# Research

## Photonic Weyl Points

Weyl points are band degeneracies that occur in the momentum space of 3D periodic materials and are enforced by an integer topological charge known as the Chern number. Weyl materials are associated with a range of interesting physical phenomena directly connected to their non-trivial topological charge. For example, due to the bulk-boundary correspondence principle, these materials exhibit unique surface states whose dispersion does not span the entire Brillouin zone but instead terminates at Weyl points with opposite charges. Weyl points can carry arbitrary integer charges, and those with a charge greater than one are known to occur in the presence of certain non-symmorphic symmetries found in chiral structures.

In the photonic domain, Weyl points may enable the creation of large-volume single-mode lasing devices. Furthermore, they can mediate unique long-range interactions between embedded quantum emitters. However, due to fabrication challenges, experimental realization of photonic Weyl points at near-IR wavelengths has remained elusive.

Our work on Weyl points addressed these challenges by experimentally observing charge-2 Weyl points at mid- and near-infrared wavelengths in a chiral woodpile photonic crystal. This photonic crystal was micro-printed using a low refractive index material via two-photon polymerization and was characterized using FTIR spectroscopy. Additionally, we experimentally demonstrated that when the protective symmetry is broken, a charge-2 Weyl point splits into charge-1 Weyl points. Importantly, this splitting can be restricted to high-symmetry directions in momentum space, resulting in unprecedented control over the location of Weyl points.

Recently, we also explored the extent to which the topology and chirality of Weyl points are meaningful when the underlying momentum-space manifold is rendered non-orientable.

In the photonic domain, Weyl points may enable the creation of large-volume single-mode lasing devices. Furthermore, they can mediate unique long-range interactions between embedded quantum emitters. However, due to fabrication challenges, experimental realization of photonic Weyl points at near-IR wavelengths has remained elusive.

Our work on Weyl points addressed these challenges by experimentally observing charge-2 Weyl points at mid- and near-infrared wavelengths in a chiral woodpile photonic crystal. This photonic crystal was micro-printed using a low refractive index material via two-photon polymerization and was characterized using FTIR spectroscopy. Additionally, we experimentally demonstrated that when the protective symmetry is broken, a charge-2 Weyl point splits into charge-1 Weyl points. Importantly, this splitting can be restricted to high-symmetry directions in momentum space, resulting in unprecedented control over the location of Weyl points.

Recently, we also explored the extent to which the topology and chirality of Weyl points are meaningful when the underlying momentum-space manifold is rendered non-orientable.

## Theory of Topological Insulators

Topological insulators are a fascinating class of materials that have recently emerged as a prominent subject of study in condensed matter physics. They represent new phases of matter that possess unique properties at their surfaces, hinges, edges or corners, distinct from those in the bulk. This results ultimately from the underlying non-trivial topology of the electronic band structure rather than any specific material property. In the last decade, many of these topological ideas have been extended to other systems that host wave-like excitations (such as light propagating in photonic crystals and sound waves in acoustic metamaterials). I am interested in extending the theory of topological phases to photonic systems, and finding novel occurrences of topology in condensed matter physics.

In our recent work, we developed a complete classification of topological phases in photonic crystals under crystalline symmetries and proposed a design strategy based on this classification. In a different paper, we resolved a long-standing debate on whether the concept of electric polarization is meaningful in topological insulators.

In our recent work, we developed a complete classification of topological phases in photonic crystals under crystalline symmetries and proposed a design strategy based on this classification. In a different paper, we resolved a long-standing debate on whether the concept of electric polarization is meaningful in topological insulators.

## Localization in Photonic Quasicrystals

Anderson localization is the ubiquitous phenomenon involving the localization of waves and the cessation of wave transport in disordered media. In three dimensions, a sharp transition separates the extended and localized regimes as a function of the strength of disorder. A similar transition can also occur in one-dimensional systems when random disorder is replaced by quasiperiodicity. In photonics, the localization of light is particularly interesting, as it finds applications in various areas, including random nanolasing, the formation of photonic stop bands, the creation of high-Q nanocavities, and the reduction of crosstalk between components in telecommunication devices.

In our recent work, we demonstrated localization/delocalization transitions in one-dimensional photonic quasicrystals comprising alternating layers of silicon and silica. In particular, we observed a surprising and counterintuitive phenomenon within this system: a second transition of certain localized states to a delocalized regime upon increasing quasiperiodic disorder. The degree of localization of photonic states has a measurable effect on the transmission of light through these structures, enabling a clear experimental demonstration of these transitions.

In our recent work, we demonstrated localization/delocalization transitions in one-dimensional photonic quasicrystals comprising alternating layers of silicon and silica. In particular, we observed a surprising and counterintuitive phenomenon within this system: a second transition of certain localized states to a delocalized regime upon increasing quasiperiodic disorder. The degree of localization of photonic states has a measurable effect on the transmission of light through these structures, enabling a clear experimental demonstration of these transitions.

## Bound States in the Continuum

Photonic crystals are lattices of dielectric materials, such as glasses or semiconductors, that enable fine control over the properties of light. They are known to possess band gaps, making them act as perfect mirrors for a range of frequencies. These band gaps have traditionally been utilized for trapping light to defects, creating one-dimensional waveguides and zero-dimensional nanocavities. However, the reliance on a band gap limits the choice of materials to those with a sufficiently high refractive index.

We proposed a new method for trapping light within nanocavities embedded in two-dimensional photonic crystals that lack band gaps. We demonstrated that it is possible to engineer the photonic crystal and nanocavity such that a symmetry mismatch with the photonic crystal's modes prohibits light within the cavity from leaking away. This state of light is an example of a "bound state in the continuum", which is a localized state that co-exists with a continuum of propagating states of the photonic crystal. Furthermore, we showed that such states can be utilized to create slow-light modes in complex photonic crystal fibers. Our work enables the construction of nanocavities within photonic crystals made of versatile, low-index materials like glasses and polymers.

We proposed a new method for trapping light within nanocavities embedded in two-dimensional photonic crystals that lack band gaps. We demonstrated that it is possible to engineer the photonic crystal and nanocavity such that a symmetry mismatch with the photonic crystal's modes prohibits light within the cavity from leaking away. This state of light is an example of a "bound state in the continuum", which is a localized state that co-exists with a continuum of propagating states of the photonic crystal. Furthermore, we showed that such states can be utilized to create slow-light modes in complex photonic crystal fibers. Our work enables the construction of nanocavities within photonic crystals made of versatile, low-index materials like glasses and polymers.