There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables 1 . In the case of the Hamiltonian operator, this requirement not only implies real eigenenergies but also guarantees probability conservation. Interestingly, a wide class of non-Hermitian Hamiltonians can still show entirely real spectra. Among these are Hamiltonians respecting parity‐time (PT) symmetry 2‐7 . Even though the Hermiticity of quantum observables was never in doubt, such concepts have motivated discussions on several fronts in physics, including quantum field theories 8 , nonHermitian Anderson models 9 and open quantum systems 10,11 , to mention a few. Although the impact of PT symmetry in these fields is still debated, it has been recently realized that optics can provide a fertile ground where PT-related notions can be implemented and experimentally investigated 12‐15 . In this letter we report the first observation of the behaviour of a PT optical coupled system that judiciously involves a complex index potential. We observe both spontaneous PT symmetry breaking and power oscillations violating left‐right symmetry. Our results may pave the way towards a new class of PT-synthetic materials with intriguing and unexpected properties that rely on non-reciprocal light propagation and tailored transverse energy flow. Before we introduce the concept of spacetime reflection in optics, we first briefly outline some of the basic aspects of this symmetry within the context of quantum mechanics. In general, a Hamiltonian HD p 2 =2mCV(x

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Observation of parity–time symmetry in optics

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.

Parity–time-symmetric whispering-gallery microcavities

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.

Parity–time synthetic photonic lattices

Low energy ion implantation induced intermixing has been used to selectively blueshift 1.55μm InP/lnGaAs/InGaAsP material. Intra-cavity electro-absorption modulators have been fabricated using this method. Integrated laser-modulator device parameters show no indication of degradation following the intermixing process.

Post-growth processing of 1.55 um InP/InGaAs/InGaAsP material for integrated laser-modulator device fabrication

In this paper, we present an analysis of conduction in silicon nanocrystals (nc-Si) of small area nanopixels in dark conditions and under illumination. The photosensitive layer of the analyzed devices is mad up a small number of (nc-Si) embedded in SiO2. The interface between the oxide and the silicon substrate is shown to play a significant role in the conduction process: we observed that the presence of (nc-Si) situated inside the oxide, at some angstroms from the interface with the active region, induced discrete variations in the current. In dark conditions the transport of electrons is dominated by trap-assisted mechanisms (Poole-Frenkel, Hopping) at low electric fields and a Fowler-Nordheim mechanism at high electric fields. Under illumination, a new generation-recombination contribution is observed. This mechanism has been carefully studied by Random Telegraph Signal (RTS) measurements. This work shows that the photo-induced current fluctuations (RTS) could be related to the interaction between single photogenerated charges.

Effect of illumination on the electron transport mechanisms in Silicon nanocrystal-based nanopixels

We propose comb filters using sidewalled sampled gratings, where the etch depths in the fingers and spaces have been apodized in a complementary fashion. We numerically demonstrate filters with 40 dB SMSR, 92 GHz bandwidth, 200 GHz channel spacing, and 120 dB/decade roll-off.

Apodized comb filters on SOI using sidewalled sampled gratings

The design, simulation and testing of a 1times6 optical switch is presented. Switching is achieved through a voltage-controlled optical phase array. Electrode voltages are provided by a high-voltage CMOS chip. Switching angles are within 2deg

Reprogrammable Optical Phase Array (ROPA) used as a 1×6 space switch

In PV manufacturing, process costs fall rapidly with scale, but a slower decrease in material costs limits cost reduction. Analysis of a proposed multi-stage-concentration module shows that even with additional concentration stages for low tandem-cell cost, initial concentration by a trough mirror can greatly reduce overall materials usage compared to Fresnel/box CPV. A compact sealed module at the trough’s focus allows high-performance materials for efficiency and durability, and estimated costs (¢/W, LCOE, capital-to-scale) compare favorably to even silicon PV.

Vincent Aimez

Papers

Post-growth processing of 1.55 um InP/InGaAs/InGaAsP material for integrated laser-modulator device fabrication

Effect of illumination on the electron transport mechanisms in Silicon nanocrystal-based nanopixels

Apodized comb filters on SOI using sidewalled sampled gratings

Reprogrammable Optical Phase Array (ROPA) used as a 1×6 space switch

Reducing CPV Materials Cost Through Multistage Concentration