - i\tilde{Q}_{xy})$} basis. The two modes are now clearly separated, with the $(m_z + i\tilde{Q}_{xy})$ mode accounting for the flatband. (d) Energy dispersion of the $(m_z + i\tilde{Q}_{xy})$ (blue dots) and $(m_z - i\tilde{Q}_{xy})$ modes (red dots) as a function of the in-plane wavevector $k_x$. Near field distributions of the $(m_z + i\tilde{Q}_{xy})$ (e) and $(m_z - i\tilde{Q}_{xy})$ (f) modes. Theoretical far-field emission of the $(m_z + i\tilde{Q}_{xy})$ (g) and $(m_z - i\tilde{Q}_{xy})$ (h) modes for an array with N = 750 unit cells. Note that the y-polarized emission from panel (g) reproduces the experimental emission from Fig. \ref{['fgr:Figure4']}i.