Publish or perish

April was an unusually busy month for me for proof-checking, with five papers published:

Moiré Lattice in One-Dimensional Synthetic Frequency Dimension

This work led by collaborators at Shanghai Jiao Tong University analyzes frequency domain synthetic photonic lattices from a transfer matrix perspective, finding that the interplay between an incommensurate time modulation and off-resonant ring modes (not captured by the usual tight binding approximation) can be used to generate flat bands in a simple system of two coupled ring resonators.

Band relaxation triggered by modulational instability in topological photonic lattices

This was a long-delayed follow-up to our work on modulational instability in topological photonic lattices which we initiated during the start of the covid pandemic. Initially we had tried to understand the nonlinear wave dynamics in terms of an effective thermalization process, but it turned out that we could not observe any genuine thermalization within an experimentally-feasible time scale. This paper presents a detailed characterization of the long-lived pre-thermal state that is generated by the modulational instability. While our studies in this area are entirely theoretical / numerical, the dynamics of complex multimode nonlinear optical systems are now starting to be studied in a variety of experimental platforms, reviewed in Nature Physics last year.

Unravelling quantum chaos using persistent homology and Pseudospin-2 in photonic chiral borophene

I posted about these two papers when they were posted to arXiv late last year. The former made it into Physical Review E after a round of revisions. The latter was rejected by Nature Communications before being resubmitted to Photonics Research and accepted for publication after one round of revisions.

Topological data analysis and machine learning

This was a challenging review to prepare, given the need to concisely capture both the surprisingly-long history of applications of topological data analysis to physics (from the early 2000s) and a more recent wave of papers combining TDA with machine learning techniques. While it is far from perfect I hope it can still be a useful anchor for ongoing research in this area.

I'm hoping to have the next set of (now overdue) drafts finished and on arXiv sometime in June. Watch this space!

The best of both worlds

A wealth of photonic devices including precision sensors and quantum light sources depend on strong light-matter interactions.

Two leading platforms for enhancing (usually weak) light-matter interactions are photonic crystal waveguides and whispering gallery resonators.

In photonic crystal waveguides light is scattered back and forth by a periodic wavelength-scale modulation of the dielectric constant. This multiple scattering reduces the speed at which light pulses propagate, resulting in slow light that has more time to interact with matter. While photonic crystals can be used to slow or even stop light, the enhanced interaction strength is accompanied by increased sensitivity to scattering losses due to imperfections and roughness in the periodic modulation, which limits their performance in practical applications.

On the other hand, whispering gallery resonators guide light along the boundary large (many wavelengths in size) dielectric particles. These boundaries can be exceptionally smooth, resulting in ultralow scattering losses, allowing light to circulate millions of times before being lost from the cavity. However, one is limited to cavity sizes somewhat larger than the operating wavelength and cannot confine light to the nanoscale volumes achievable using photonic crystals.

Published yesterday in Nature Photonics, a collaboration between researchers at NIST and the University of Massachusetts report a novel hybrid whispering gallery microring resonator. The outer edge of the microring is smooth, leading to whispering gallery modes with high quality factors. The inner edge of the microring is periodically modulated, forming a one-dimensional photonic crystal that reduces the group velocity of the whispering gallery modes by a factor of 10. Moreover, defects in the inner edge photonic crystal can be used to confine the whispering gallery modes to a small part of the ring, enhancing their interaction with localized emitters such as quantum dots.

The exceptional lifetimes of whispering gallery modes combined with the ability to tailor modal properties using periodic modulations of the inner edge makes this a highly promising platform for a variety of nonlinear optics applications.

 

Tying knots in energy bands

The generation of knots in optical systems has fascinated me since my PhD days. Influential early works focused on optical vortex knots. Optical vortices trace out curves in 3D space; in certain circumstances the curves trace out knotted trajectories. Influential early works include the generation of knotted vortices in light beams using a spatial light modulator, large-scale statistical analysis of the probability of knots forming in random optical beams, and the spontaneous formation of vortex knots in the tails of self-trapped nonlinear optical beams. 

More recently, with the surge in interest in topological photonics, interest has turned to the study of knots in other objects, including the energy bands of periodic systems.

An article just published in Nature reports the observation of braided energy bands using a pair of coupled modulated ring resonators. Braids are closely related to knots (knots can be obtained by connecting the ends of non-trivial braids). Braids are more natural to study in the context of band structures, owing to the periodicity of the Brillouin zone.

In order to generate knots or braids, one needs to consider curves in a 3D space. In this work, one of the dimensions is provided by the momentum (k) space, while the other two dimensions are played by the real and imaginary parts of the complex energy eigenvalues E. Using phase and amplitude modulators it is now possible to implement near-arbitrary non-Hermitian Hamiltonians using coupled ring resonators, allowing exquisite of the trajectories of the energy eigenvalues in the complex plane.

To observe the energy band braiding, the authors probed their ring resonator system using a continuous wave laser beam, measuring the time-dependent transmission, with time playing the role of k. Scanning the frequency of the probe beam, a peak in transition occurs at frequencies corresponding to resonances (real parts of the eigenvalues) of the system, with the linewidth of the resonance corresponding to the imaginary part of the eigenvalue. This allows the reconstruction of various braids, including those corresponding the simplest Hopf link (two threaded rings) and more complex objects such as trefoil knots.