Weak and strong coupling properties of surface excitons

With high enough doping concentrations, organic dye–doped polymer materials exhibit a negative real part of the permittivity within an energy range just above their material absorption, incurring surface exciton (SE) modes at these energies. Here, we report on how such modes can be used to realize strong light-matter coupling with photoactive molecules. Our simulations reveal that SEs can facilitate strong coupling by sustaining the energy-splitting-induced transparency; however, the polaritons may not be visible in the absorption since they can easily be located outside of the narrow negative permittivity regime. Moreover, we show that the SE modes cannot couple strongly with the surface plasmons. Our findings shed light on the weak and strong coupling properties of SEs.

Figure 1

Real part of the dielectric function $\left[\text{Re}\right\{\epsilon \left(\omega \right)\left\}\right]$ of (a) Au [20] and (b) polyvinyl alcohol (PVA) doped with a high concentration of TDBC J aggregates as a function of energy. The excitonic TDBC material is modeled using Eq. (1) explained in the text, with the same parameters as used in Fig. 2. The surface mode region (SMR)—i.e., the spectral range where $\text{Re}\left\{\epsilon \right(\omega \left)\right\}<0$, and thus, the surface modes, SPs or SEs, are supported—is marked for the both materials. (c) Core-shell nanoparticle geometry where core radius $r_{\text{core}}=50$ nm, shell thickness $t_{\text{shell}}=25$ nm, and shell outer radius $r_{\text{shell}}=75$ nm. The complex-dispersive dielectric functions of the core and shell materials are ${\epsilon }_{\text{core}}\left(\omega \right)$ and ${\epsilon }_{\text{shell}}\left(\omega \right)$, respectively.

Figure 2

(a) Absorption spectra of generic dye shell (black), Au core (red), and the core-shell coupled system for different values of $f_{\text{dye}}$ (0.01, 0.03, 0.05, 0.10, 0.15, and 0.20) and for $\gamma =0.1\mathrm{eV}$. The spectra are shifted vertically for clarity. The absorption of the dye shell is spectrally tuned to the same as the Au core absorption maximum, i.e., $E_0=E_c=2.28\mathrm{eV}$ (vertical dashed line). The lower polariton (LP) and upper polariton (UP) branches are shown by the tilted black dashed lines. (b) Absorption spectra of generic dye shell (black), TDBC core (red), and the core-shell coupled system with the same $\gamma$ and $f_{\text{dye}}$ values as in (a). The spectra are shifted vertically for clarity. The surface exciton (SE) mode of the TDBC core ($E_c=2.15\mathrm{eV}$) and the material absorption of TDBC ($E_m=2.08\mathrm{eV}$) are shown by the vertical dashed black lines. The absorption of the dye shell is spectrally tuned with $E_c$. (c) Absorption at $E_c$ for Au-core/dye-shell ($E_c=2.28\mathrm{eV}$) and TDBC-core/dye-shell ($E_c=2.15\mathrm{eV}$) coupled systems as a function of $f_{\text{dye}}$. The blue and red horizontal dashed lines show the core absorption for Au and TDBC, respectively. The blue squares and red circles on the curves of corresponding color depict the discrete data points. In (a)–(c), absorption means absorption efficiency, i.e., absorption cross-sections normalized by geometrical cross-section.

Figure 3

(a) Real part of the dielectric function $\left[\mathrm{Re}\right\{\epsilon \left(\omega \right)\left\}\right]$ of MTDBC as a function of energy. The surface mode region (SMR)—i.e., the spectral range where $\text{Re}\left\{\epsilon \right(\omega \left)\right\}<0$, and thus, the SE modes are supported—is marked for MTDBC. (b) Absorption spectra of generic dye shell (black), MTDBC core (red), and the core-shell coupled system for different values of $f_{\mathrm{dye}}$ (0.0001, 0.0005, 0.001, 0.005, and 0.01). The spectra are vertically shifted for clarity. The absorption of the dye shell is spectrally tuned to match the SE mode of the MTDBC core, i.e., $E_0=E_c=5.9\mathrm{eV}$ (vertical dashed line). The lower polariton (LP) and upper polariton (UP) branches are shown by the tilted black dashed lines. In the figure, absorption means absorption efficiency, i.e., absorption cross-sections normalized by geometrical cross-section.

Figure 4

(a) Absorption spectra of TDBC shell possessing two surface exciton (SE) modes ($E_{L1}$ and $E_{L2}$) along with the material absorption ($E_m$), when located around an inert dielectric core (green curve). An absorbing core along with the shown absorption (blue curve) yield merging of the two SE modes (red curve). (b) Absorption spectra as a function of energy difference ($E-E_m$) for the TDBC shell and the Au-core/TDBC-shell system for different values of $E_m$ (1.9, 2, 2.1, 2.2, and 2.3 eV). On each curve (except the black one), the thick black vertical line represents the position of the surface plasmon (SP) mode of the Au core ($E_c=2.28\mathrm{eV}$) on the energy difference scale. In (a) and (b), two SE modes of the TDBC shell ($E_{L1}$ and $E_{L2}$) and the material absorption of TDBC ($E_m$) are shown by the vertical dashed black lines, while in (b), the lower polariton (LP) branch is shown by the tilted black dashed line. In the figures, absorption means absorption efficiency, i.e., absorption cross-sections normalized by geometrical cross-section. (c) Energy splitting ($E_m-E_{\text{LP}}$) as a function of detuning ($E_c-E_m$), where the red squares on the red curve depict the discrete data points.