Nonlinear X-ray Optics

At high radiation intensities, it possible for light to interact with light via a medium through nonlinear interactions: photons can interact with each other, which can lead to a change in their energy and momentum. However, nonlinear interactions in the X-ray range are virtually unexplored due to their extremely small cross sections. Only recent advances in the development of X-ray sources, namely the realization of the X-ray free-electron laser (XFEL), has opened the door to this research field. We investigate fundamental nonlinear X-ray matter interactions using the coherent, high-intensity pulses of XFELs. Recently, we have performed experiments at both so far existing XFELs, located at SLAC National Laboratory and the SPring8 Research Center in Japan. In particular, we have observed the mixing of optical light with X-rays, nonlinear Compton scattering in the X-ray range, X-ray second harmonic generation and two-photon X-ray absorption.

Schematic of the setup used for the NL Compton experiment. The FEL beam (green) gets focused to a 100nm spot by reflective mirrors onto a solid beryllium target. Photons get nonlinearly scattered at electrons in the Be sample and emit radiation at the sum frequency (blue). The nonlinear radiation is angularly resolved using an array of 2D detectors.

Nonlinear X-ray Compton Scattering

The most fundamental nonlinear light-matter interaction is the the simultaneous scattering of two photons at an electron into a single photon at the sum of their frequencies. For X-ray wavelengths, the quantum aspect of the process becomes measurable in form of a red-shift in the wavelength of the nonlinearly scattered photon [Compton scattering]. Using pulses of the LCLS X-ray free-electron laser, we have recently succeeded in observing nonlinear X-ray Compton scattering for the first time. For X-ray wavelengths, the quantum aspect of the process becomes of importance and the interaction is in the regime of nonlinear quantum electrodynamics (NLQED), an area of physics, which has been experimentally rarely tested so far.

X-ray Second Harmonic Generation

Second harmonic generation (SHG) of visible light was first demonstrated in 1961 and meanwhile has led to numerous applications in many fields of science. Using XFEL radiation, we have recently observed the first second harmonic generation at X-ray wavelengths. We used a diamond crystal in a Bragg geometry for the 2nd harmonic in order to fulfill the phase matching condition.

X-ray Two-Photon Absorption

X-ray Optical Mixing

We have recently demonstrated the mixing of optical with X-ray radiation, i.e. the sum-frequency generation of the optical and X-ray photons. The process is, in essence, optically modulated X-ray diffraction: X-rays inelastically scatter from optically induced charge oscillations. This method allows to investigate the microscopic details of optical interactions on an atomic scale, more specifically, the optically induced microscopic field can be determined through the close relation to the induced charge.

Anomalous Nonlinear X-ray Compton Scattering

image: courtesy Greg Stewart, SLAC

What did we do?

In this experiment we have investigated one of the most fundamental interactions between X-rays and matter. More specifically, we have observed a process where two X-rays photons (particles of light) interact at the same time with an atom. During this process the two photons are converted into a single higher-energetic X-ray photon. Under “normal” circumstances such a conversion does not happen, but we know from experiments using visible light that it can occur for extremely high light intensities. This process was discovered at optical wavelengths in the 1960s using a (back then) revolutionary novel device: a laser. Since then it has been heavily exploited in research and is being used in almost every laboratory that uses lasers, even some readily available laser pointers are based on this technology. Because the rate of the converted higher-energy photons depends nonlinearly on the incoming light intensity, these interactions are also called “nonlinear processes”. However, until recently it has not been possible to observe such interactions at X-ray wavelengths because X-rays sources that can produce sufficiently high intensities have not existed.

