An advanced mathematical model that can describe high-energy interactions
between light and matter has been developed by two RIKEN researchers and a
collaborator. The approach could be extended to offer new insights in other
areas of physics.

High-harmonic generation is a powerful technique that converts laser light
from one wavelength, or color, to another (Fig. 1). Put simply, it converts
a low-energy, long-wavelength photon into multiple higher energy, shorter
wavelength photons.

High-harmonic generation has several applications. For example, it offers a
way to create table-top sources of extreme ultraviolet or X-ray light using
lasers, rather than expensive synchrotron facilities. High-harmonic
generation can also produce ultrashort light pulses, as short as one
attosecond (10−18 second) or maybe even one zeptosecond (10−21 second),
which are useful for imaging extremely rapid processes such as those that
occur in atoms. But high-harmonic generation is inherently difficult to
model mathematically, and thus understand fully.

Now, Hidetoshi Taya and Masaru Hongo from the RIKEN Interdisciplinary
Theoretical and Mathematical Sciences (iTHEMS) Program, together with their
colleague Tatsuhiko Ikeda from the University of Tokyo, have developed an
analytical approach to high-harmonic generation in the so-called
non-perturbative regime for the first time.

Perturbation theory is a powerful mathematical tool that starts with a
simplified, but mathematically solvable, version of a problem. It then adds
small variations, or perturbations, to achieve a more accurate answer.

However, not all processes are amenable to perturbation theory. "Many
physical phenomena can't be analyzed using the standard perturbative
approach," says Taya. "Thus, establishing theoretical approaches for
non-perturbative regimes is one of the biggest challenges in theoretical
physics."

Taya, Hongo and Ikeda used mathematical techniques that had not previously
been applied to high-harmonic generation. Their approach revealed the
microscopic mechanism that converts incoming intense light into high
harmonics, and enabled any experimental observable to be calculated with
just a pen and paper—no need for computers.

This research could help shed light on several intriguing experimental
results that have features not exhibited by high-harmonic generation in the
perturbative regime.

The same mathematical tool could also be useful in other areas of physics.
"I'm particularly interested in application to the physics of high-energy
particles," says Taya. "For example, our theory can be applied to quantum
electrodynamics—the fundamental theory for electrons and photons. It
predicts that high-harmonic generation will occur not only in materials but
also in a vacuum—an interesting possibility that could be tested with future
intense laser facilities."

## Reference:

Hidetoshi Taya et al, Analytical WKB theory for high-harmonic generation and
its application to massive Dirac electrons, Physical Review B (2021).
DOI: 10.1103/PhysRevB.104.L140305

Tags:
Physics