  Disordered systems exhibit universal excitation, referred to as the boson
peak, in the terahertz region. Meanwhile, the so-called fracton is expected to
appear in the nanoscale region owing to the self-similar structure of monomers
in polymeric glasses. We demonstrate that such excitations can be detected
using terahertz spectroscopy. For the interaction between terahertz light and
the vibrational density of states of the fractal structure, we formulate an
infrared light-vibration coupling coefficient for the fracton region.
Accordingly, we show that information concerning fractal and fracton dimensions
appears in the exponent of the absorption coefficient. Finally, using terahertz
time-domain spectroscopy and low-frequency Raman scattering, we experimentally
observe these universal excitations in a protein lysozyme system that has an
intrinsically disordered and self-similar nature in a single supramolecule.
These findings are applicable to disordered and polymeric glasses in general
and will be key to understanding universal dynamics of disordered systems by
terahertz light.
