The coupling of internal photon degrees of freedom like frequency, spatial mode, and orbital angular momentum generates extra dimensions in the photonic synthetic dimension in addition to real space. Utilizing low-dimensional platforms that offer advantages in terms of engineering and control, this strategy is a potent tool for investigating novel physical phenomena that are exclusive to high-dimensional systems.
Band structure measurements can reveal a lot of nontrivial high-dimensional physics aspects. Existing measurements of band structure are restricted to one-dimensional Brillouin zones or one-dimensional subsets of two- or three-dimensional Brillouin zones in the photonic synthetic frequency dimension.
Subsequently, there is a requirement for a procedure that empowers band structure estimations across the whole multi-faceted Brillouin zone. Researchers can gain insight into the distinctive behaviors that emerge in high-dimensional regimes and a deeper comprehension of the underlying physics thanks to this method.
“The essence of the synthetic dimension is the possibility of expanding our toolbox in high-dimensional physics. We feel that multi-dimensional band structure spectroscopy marks a critical milestone in this direction, given the amount of physical information inherent in band structures. It will aid our understanding and management of high-dimensional systems and may serve as inspiration for optical devices with novel features.”
Professor Shanhui Fan from Stanford University
In a recent Light publication, In the photonic synthetic frequency dimension, such multi-dimensional band structure spectroscopy has been reported by a Stanford University team led by Professor Shanhui Fan. The experimental platform was a photonic resonator that was subjected to dynamical modulation by the researchers. With this single resonator, a multi-dimensional lattice in the synthetic frequency dimension was created with multiple modulation frequencies.
To gauge the band construction of this cross section, the resonator was energized by a laser with tunable recurrence, and the time-subordinate transmission signal was gathered by a photodetector. The transmission spectrum’s resonance features were used to calculate the band energies as the frequency of the input laser was swept. The researchers were able to pinpoint the entire multi-dimensional Brillouin zone’s lattice band structure by adjusting the relative phases of the various modulation frequencies.
Utilizing this multi-faceted band structure spectroscopy, the specialists estimated the two-layered band design of a non-Hermitian framework and disclosed a few properties connected with the nontrivial eigenvalue geography. The non-Hermitian skin effect, an exotic phenomenon in which all the eigenstates of a finite non-Hermitian system are sexponentially located on the boundaries, is linked to these properties, which makes them even more intriguing.
We are now one step closer to realizing the potential of non-Hermitian systems thanks to the demonstration of these properties.
The findings of the researchers emphasize the significance of multi-dimensional band structure spectroscopy as a method for delving into the mysteries of high-dimensional systems and ultimately propelling advancements in physics and engineering.
“The essence of the synthetic dimension lies in the potential to expand our toolbox in high-dimensional physics,” the researchers stated. We believe that multi-dimensional band structure spectroscopy is a significant step in this direction due to the abundance of physical information contained within the structures. It will make it easier for us to understand and manipulate high-dimensional systems, and it might serve as an inspiration for optical devices with novel functions.”
The spectroscopic method’s adaptability to more complex systems was also emphasized by the researchers.
More information: Dali Cheng et al, Multi-dimensional band structure spectroscopy in the synthetic frequency dimension, Light: Science & Applications (2023). DOI: 10.1038/s41377-023-01196-1
