Spatiotemporal Visualization of Long-Range Anisotropic Plasmon Polaritons in Hyperbolic MoOCl2

Abstract

Manipulating light at the nanoscale with minimal loss remains a central challenge for nanophotonic technologies that can be tackled by using the direction-dependent polariton modes supported by anisotropic materials. Although best known for their highly confined polaritons, hyperbolic materials can also host long-range directional polaritons, whose direct observation has remained challenging as it requires experimental techniques that combine nanometre and femtosecond spatial and temporal resolution, respectively. Here, we use time-resolved photoemission electron microscopy for direct nanoscale visualization of long-range anisotropic plasmon polariton (LRAPP) dynamics on a flake of the van der Waals hyperbolic material molybdenum oxydichloride. We directly image plasmon polaritons with propagation lengths larger than 10 $μ$m, exhibiting an approximately three times longer propagation length and intrinsically lower optical loss than short-range polaritons previously reported on the same material. By tracking the spatiotemporal evolution of LRAPPs, we determine their phase and group velocities at the nanoscale and directly observe their reflections at flake edges. These results establish molybdenum oxydichloride as a versatile platform for integrated nanophotonics, supporting both low-loss directional transport and deeply subwavelength field confinement within a single natural material, in the visible spectral range.

Figures (5)

• Figure 1: Structural anisotropy and ultrafast imaging of plasmon polaritons in MoOCl$_2$. (A) Crystal structure of MoOCl$_2$ and schematic of the samples used in the experiment. The inset shows the difference in Molybdenum bonding in the $a$ and $b$ crystal directions that gives rise to anisotropic polaritons. (B) Time resolved-photoemission electron microscopy (TR-PEEM) with the delay between two interferometrically locked ultrafast laser pulses, $\Delta t$, enables direct imaging of the evolution of anisotropic plasmon polaritons in space with sub-cycle time-accuracy.
• Figure 2: Polarization-dependent anisotropic polariton dispersion in MoOCl$_2$. (A) Experimental PEEM image of MoOCl$_2$ with 1.57 eV (787 nm) photons with the laser polarized along the crystal $a$ (metallic) axis. (B) and (C) indicate the isofrequency contours for the real and imaginary components, respectively, of $k_z$ of MoOCl$_2$ at 1.61 eV (770 nm) for light polarized primarily along the $x$ direction. (D) Experimental PEEM image of MoOCl$_2$ with 1.57 eV (787 nm) photons with the laser polarized along the crystal $b$ (non-metallic) axis. (E) and (F) indicate the isofrequency contours for the real and imaginary components, respectively, of $k_z$ of MoOCl$_2$ at 1.61 eV (770 nm) for light polarized primarily along the $y$ direction.
• Figure 3: Long- and short-range anisotropic plasmon polaritons in MoOCl$_2$. (A) Experimental measurements of plasmon polaritons in MoOCl$_2$ extracted from static PEEM measurements (insets, scale bar 3 $\mu$m) compared with a model of the imaginary component of the pole of the reflectivity coefficient and analytical models for both the long-range and short-range anisotropic plasmon polaritons (LRAPP and SRAPP). Calculations of the Electric Field (B) and Poynting vector (C) for the LRAPP and the Electric Field (D) and Poynting vector (E) for the SRAPP for the energies shown in (A). Also see Supplementary Figure 6 for charge density for these modes.
• Figure 4: Sub-cycle interferometric tracking of anisotropic plasmon polariton propagation. (A) Image at $\Delta t= 0$ for an interferometric PEEM experiment with h$\nu=1.60$ eV. (B) Expansion of the black box from (A) for different phase delays of the two phase-locked laser pulses. For this photon energy a phase shift of $\pi/2=0.645$ fs. The same peak is traced in a white dotted line through each image. (C) Linecuts along the yellow line in (B) for each phase delay. (D) Linecuts from the white box in (A) where the intensity has been integrated along the $b$ axis showing the group velocity of the LRAPP wavepacket as it propogates from the edge. (E) The fit gaussian center of the LRAPP wavepacket as it propagates away from the edge as a function of time. The group velocity is fit to the propagating wave between 44 and 64 fs. $v_p$ and $v_g$ indicate phase and group velocitues, respectively.
• Figure 5: Spatiotemporal dynamics and edge reflection of anisotropic plasmon polariton wavepackets. (A) Space-time contour plot of a PEEM movie with 1.60 eV (Movie S2 on Flake C) where LRAPPs are launched from the edges of the inset flake snapshot along the $a$ axis. As a function of time the LRAPP wavepackets propagate away from the edges (1), pass each other in the middle of the flake (2), and reflection off of the other edge (3). A zoom in of the reflection dynamics are shown in (B) where the arrows trace the dynamics of the LRAPP wavepacket. (C) Accompanying line cuts integrated along the $b$ axis where the dotted and dashed arrows demonstrate the direction of the LRAPPs launched from the left and right edges, respectively as they undergo propagation.