What's new in topological photonics

Quite a few significant pre-prints relevant to different aspects of topological photonics appeared on arXiv this week:

Nonlinear topological photonics

Combining strong single photon interactions with topological bands is being hotly pursued as a means of creating fractional quantum Hall states of light. In contrast to their electronic counterparts, photons can be lost due to absorption or scattering. Researchers from Yale University ask whether photonic fractional quantum Hall states stable against losses. It turns out the simplest way to protect against losses (by injecting more photons) doesn't work for these exotic topological states due to their nonlocality: photon loss can generate "fractional" holes in the state, whereby half a photon is lost from one part of the system, and half a photon from another part. Due to this nonlocality, adding a single photon to one part of the system is insufficient to restore the ideal fractional quantum Hall state.

In the weak mean field interaction regime, a collaboration between Russia, Germany, and Portugal has developed theory for edge solitons supported by quadratic nonlinear media. Such solitons comprise a bound state between some fundamental frequency and its second harmonic. Because of the need to take two very different propagation frequencies into account, modelling must be based on the full continuum paraxial equation, rather than simpler tight binding models.

Performance of topological photonic crystal waveguides

As I mentioned a few weeks ago, an exciting trend is that research groups not specifically focused on topological photonics are starting to become interested in topological designs. Researchers from the Niels Bohr Institute report full wave simulations of photonic crystal waveguides for quantum photonics, comparing the performance of their non-topological glide-plane waveguide against topological valley Hall waveguides. The valley Hall waveguides can exhibit stronger coupling between quantum emitters and the optical modes, and with lower scattering losses due to fabrication imperfections. The authors emphasise that the lower losses are not due to the topological protection, but rather due to the differing modal profile, which is less strongly localized to the air-dielectric interfaces responsible for the losses.

Topological phases using orbital hybridization

Most designs for topological photonic systems are based on suitably-designed coupling between identical "atoms" formed by modes of a fixed symmetry bound to waveguides or resonators. This is because modes with different symmetries typically have very different energies or propagation constants, making the interaction (or hybridization) between them weak. But by suitable fine-tuning it is possible to engineer near-degeneracies between modes with different symmetries, opening up new possibilities for controlling photonic band structures. A proof of concept demonstration using one-dimensional optical waveguides was published in PRL a few months ago. Now a team from ITMO University have predicted that hybridization between s- and d-type orbital modes of two-dimensional lattices can give rise to higher order topological phases. Since this approach does require fine-tuning to ensure the degeneracy between the different orbitals, microwave implementations will be a lot easier than optical frequency ones.

Non-Hermitian topology without gain and loss

A pet peeve of mine regarding many studies of non-Hermitian topology is that they consider Hamiltonians that are intrinsically unstable due to the presence of amplifying modes. To determine the fate of these amplifying modes, higher-order corrections such as gain saturation should be taken into account. The simplest solution - add some overall loss to make the system stable - tends to make any topological modes strongly lossy, which is undesirable for applications. 

 

An alternate solution is to come up with conservative systems that can somehow support non-Hermitian topological phenomena. One example we found was simply Maxwell's equations, where non-Hermiticity emerges because the inner product depends on the local constitutive parameters of the medium. 

 

This week, researchers from IFW Dresden report that the reflection matrix describing scattering of waves from insulating (gapped) systems could be a simple setting for observing non-Hermitian topological effects. In another study, researchers from NTU Singapore show how non-reciprocal coupling can be designed to achieve non-Hermitian topological phases with purely real spectra.