A laser exhibits both controllable gain and loss and, under proper design conditions, is an ideal non-Hermitian system allowing the direct observation and engineering of spectral singularities such as exceptional points (EPs). A dual section distributed feedback (DFB) quantum cascade laser (QCL) is a prototype of such a system, allowing the controlled coupling of a ladder of cavity Fabry-Perot (FP) modes to a quarter wave shifted DFB mode. Tuning the coupling strength and the gain difference between these two set of modes enables probing the regimes from weak coupling to strong coupling and the robust observation of exceptional point singularities. At these exceptional points, the laser exhibits a sequence of lasing and coherent prefect absorption dynamics1,2 when pumped above transparency. Additionally, the pumping scheme allows the deliberate lifting of the exceptional point degeneracy. These results show that dual section QCL is a perfect platform to study exceptional points because the coupling parameter and system loss can be tuned in a single device.
We explore exceptional points (EP) in a dual-mode symmetric planar optical waveguide with transverse variation of inhomogeneous loss profile; where modal evolution alongside an EP is reported in the context of selective optical mode conversion.
We report an open three-state perturbed system with quasi-statically varying Hamiltonian depending on the topological parameters. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point (EP3) is explored with simultaneous encirclement of two EP2s by adiabatic variation of topological parameters. We study the robust successive state-exchange around the EP3. Applying adiabatic theorem, we estimate the evolution of total phase accumulated by each state during encirclement; where interestingly, the state-common to the pairs of coupled state picks…
Exceptional points play a pivotal role in the topology of non-Hermitian systems, and significant advances have been made in classifying exceptional points and exploring the associated phenomena. Exceptional surfaces, which are hypersurfaces of exceptional degeneracies in parameter space, can support hypersurface singularities, such as cusps, intersections and swallowtail catastrophes. Here we topologically classify the intersection singularity of exceptional surfaces for a generic pseudo-Hermitian system with parity-time symmetry. By constructing the quotient space under equivalence relations …
We present a nanoscale active plasmonic waveguide system consisting of an array of periodic slits that can exhibit exceptional points and spectral singularities leading to several novel functionalities. The proposed symmetric active system operates near its cut-off wavelength and behaves as an effective epsilon-near-zero (ENZ) medium. We demonstrate the formation of an exceptional point (EP) that is accessed with very low gain coefficient values, a unique feature of the proposed nanoscale symmetric plasmonic configuration. Reflectionless ENZ transmission and perfect loss-compensation are reali…
We demonstrate general classifications of Riemann surface topology generated by multiple arbitrary-order exceptional points of quasi-stationary states. Our studies reveal all possible product permutations of holonomy matrices that describe a stroboscopic encircling of 2nd order exceptional points. The permutations turn out to be categorized into a finite number of classes according to the topological structures of the Riemann surfaces. We further show that the permutation classes can be derived from combinations of cyclic building blocks associated with higher-order exceptional points. Our res…
Propagation Maps, Maradona Exceptional Points, and Pele Singularities in Anisotropic, Tellegen, Chiral, Moving-Medium, Omega and Other Isotropy-Broken Materials
Exceptional points as branch singularities describe peculiar degeneracies of non-Hermitian systems that do not obey energy conservation. This work shows that exceptional points can emerge in a topological photonic system, for example, the topological photonic waveguide coupled with two degenerate counter-propagation topological whispering gallery modes. Such a photonic architecture is designed by crystal-symmetry-protected topological photonic insulators based on air rods in conventional dielectric materials. The relevant exceptional point reveals the breaking of the parity-time symmetry, refl…
The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has drawn a great deal of attention in recent years. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. Among several peculiar phenomena observed at exceptional points, an especially intriguing property, with relevant practical potential, consists in the inherently enhanced sensitivity to small-scale perturbations. So far, however, these principles have been implemen…
Recent studies on non-Hermitian optical systems having exceptional points (EPs) have revealed a host of unique characteristics associated with these singularities, including unidirectional invisibility, chiral mode switching and laser self-termination, to mention just a few examples. The vast majority of these works focused either on passive systems or active structures where the EPs were accessed below the lasing threshold, i.e. when the system description is inherently linear. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accesse…
Recent experiments have demonstrated the feasibility of exploiting spectral singularities in open quantum and wave systems, so-called exceptional points, for sensors with strongly enhanced sensitivity. Here, we study theoretically the influence of classical parametric noise on the performance of such sensors. Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the resolvability of frequency splittings and the dynamical stability of the sensor, and show that these properties are interrelated. Of central importance are the different features of exceptional points in the spect…
Band topology has been studied as a design principle of realizing robust boundary modes. Here, by exploring non-Hermitian topology, we propose a three-dimensional topological laser that amplifies surface modes. The topological surface laser is protected by nontrivial topology around branchpoint singularities known as exceptional points. In contrast to two-dimensional topological lasers, the proposed three-dimensional setup can realize topological boundary modes without judicious gain at the edge or symmetry protection, which are thus robust against a broad range of disorders. We also propose a…
Exceptional points (EPs), i.e. branch point singularities of non-Hermitian Hamiltonians, are ubiquitous in optics. So far, the signatures of EPs have been mostly studied assuming classical light. In the passive parity-time ($\mathcal{PT}$) optical coupler, a fingerprint of EPs resulting from the coalescence of two resonance modes is a qualitative change of the photon decay law, from damped Rabi-like oscillations to transparency, as the EP is crossed by increasing the loss rate. However, when probed by non-classical states of light, quantum interference can hide EPs. Here it is shown that, unde…
Exceptional-Point Geometry of Weak Topological Boundary States
Instituto de Estructura de la Materia (IEM-CSIC)（物质结构研究所）；Departamento de Física, Universidad Técnica Federico Santa María（圣地亚哥技术大学物理系）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学物理研究所）
