Twist-tunable polaritonic crystals manipulating Bragg resonance

1.Introduction

Van der Waals (vdW) materials that support phonon polaritons (PhPs)—light coupled with lattice vibrations—have attracted considerable interest due to their intrinsic anisotropy and low losses. Notably, α-MoO₃ supports PhPs with in-plane anisotropic propagation, a feature that has enabled phenomena such as negative refraction, light focusing, and canalization of light at the nanoscale. A promising approach to controlling the propagation of polaritons involves the use of polaritonic crystals (PCs)—lattices with periodicity comparable to the polariton wavelength. These PCs support ultra-confined Bloch modes, which can favor a topological funneling of PhPs. In particular, twist-induced manipulation of the Bragg condition has been demonstrated in hole arrays (HAs) fabricated in α-MoO₃, where the lattice vectors are rotated relative to the crystallographic axes of the vdW layer. However, once fabricated, these lattices have a fixed orientation, limiting the ability to actively manipulate the Bragg resonance condition. Moreover, the process of creating holes within the vdW layer introduces significant optical losses due to scattering.

To address these challenges, Prof. Pablo Alonso-González’s group at the University of Oviedo and Prof. Alexey Nikitin’s group at the Donostia International Physics Center (DIPC) have proposed a novel polaritonic crystal design based on twistable α-MoO₃/metal heterostructures. This innovative concept overcomes the aforementioned limitations by enabling low-loss optical twist-tunability. As shown in Figure 1, the structure consists of a twisted, pristine α-MoO₃ layer on top of a periodic HA in a gold layer, where the lattice period is tailored to match the PhP wavelength in α-MoO₃ on gold. Using a combined theoretical approach that incorporates full-wave simulations and an analytical approximation, we explore the formation of the PhP band structure and the excitation of Bragg resonances. Additionally, we conduct near-field measurements at various rotation angles, successfully isolating the contributions of individual PhP Bloch modes that emerge in this configuration.

Our findings expand the scope of twistoptics and hold significant promise for the development of actively tunable two-dimensional polaritonic elements.

2. Background

Bragg resonances are collective light modes that emerge in PCs when the lattice vector matches the polariton wavelength. In isotropic materials, where the momentum of polaritons is the same along all the in-plane directions, the Bragg resonance condition can be controlled by modifying lattice parameters such as periodicity or geometry. However, these parameters must be defined before fabrication, so once the sample is created, the Bragg resonance condition cannot be actively manipulated.

Recent studies have demonstrated an alternative method for tuning the Bragg resonance condition using anisotropic vdW materials, such as α-MoO₃. By rotating the periodic lattice relative to the crystallographic axes, a dependence of the Bragg resonance on the twisting angle has been observed, both theoretically and experimentally, in HAs fabricated in α-MoO₃. However, this approach does not allow for active control of the Bragg resonances once the structure is fabricated, as the holes are etched into the vdW layer, thus fixing the lattice orientation.

3. Innovative research

We propose a twist-tunable PC based on an α-MoO₃/metal heterostructure to enable active manipulation of Bragg resonances. In Figure 2, we demonstrate the tunability of the (±1,0) Bragg resonance as a function of the twist angle (ϕ). This Bragg resonance is characterized by a plane wave whose perpendicular direction is oriented at an angle ϕ. The fringes of this plane wave, marked by black solid lines, are spaced according to the polariton wavelength at that frequency, confirming that they correspond to Bragg modes. An additional verification occurs at ϕ = 45º, where a square-like pattern emerges due to the high symmetry of the PC at this angle. In this configuration, the frequency at which the Bragg condition for the (±1,0) mode is fulfilled coincides with that of the (0,±1) mode.

By performing a Fourier transform (FT) on the measured data, we can visualize the momentum of the polaritons propagating within the PC, as shown in the color plots insets in Figures 2a,c,e,g. These plots reveal a pair of bright dots whose momentum aligns with the reciprocal lattice vector. As the twist angle changes, the orientation of these dots rotate, illustrating how the twist angle of the lattice actively manipulates the momentum of the polaritons.

Our analytical theory also allows us to obtain the complete band structure of the PC, as illustrated in the color plot in Figure 3a for ϕ = 30º. This plot provides a comprehensive view of all accessible in-plane momentum states at various frequencies. The tunability of the band structure of the PC is further demonstrated by varying the twist angle from ϕ = 0º to ϕ = 45º, as shown in the zoomed-in views in Figures 3b-e. Additionally, the band structure along different reciprocal directions can be reconstructed from the experiments by measuring the in-plane wavelength, indicated by the separation between the fringes along the in-plane directions.

4. Applications and perspectives  

The proposed PC is based on a heterostructure featuring a twistable α-MoO₃ crystal layer on top of gold HA substrate, enabling tunability of the Bragg resonances, as experimentally demonstrated. Our design preserves the pristine properties of α-MoO₃, thus allowing it to be rotated while maintaining the low-loss characteristics of its polaritons. Even though the results are demonstrated for α-MoO₃, the underlying concept is applicable to any similar heterostructure based on in-plane anisotropic crystal layers supporting polaritons. These findings broaden the scope of twistoptics and hold significant promise for the development of actively rotatable two-dimensional polaritonic devices.

These research results are published online with the title “Twist-tunable in-plane anisotropic polaritonic crystals” on Nanophotonics.

The authors of this article are Nathaniel Capote-Robayna，Ana I. F. Tresguerres-Mata, Aitana Tarazaga Martín-Luengo, Enrique Terán-García, Luis Martin-Moreno, Pablo Alonso-González, and Alexey Y. Nikitin. Pablo Alonso-González and Alexey Nikitin are the corresponding authors of this work. Prof. Pablo Alonso-González’s research group is affiliated to University of Oviedo, Oviedo 33003, Spain; and Prof. Alexey Nikitin’s research group is affiliated to Donostia International Physics Center (DIPC), Donostia-San Sebastián 20018, Spain.