Long-range mid-infrared energy transfer mediated by hyperbolic phonon polaritons

Abstract

We provide a framework to theoretically describe long-range energy transfer in single and twisted two-dimensional hyperbolic slabs. We demonstrate that phonon polaritons (PhPs, quantum superpositions of photons and lattice vibrations in polar dielectrics) can mediate and enhance room-temperature energy transfer at ranges far exceeding those of conventional mid-infrared (MIR) platforms, and with extreme directionality. This is because the dipole-dipole interaction potential energy diverges along the asymptotes of the real-space hyperbolic opening angle. Our findings allow us to extend classical and quantum interactions between dipoles, typically strictly confined to the near-field, beyond several free-space MIR wavelengths. We use $α$-MoO$_3$ as a representative material, but this mechanism is not limited to the MIR: it is general to anisotropic media across the whole electromagnetic spectrum.

Figures (4)

• Figure 1: Landscape of platforms for long-range DDIs across the electromagnetic spectrum. DDI mediators are compared by their normalized interaction length $d/\lambda_0$. Platforms are arranged by operating frequency. Shading denotes relative field enhancement and orange stripes indicate directionality.
• Figure 2: Long-range MIR DDIs mediated by hyperbolic PhPs in a single $\alpha$-MoO3 slab.(a) Two dipoles on a 200-nm-thick $\alpha$-MoO3 slab, interacting via PhPs described by the DGF $\tilde{\mathbf{G}}(\mathbf{r}_A,\mathbf{r}_D)$. (b) IFCs for isotropic (left), hyperbolic (middle), and canalized (right) PhPs; grey and black arrows indicate $\mathbf{k}_p$ and the propagation direction $\mathbf{S}$. (c) Opening angle $\varphi$ of hyperbolic PhP propagation from 800 to 920 cm-1, calculated using complex (blue) and real-part (red) permittivities; canalization occurs around 820–850 cm-1. (d1–d3) Normalized DDI enhancement $F_{\rm DDI}$ at 900, 850, and 825 cm-1 for a 200-nm $\alpha$-MoO3 slab. (e1–e3) Normalized imaginary part $\mathrm{Im}[G_{zz}/|G_{zz}^0|]$ at the same frequencies, showing phase and LDOS patterns.
• Figure 3: Benchmarking long-range MIR DDIs mediated by hyperbolic PhPs in a single $\alpha$-MoO3 slab against existing MIR platforms.Left:$F_{\rm DDI}$ for SPPs on Au, SPhPs in SiC, and graphene plasmons. Right:$F_{\rm DDI}$ in a 200-nm $\alpha$-MoO3 slab along the direction of maximum enhancement in the 825–920 cm-1 range.
• Figure 4: Long-range MIR DDIs mediated by canalized PhPs in twisted bilayer $\alpha$-MoO3.(a) Two dipoles on twisted $\alpha$-MoO3 slabs at angle $\theta$, interacting via PhPs described by the DGF $\tilde{\mathbf{G}}(\mathbf{r}_A,\mathbf{r}_D)$. (b) Normalized DDI enhancement $F_{\rm DDI}$ at 910 cm-1 for twist angles $\theta=0^\circ$, $69.3^\circ$, and $90^\circ$. (c)$F_{\rm DDI}$ along the direction of maximum coupling (canalization or asymptotes) for the same system. (d) Real-space PhP intensity patterns as a function of twist angle, obtained analytically from the DGF. (e) Ratio of PhP power $P_{\rm PhP}$ to total dipole decay $P_0$ versus twist angle for several distances from the donor.