 

X-ray free-electron lasers (XFELs)

Therefore, we had to use a completely new source of X-rays, a so-called X-ray free-electron laser (XFEL) for this experiment. These lasers are nothing like a “typical” laser, particularly in that they are enormous machines with a length of more than a kilometer. They have only recently become operational after decades of development and to this day only two of them exist worldwide, one at the SLAC National Accelerator Laboratory in California (called the LCLS) and the other one in Japan (called SACLA). These XFELs are capable of generating radiation with unprecedented properties. For our experiment we took advantage of the fact that that they can produce extremely intense X-rays, which are more than a trillion (one thousand billion or 10¹²) times brighter than the sun.

Experiments at XFELs usually require a broad range of expertise in many different areas. The experimental team for this particular experiment consisted of researchers from SLAC, Stanford University, Bar-Ilan University in Israel and the University of Nebraska, Lincoln.

 

Experiment

During the experiment we generated an extremely intense X-ray beam by focusing the full XFEL output from the LCLS into an extremely small spot of only 100 nm (1 nm = 1 billionth of a meter). The resulting X-ray intensity is equivalent to a scenario where all of the sun’s radiation hitting the Earth's surface would be combined into a spot size of approximately the diameter of a human hair; however we directed the X-rays onto a small piece of beryllium metal. We needed such extreme intensities to improve the chances of both of the two photons meeting up at exactly the right place and exactly the right time on one of the many atoms that are illuminated.  Even so, the probability that the nonlinear interaction occurs on any given atom is less than winning the lottery. This is because already “normal” interactions using X-rays are very weak (hence X-rays are mostly transmitted through many materials), but in order to be able to observe nonlinear X-ray matter interactions requires significantly more intensity than for optical wavelengths (roughly 100 million times more intense).

The experiment was the very first investigation of this kind, which means that we were entering what you would call “Neuland” (uncharted territory) in German. From theoretical predictions and extrapolations of previous optical nonlinear experiments and linear X-ray interactions, we were able to predict the expected signal.

 

Unexpected Results

However, the signal that we observed did not agree with what you would expect from the existing theory and extrapolations. During the X-ray process an electron can be ejected from the atom at the same time that the higher-energy photon is emitted. The X-ray and electron must share their energy such that their sum is equal to the two initial X-ray photons.  Our measurements did not agree with our best theoretical predictions for how that energy is shared. Particularly, the energy of the converted higher-energy X-ray photons was much lower than expected! This shows that the physics of the interaction seems to be much richer and even much more interesting than initially anticipated.

When we first proposed to do this experiment, we got a lot of questions asking: “Why do you want to do this experiment, all of this is already known”. The fact that our measurements do not agree with the initially expected results just shows the tremendous value of basic science. It is extremely exciting to work on investigations of such fundamental processes. As one anonymous peer reviewer wrote: “Ultimately, as this becomes better understood, it will appear in all text books on X-ray physics and nonlinear optics”.

 

Outlook

This experiment is just the beginning. We will soon perform even more sophisticated experiments with better instrumentation to better understand this newly discovered phenomena. If our new understanding of this fundamental process can be confirmed by those experiments, it can have significant impact on future experiments that are performed with high X-ray intensities (most experiments at XFELs) and can lead to novel diagnostic methods of matter.

 

A few more details on the underlying physics

It has been shown that when X-rays interact with solids that the atomic electrons can behave almost as if they were free from the atoms that bind them. However, our experimental results indicate that for the nonlinear interaction which we have observed, the binding of the electrons plays an oversize role compared to the ordinary linear interactions. This is all the more astonishing since the energy that is required to break the bond of the electron to the beryllium atoms that we studied is a very small fraction of the energy that a single X-ray photon packs.

 

Background: What are X-rays good for?

In physics, X-rays are routinely used to take a “deep look” into matter. This is because X-rays are transmitted through many materials and also because they have such a small wavelength that it allows us to resolve matter down to size of the constituent atoms. One of the most famous discoveries using X-rays is that the atomic structure of DNA forms a double helix. Overall 15 Nobel prizes have been awarded in the field of X-rays (and even up to 28 Nobel prizes counting discoveries that indirectly use X-rays).