Unveiling the Mechanism of Phonon-Polariton Damping in α-MoO3

Abstract

Phonon polaritons (PhPs), light coupled to lattice vibrations, in the highly anisotropic polar layered material molybdenum trioxide (α-MoO₃) are currently the focus of intense research efforts due to their extreme subwavelength field confinement, directional propagation, and unprecedented low losses. Nevertheless, prior research has primarily concentrated on exploiting the squeezing and steering capabilities of α-MoO₃ PhPs, without inquiring much into the dominant microscopic mechanism that determines their long lifetimes, which is key for their implementation in nanophotonic applications. This study delves into the fundamental processes that govern PhP damping in α-MoO₃ by combining ab initio calculations with scattering-type scanning near-field optical microscopy (s-SNOM) and Fourier transform infrared (FTIR) spectroscopy measurements across a broad temperature range (8-300 K). The remarkable agreement between our theoretical predictions and experimental observations allows us to identify third-order anharmonic phonon-phonon scattering as the main damping mechanism of α-MoO₃ PhPs. These findings shed light on the fundamental limits of low-loss PhPs, which is a crucial factor for assessing their implementation into nanophotonic devices.

Figure 1

Experimental (FTIR) and theoretical (DFPT) reflectivity spectra of α-MoO₃. A, B. Experimental (top panels) and theoretical (bottom panels) reflectivity spectra of α-MoO₃ for the [100] and [001] polarizations, respectively. Experimental measurements were taken by FTIR, whereas theoretical curves were calculated by employing the ab initio extracted permittivity and supposing a normal incidence of light.

Figure 2

Comparison between experimental and theoretical temperature dependence of the phonon parameters in α-MoO₃. (a) Experimental and theoretical shift of the TO phonon position Δω_TO values showing the same trend with temperature. A hardening of 3 cm^–1 is found in both cases. (b) Comparison between the experimentally extracted and theoretically calculated α-MoO₃ phonon line-width, γ, for the phonon resonance along the [100] direction, that gives rise to the RB between ≈800 cm^–1 and ≈1000 cm^–1.

Figure 3

Experimental cryo-SNOM measurements of PhPs in α-MoO₃. (a) Topography and s-SNOM images taken in a 104 nm-thick α-MoO₃ flake at an illuminating frequency of 880 cm^–1 and temperatures 225, 150, 90, and 10 K. The α-MoO₃ crystal directions are shown within the topographic image. (b) Near-field amplitude profiles extracted along the white dashed lines in panel (a). Fittings using eq 2 are shown as black curves. (c) Experimental polaritonic wavelength λ_p extracted from the fitting of these profiles for the hyperbolic regime at all measured temperatures and frequencies. (d) Experimental polaritonic propagation length L_p extracted from the fittings of the profiles shown in panel (b) employing eq 2 for all temperatures and frequencies measured. A clear increase in the propagation length is found as the temperature decreases.

Figure 4

Phonon-polariton lifetimes in α-MoO₃ as a function of the temperature. Theoretically calculated (circles) and experimentally extracted (star symbols) temperature-dependent lifetimes of PhPs for α-MoO₃ (104 nm-thick flake) for the hyperbolic RB (ω₀ = 860 cm^–1 and ω₀ = 895 cm^–1). Gray straight lines serve as visual guides.