Smooth Fourier crystals: Taming polaritons for nanoscale light control

Light can do remarkable things, but it has limitations. Ordinary photons are bound by diffraction, which sets a limit on how tightly they can be confined in space. This is why focusing light to spots smaller than about half its wavelength is so difficult. But in certain materials, photons couple to vibrations of atoms or oscillations of electrons, forming hybrid quasiparticles called polaritons. These waves carry the character of light but can be squeezed into volumes far smaller than the wavelength of the original photons.

In layered crystals known as van der Waals (vdW) materials — such as graphene or hexagonal boron nitride (hBN) — polaritons can travel long distances while being confined to nanometre scales. This makes them excellent candidates for manipulating light at the nanoscale, opening doors to technologies like ultrasensitive sensors, compact optical circuits, and enhanced light–matter interactions.

The challenge with polaritonic crystals

Researchers have long known that arranging materials periodically can control waves. For light, these arrangements are called photonic crystals, which can block certain wavelengths or guide them in unusual ways. Polaritons can also form such periodic patterns, known as polaritonic crystals. In theory, these should give even stronger control over light at tiny scales.

But there is a catch: to make a polaritonic crystal, one usually patterns the surface of the material into sharp-edged nanostructures. Those edges scatter the polaritons strongly, causing them to leak energy and break into many competing modes. Instead of a clean band structure with a clear bandgap, you get a messy spectrum filled with overlapping signals. This makes it hard to design practical devices.

A new idea: the Fourier crystal

The authors of a new study ¹ propose a different approach: rather than carving the material into a pattern full of edges, they use a smooth, harmonically modulated surface — essentially a gentle sinusoidal corrugation covered with a thin layer of gold. When a thin slab of hBN is placed on top of this “Fourier surface,” the distance between the hBN and the gold mirror varies smoothly in space.

Because polaritons in hBN are very sensitive to this distance, their momentum becomes periodically modulated — not by sharp jumps, but gradually, in a way described mathematically by Fourier harmonics. This is why the structure is called a polaritonic Fourier crystal.

This smooth modulation has three major advantages:

Minimal scattering. Without sharp edges, polaritons are less likely to scatter into unwanted higher-order modes.

Mode selectivity. The fundamental polariton mode (called M0) is strongly affected, while higher-order modes are barely touched. This makes the band structure clean and simple.

Design flexibility. By combining different harmonics in the surface profile, one can engineer which modes experience bandgaps and how wide those gaps are.

What they found in the lab

The team fabricated these Fourier crystals using holographic lithography on a polymer film, creating wafer-scale sinusoidal surfaces with a gold coating. A slab of hBN, about 100 nm thick, was then placed on top.

They used scattering-type scanning near-field optical microscopy (s-SNOM) to directly image how polaritons propagate within the crystal. Unlike regular microscopes, s-SNOM can resolve features down to ~10 nm, letting researchers “see” the waves as they ripple inside the material.

The images revealed that almost exclusively the M0 mode propagates in the crystal, with a clearly defined polaritonic bandgap. This is striking because in traditional etched polaritonic crystals, many modes clutter the spectrum. Here, the smooth Fourier modulation filters everything down to a single, well-behaved Bloch mode.

The team also confirmed these observations with numerical simulations and analytical models, which matched the experimental data closely. They even tested different hBN thicknesses and showed that the Fourier crystal design remains robust.

Why this matters

This work demonstrates a fundamentally new way of building polaritonic crystals that avoids the biggest problem of scattering at rough edges. By using smooth Fourier modulation, one can selectively engineer polaritonic band structures and open bandgaps in specific modes, even in materials like naturally abundant hBN that are not perfectly lossless.

The implications are significant. To name a few:

Enhanced light–matter interaction. By confining light more strongly and controlling its band structure, devices could couple more efficiently to quantum emitters, molecules, or other nanoscale systems.

Nanolight guiding. Clean bandgaps allow polaritons to be guided reliably over long distances, which is essential for integrated nanophotonic circuits.

Dispersion engineering. Just as photonic crystals revolutionized optical communications, polaritonic Fourier crystals could become building blocks for mid-infrared and terahertz technologies.

Moreover, the fabrication technique — holographic inscription of smooth Fourier patterns — is flexible and scalable, meaning it can produce one-dimensional, two-dimensional, or even quasiperiodic designs over large areas. This could greatly accelerate practical applications.

A new paradigm for manipulating light–matter hybrids at the nanoscale

At its heart, this research shows that when dealing with waves, sometimes gentleness works better than brute force. Instead of carving sharp nanostructures that tear polaritons apart, a carefully modulated Fourier landscape can guide them smoothly, giving rise to clean, tunable band structures.

By introducing the concept of polaritonic Fourier crystals, the authors have provided a new paradigm for manipulating light–matter hybrids at the nanoscale. It’s a step that could bring polaritons closer to real-world devices, bridging the gap between elegant physical concepts and usable nanophotonic technology.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.