A team of scientists from Skoltech (part of the VEB.RF Group) and MIPT has investigated how the Casimir effect can be used to precisely control the angular orientation of nanostructures. The results of the study, supported by the Russian Science Foundation (project 22-12-00351-P), have been published in the journal Physical Review A (Letter).

In 1948, Dutch physicist Hendrik Casimir predicted something that seemed impossible at first glance: two electrically neutral ideal conductors placed in a perfect vacuum should attract each other. It turned out that the exact value of this attractive force can be calculated by analyzing vacuum fluctuations.

The Russian researchers focused on one-dimensional photonic gratings made of an anisotropic dielectric: parallel strips of a material in which the speed of light varies depending on direction and polarization. Such photonic crystal layers are well studied. However, the scientists examined a system of two gratings rotated relative to each other, where in each grating the anisotropy axis is additionally rotated relative to the strip direction. This rotation breaks one of the mirror symmetries, making the sublattices in-plane chiral and leading to a nontrivial Casimir interaction between them.

To calculate the interaction between two such gratings, the authors employed the scattering matrix method within the Casimir–Lifshitz formalism — an approach that accounts for the real optical properties of the material, its losses, dispersion, and complex geometry.

The results revealed intriguing behavior. In the symmetric case (anisotropy axis parallel or perpendicular to the strips), the energy is proportional to the cosine of the angle: the system tends toward either parallel or perpendicular orientation — a classical result already known. However, as soon as the anisotropy axis deviates by some angle, the symmetry is broken, and the energy minimum occurs at a nonzero relative rotation angle of the gratings. Remarkably, this equilibrium angle is such that the anisotropy axes of both gratings become nearly parallel regardless of the distance between them.

This last point is fundamentally important: the equilibrium angle does not depend on the gap between the gratings. This means that once two chiral gratings are brought sufficiently close together, they “know” which orientation to adopt and do so autonomously under the action of the Casimir torque. This property makes them promising candidates for self-assembly elements in nanophotonics.

Natalia Salakhova, a junior research scientist at the Skoltech Engineering Physics Center and an MIPT graduate, commented: “The key finding is that the equilibrium angle is determined by the intrinsic parameters of the material. This provides a new degree of freedom for designing photonic nanostructures with predetermined behavior.”

Ilya Fradkin, a research scientist at the Skoltech Engineering Physics Center and at the MIPT Laboratory of Nanooptics and Plasmonics, described the significance of the work as follows: “Until now, the Casimir torque has been viewed as a curious physical phenomenon that is difficult to use practically — its magnitude is small, and its angular dependence is too simple. The introduction of chirality fundamentally changes the picture: a nonzero equilibrium angle emerges, dictated by the material’s properties. This makes it possible to design nanostructures that autonomously find the correct orientation without any external control.”

According to co-author Sergey Dyakov, an associate professor and the head of a research group at the Skoltech Engineering Physics Center, the practical application of this discovery lies in the field of reconfigurable nanophotonics. Optical components capable of autonomously assuming a specified angular position without mechanical actuators could be used in ultra-miniature sensors, optical switches, and quantum optical circuits where external mechanical intervention is either impossible or undesirable.

As stated by Nikolay Gippius, the head of the Theoretical Nanophotonics Group and Professor at the Skoltech Engineering Physics Center, the research team’s next step is to search for materials with optimal anisotropy to maximize the Casimir torque.