Optical Axes of Triclinic Crystals in Wanderland

Wandering of optical axes of van der Waals rhenium disulphide or diselenide are enabled by the unique disposition of excitons in their lattices and broken crystal symmetries that together lead to the decoupling of absorption and refraction dielectric permittivities.
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It is a common knowledge that material’s absorption follows the refraction by the causality principle leading to Kramers-Kronig relations. This in its stead, ordinarily leads to a maximum of three principle independent directions that describe the dielectric function of a material. Those principal directions are usually fixed (they do not change with wavelength) in crystalline materials. Here, we found that such a paradigm can shift if a crystalline material is of very low symmetry and it also exhibits a strong light-matter interaction, which is the case of van der Waals rhenium disulphide (ReS2) or diselenide (ReSe2) that have triclinic crystal structures and pronounced excitonic resonances. It turned out that absorption and refraction in these materials have different principal directions (or basises), implying “six degrees of freedom” instead of classical three as in traditional materials. As a result, van der Waals ReS2 and ReSe2 allow controlling the light propagation directions by the fine-adjustment of wavelength, and more importantly, without implementation of control knobs or technological steps usually required for traditional materials, such as silicon or titanium dioxide.

Physics behind

Figure 1| The source of wandering optical axes in van der Waals ReS2 and ReSe2. (a) Triclinic crystal structure of ReS2 and ReSe2. (b) Cartoon depiction of non-orthogonal excitons in triclinic ReS2 and ReSe2.

The origin of decoupling of the absorption and refraction in van der Waals ReS2 and ReSe2 is the broken symmetry. Symmetry itself plays a fundamental role in nature and material science. In ancient times, it was referred to as “harmony” or “beauty”. Symmetry is closely related to the basic physical principles, such as momentum and energy conservation. In its turn, asymmetry causes significant alterations in material’s properties as well as the appearance of novel physical effects. In the case of ReS2 and ReSe2, the crystal lattices have the lowest possible degree of symmetry (see Fig. 1a), which in combination with the rich excitonic response (see Fig. 1b) boosts the rotation of their optical axes: the chosen directions of optical symmetry of the material, which was previously observed exclusively in organic materials [1]. As a result, it explicitly allows one to control the light’s propagation direction  by changing the excitation wavelength.

Observations of wandering optical axes
The wandering of optical axes can be observed in both far- and near-field experiments. In far-field measurements, the wandering of optical axes results in the change of positions of maximums and minimums observed in polarization dependent transmittance spectra of triclinic van der Waals materials (see Fig. 2a). On the other hand, near-field scanning optical microscopy measurements (see Fig. 2b) reveal wavelength-dependent propagation directions of their waveguides modes. Therefore, the effect of wandering optical axes gives an indispensable way for the manipulation of light.

Figure 2| The direct observation of the phenomenon of wandering optical axes in triclinic van der Waals materials. Effect of wandering optical axes in (a) far- and (b) near-field.

Future perspectives

Apart from fundamental scientific interest in novel manifestations of optical anisotropy in crystalline materials, the phenomenon of wandering optical axes observed in triclinic van der Waals ReS2 and ReSe2 offers numerous advantages for applied research and applications. For example, it can be used in photonic integrated circuits enabling the spatial control of waveguide propagation mode directions [2]. Van der Waals ReS2 and ReSe2 are perfect materials for optical sensors [3]. Indeed, those usually rely on the spectral shift of a resonance occurring due to the modification of optical response in the presence of biomarkers. Here, that spectral shift can be significantly amplified by rapid optical axes rotation. Furthermore, we also envision that van der Waals ReS2 and ReSe2 based metamaterials or metasurfaces can potentially revolutionize photonic elements for countless applications starting from augmented reality [4] to machine learning [5]. 

Check out our manuscript at https://www.nature.com/articles/s41467-024-45266-3.


  1. M. Dressel, et al., Optics Express 16, Issue 24, 19770-19778 (2008).
  2. A. Vyshnevyy, et al., Nano Letters 23, Issue 17,  8057–8064 (2023). 
  3. G. Ermolaev, et al., Nature Communications 13, Article number: 2049 (2022).
  4. Z. Li, et al., Science Advanced 7, Issue 5, abe4458 (2021).
  5. L. Li, et al., Nature Communications 10, Article number: 1082 (2019).

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Optical Materials
Physical Sciences > Materials Science > Optical Materials
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Physical Sciences > Materials Science > Materials Characterization Technique > Characterization and Analytical Technique > Physical Properties of Materials
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