Spawning rings of exceptional points out of Dirac cones

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an 'exceptional ring' in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.

Inversed Vernier effect based single-mode laser emission in coupled microdisks

Recently, on-chip single-mode laser emissions in coupled microdisks have attracted considerable research attention due to their wide applications. While most of single-mode lasers in coupled microdisks or microrings have been qualitatively explained by either Vernier effect or inversed Vernier effect, none of them have been experimentally confirmed. Here, we studied the mechanism of single-mode laser operation in coupled microdisks. We found that the mode numbers had been significantly reduced to nearly single-mode within a large pumping power range from threshold to gain saturation. The detail laser spectra showed that the largest gain and the first lasing peak were mainly generated by one disk and the laser intensity was proportional to the wavelength detuning of two set of modes. The corresponding theoretical analysis showed that the experimental observations were dominated by internal coupling within one cavity, which was similar to the recently explored inversed Vernier effect in two coupled microrings. We believe our finding will be important for understanding the previous experimental findings and the development of on-chip single-mode laser.

Defect states and exceptional point splitting in the band gaps of one-dimensional parity-time lattices

We investigated defect states in band gaps of one-dimensional photonic lattices with delicate modulations of gain and loss that respect parity-time-symmetry (PT-symmetry), viz. n(z) = n*(-z). For the sake of generality, we employ not only periodic structures but also quasiperiodic structures, e.g. Fibonacci sequences, to construct aperiodic PT lattices. Differed from lossless systems for which the defect state is related to only one exceptional point (EP) of the S-matrix, we observed the splitting of one EP into a pair after the introduction of judiciously designed gain and loss in those PT systems, where the defect state enters a non-threshold broken symmetry phase bounded by the EP pair. Some interesting properties associated with defect states and EP splitting are demonstrated, such as enhanced spectral localization, double optical phase abrupt change, and wavelength sensitive reversion of unidirectional transparency.

Symmetry recovery for coupled photonic modes with transversal PT symmetry

Typical parity-time (PT) symmetric structures switch from the unbroken to the broken phase when gain increases through an exceptional point. In contrast, we report on systems with the unusual, reverse behavior, where the symmetric phase is recovered after a broken phase. We study this phenomenon analytically and numerically in the simplest possible system, consisting of four coupled modes, and we present potential dielectric and plasmonic implementations. The complex mode merging scheme, with two distinct unbroken PT phases encompassing a broken one, appears for a specific proportion range of the coupling constants. This regime with "inverse" exceptional points is interesting for the design of novel PT devices.

Observation of optical solitons in PT-symmetric lattices

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

Parity–time symmetry can impose a stable energy flow in photonic systems with simultaneous amplification and attenuation. Here, Wimmer et al. demonstrate optical solitons belonging to a continuous parametric family of solutions in a parity–time-symmetric lattice and observe saturable absorber action.

Temperature and gain tuning of plasmonic coherent perfect absorbers

We experimentally demonstrate temperature-tuned and gain-assisted surface-plasmonic coherent perfect absorbers. In these devices, coherent perfect absorption (CPA) is supported by balancing the absorber's radiative and non-radiative decay rates under thermal tuning of free-electron collision frequency in the Ag layer and optical tuning of the amplification rate in the adjacent dielectric film with optical gain, respectively. The results show that these methods are experimentally feasible and applicable to various CPA configurations.

Parity-time symmetric coupled microresonators with a dispersive gain/loss

The paper reports on the coupling of Parity-Time (PT)-symmetric whispering gallery resonators with realistic material and gain/loss models. Response of the PT system is analyzed for the case of low and high material and gain dispersion, and also for two practical scenarios when the pump frequency is not aligned with the resonant frequency of the desired whispering gallery mode and when there is imbalance in the gain/loss profile. The results show that the presence of dispersion and frequency misalignment causes skewness in frequency bifurcation and significant reduction of the PT breaking point, respectively. Finally, we demonstrate a lasing mode operation which occurs due to an early PT-breaking by increasing loss in a PT system with unbalanced gain and loss.

Parity-time-symmetry breaking in double-slab surface-plasmon-polariton waveguides

We theoretically demonstrate spontaneous PT-symmetry breaking behavior of surface-plasmon polaritons (SPP) in coupled double-slab (DS) waveguides. By virtue of a flat-top field at critical wavelength, the imaginary index of a DS-SPP mode can be controlled via changing the core thickness, while the real index is kept constant. Therefore, a waveguide coupler that consists of a pair of DS-SPP waveguides with different core thicknesses can represent a passive PT-symmetric system, which always maintains symmetry under a real potential. This set-up also represents a good opportunity to investigate the underlying physics of PT-symmetry breaking in non-Hermitian Hamiltonian systems.

Engineering wavefront caustics trajectories in PT-symmetric lattices

We utilize caustic theory in PT-symmetric lattices to design focusing and curved beam dynamics. We show that the gain and loss parameter in these systems provides an additional degree of freedom that allows for the design of the same caustics trajectories with different intensity distribution in the individual waveguides. Moreover we can create aberration-free focal points at any paraxial distance z(f), with anomalously large focal intensity.

Selective enhancement of topologically induced interface states in a dielectric resonator chain

The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers.

At interfaces between systems with topologically distinct band structure, robust symmetry protected states emerge. Here, Poli et al. control such states in a coupled dielectric resonator chain with parity-time symmetry and exploit their topological nature to protect them from absorptive losses.

Grating integrated single mode microring laser

Microring and microdisk lasers are potential candidates for small footprint, low threshold in-plane integrated lasers; however, they exhibit multimode lasing spectra and bistability. Here, we theoretically propose and experimentally demonstrate a novel approach for achieving single mode lasing in microring lasers. Our approach is based on increasing the radiation loss of all but one of the resonant modes of microring resonators by integrating second order gratings on the microrings' waveguide. We present single mode operation of electrically pumped semiconductor microring lasers whose lasing modes are lithographically selected via the second order grating. We also show that adding the grating does not increase the lasing threshold current significantly.

Unidirectional spectral singularities

We propose a class of spectral singularities emerging from the coincidence of two independent singularities with highly directional responses. These spectral singularities result from resonance trapping induced by the interplay between parity-time symmetry and Fano resonances. At these singularities, while the system is reciprocal in terms of a finite transmission, a simultaneous infinite reflection from one side and zero reflection from the opposite side can be realized.