**The ›NOA‹ collaborative research centre (CRC) has been based at the University of Jena since 2019. NOA stands for ›Nonlinear Optics down to Atomic Scales‹. The CRC is managed by physicist Prof. Dr Ulf Peschel and chemist Prof. Dr Stefanie Gräfe. In this interview, they describe the questions addressed by the research network and explain why scientific knowledge needs a theoretical foundation.**

Interview by Ute Schönfelder

**What is NOA all about? **

*Peschel: *We’re investigating the fundamental processes of light-matter interaction – right down to the atomic level. In other words, we’re seeing what happens when light particles (photons) interact with matter particles (electrons). The light fields we use are so strong that the matter is changed by the light. The nonlinear processes involved depend on the intensity of the light.

The interesting thing about the interaction is the fact that the matter isn’t just affected by the light; the light itself is also affected by the excited matter. So, we can practically use light to control light. We’re looking at both aspects at the CRC: We’re manipulating matter with intense light; and we’re generating and controlling light by letting it interact with the matter. And we’re studying everything on very small scales.

**What specific questions do you want to answer?**

*Gräfe:* We’re interested in a number of fundamental questions. For example, we’ve long known how nonlinear interactions between light and matter work (e.g. in nonlinear crystals); for these effects, it seems to be important that the materials have a very homogeneous structure (i.e. a very regular, evenly distributed atomic structure). We’re now interested in finding out how small these homogenous structures can be to enable a nonlinear interaction, and how this interaction is influenced by unevenness, roughness and individual defects. If I have a material that only consists of one atomic layer, for example, each additional atom has an enormous impact. We’re also interested in effects that can only be achieved on these extremely small scales. For example, electrons can tunnel from atomically small metal tips to neighbouring tips and then overcome energy barriers, which would not be possible according to the theories presented in classical physics. And we want to investigate how this phenomenon can be controlled or even operated in a targeted manner using light. If we can understand and control such processes, we might even be able to use them for specific purposes in the future.

**Why are nanomaterials so interesting and important in research? **

*Peschel: *Technical components have been getting smaller and smaller for a long time – to save material and increase efficiency – but we’re interested in much more than just this aspect. Nanostructured materials simply have completely new properties. For example, we can use nanostructures to make materials ›invisible‹ or give them new colours and so on. These metamaterials have been researched and developed for around 20 years, but our materials are now even smaller – far below the wavelength of visible light. In these dimensions, at the atomic level, quantum mechanical effects are playing an increasingly prominent role. We want to understand how these effects determine the properties of the materials.

*Gräfe: *One highly specific application of nanomaterials is chip technology, where we now have standard structure sizes of 13 nanometres – that’s about 130 atoms. The latest feature are just seven nanometres wide, so only 70 atoms. And 3-nanometre technology is expected from 2022 – only 30 atoms wide. The smaller these structures become, the more relevant and influential each atom becomes. For such applications, we have to know how the atomic geometries affect the material properties and how we can control them.

**How big or small are the structures you are examining in your CRC projects? **

*Peschel: *The metallic, plasmonic nanostructures that we’re using in various projects at our CRC (see the articles Ultimativ dünn: Halbleiter aus einer Atomlage, Wenn Licht und Elektronen gemeinsam leuchten, Chemische Reaktionen in Großaufnahme) are around 200 nanometres in size. The important factor for nonlinear optical effects is usually the distance between the nano-antennas, where we work within a range of up to five nanometres – that’s the thickness of a lipid bilayer, the basic structure of biomembranes. If we magnified this distance to one centimetre to get a better idea of the size, it would be like a centimetre along the route between Jena and Weimar.

**Why do we need nonlinear optical methods to examine such small structures? **

*Peschel: *Nowadays, a number of methods are being used to research atomic and other very small structures. The advantage of nonlinear methods is that they fall well below the resolution limits of common optical methods that depend on the wavelength of the radiation used. In other words, we can now ›see‹ much smaller structures.

In addition, much more information about the structures can be obtained by observing nonlinear interactions between the light field and material than by studying simple linear interactions. So, we’re practically expanding our range of information sources.

*Gräfe: *What’s more, there are usually fewer disturbing background effects with nonlinear methods.

**Are there also resolution limits for nonlinear optical methods? **

*Gräfe: *Yes, there are. But they’re not as absolute as their linear counterparts, such as the Abbe diffraction limit (see box on the left). On the atomic scale on which we work, quantum effects play a role that affects the interactions with light. However, we don’t yet know this in detail. This is one of the questions we want to answer at our CRC.

*Peschel: *The answer to this question isn’t so much about the physical resolution limits; the limitations of our theoretical models and understanding of the phenomena on such scales are much more important for what we can see and identify. After all, we can no longer ›observe‹ the phenomena directly; we obtain information from various spectra of light and have to interpret them.

**We’ve only been able to experiment with nonlinear optical phenomena since the invention of lasers that can bundle light in the required intensity. In addition to laser technology, what role does theoretical research play? **

*Peschel: *As we’ve already mentioned, an essential one. The challenge at the moment is to consistently describe light-matter interactions at the atomic level, considering both the optical and quantum mechanical effects. As theorists, we develop models and our experimentally working colleagues provide data. Together we then see whether we can use the models to plausibly explain the data.

Our findings are always made in small steps and the purpose of theory is to generate a basic understanding. That’s why we need simple models to give us an idea, so that we can develop simulations and test them experimentally. Theory is absolutely essential for our basic understanding of the physics involved.

## The Abbe diffraction limit

*In 1873, Ernst Abbe developed his famous formula to describe the diffraction limit of a microscope, d = λ / 2n•sinα.In his formula, d is the achievable resolution as the minimum distance required between two lines for them to be discernible as two separate lines under a microscope, λ is the wavelength of light, n is the refractive index of the medium between the object and objective, and α is the half-angle of the cone of light entering the objective from one point of the object. *

*For the term n•sinα, Abbe introduced the concept of numerical aperture (NA), which describes a system’s ability to focus light. Abbe’s formula is therefore often written as d = λ / 2 NA. The maximum numerical aperture for the air between the object and objective is 1. For visible light with a wavelength of λ ≈ 400 nm, the maximum achievable resolution is therefore d ≈ 200 nm.*

*However, numerous methodological approaches have since enabled resolutions well below the limit established by Ernst Abbe.*