## Optics and Photonics

The past two decades have seen a revolution in the science of
light. *Photonic* (light-manipulating) structures can now
be engineered with size comparable to the optical wavelength,
allowing us to exploit the wave nature of light to achieve a
variety of novel effects. Devices such
as photonic
crystals,
on-chip optical circuits,
and microcavity
lasers have important technological roles in communications,
sensing, and computing. They are also fruitful platforms for
basic scientific research.

### Topological Photonics

Researchers in photonics have long been inspired by a conceptual analogy between electromagnetic waves in patterned dielectric media and quantum mechanical electron waves in solids. In the late 1980s, Eli Yablonovitch and Sajeev John conceived of the photonic crystal as a photonic analog of a conventional electronic insulator. Photonic crystals are now a staple of nanophotonics, with applications ranging from low-loss optical resonators to slow-light wave-guides.

In recent years, researchers have begun to study photonic analogs of insulating materials known as topological insulators, which are mathematically distinct from conventional insulators. A topological insulator possesses a bandgap, but its bands are topologically distinct from the bands of a conventional insulator; it is impossible to smoothly deform one into the other, in the same way that a torus cannot be deformed into a sphere without tearing its surface. One consequence of this is that the surface of a topological insulator is populated by exotic edge states with unusual properties. In the photonic context, these edge states can be used to realize a fundamentally new class of electromagnetic wave-guides, which are able to transport light around sharp corners without backscattering.

Our group has made numerous contributions to this exciting
field. For instance, we showed theoretically how a periodic
lattice of coupled ring resonators can function as a photonic
topological insulator with tunable “topological phase
transitions”
[*Physical
Review Letters*
(2013), *Physical
Review B* (2014)]. We then used this theory to design
and implement a “topological pump”, an experiment that
directly probes and provides evidence for the fact that a
bandstructure is topologically nontrivial
[*Physical
Review X* (2015)]. More recently, we have been
exploring the intersection of nonlinear optics and topological
photonics
[*Physical
Review Letters*
(2016), *New
Journal of Physics* (2017)].

We have also collaborated extensively with experimental groups, at NTU and around the world, to implement systems such as topological spoof surface plasmons, optical “Weyl modes”, and more.

### Coherent Perfect Absorbers

*Coherent perfect absorption* is a phenomenon in which a
photonic structure absorbs all of a specially-designed incoming
optical wave. The absorption is “perfect”: all of the input
light energy is delivered into the material of the photonic
structure. (The energy subsequently flows out to an external
reservoir, e.g. in the form of heat or electric current.)

Theoretically, coherent perfect absorption is tied to the
time-reversal
symmetry of electromagnetism, which states that if one
process is allowed, then so is a time-reversed process which
reverses all currents, spins, and magnetic fields. Several
years ago, we published a theoretical paper pointing out that
since the field emitted by a laser is a purely-outgoing
electromagnetic wave, the time-reversal symmetry operation maps
a laser into an “anti-laser” structure, which exhibits perfect
absorption of a certain incoming wave (the time reverse of the
laser field)
[*Physical
Review Letters* (2010)].

Coherent perfect absorption is a generalization of the concept
of “critical coupling”. We demonstrated the principle
experimentally
[*Science*
(2011)]. Currently, we are interested in applying the
principle to complex optical media. For instance, we have
shown theoretically that in weakly-absorbing “random media”,
such as foam, paint, or tissue, it should be possible to use a
specially-designed input wave-front to achieve extremely
strong absorption, even if the medium is ordinarily “white”
[*Physical
Review Letters* (2010)].

We have also written a review article on the topic [*Nature Reviews Materials* (2017)].

### PT symmetry and Non-Hermitian Photonics

Recently, there has been significant scientific interest in the properties of photonic devices containing optical amplification (gain) and/or absorption (loss). Such systems are said to be “non-Hermitian”, as they do not conserve the electromagnetic energy flowing through them. Although non-Hermitian systems have long been treated as imperfect variants of “Hermitian” (energy-conserving) systems, researchers now realize that they can also possess features completely different from the Hermitian case.

For instance, when gain and loss are *simultaneously*
present in equal and opposite amounts in two halves of a
photonic structure, it is said to be PT (parity-time)
symmetric. The exotic properties of PT symmetric photonic
structures have been studied in great detail by many research
groups. Several years ago, we showed theoretically that by
tuning the frequency and/or the gain and loss in a PT
symmetric structure, one can induce a
spontaneous
symmetry breaking transition between PT symmetric
scattering eigenmodes (which conserve energy) and PT broken
pairs of eigenmodes (one damping and one amplifying)
[*Physical
Review Letters* (2011)]. In the most extreme case, a
PT symmetric structure can simultaneously function as a
coherent perfect absorber and a laser!

We have also been working on bringing the ideas of band
topology into non-Hermitian photonics. For instance, we have
theoretically analyzed a novel class of topological edge
states that occur only in non-Hermitian lattices
[*Physical
Review Letters* (2017)], and we have experimentally
implemented a non-Hermitian version of a topological pump
[Physical
Review B (2017)].