non-Hermitian Waveguides Research Articles

Clearing a path for light through non-Hermitian media

Abstract The performance of all active photonic devices today is greatly limited by loss. Here, we show that one can engineer a low loss path in a metal-clad lossy multi-mode waveguide while simultaneously achieving high-performance active photonic devices. We leverage non-Hermitian systems operating beyond the exceptional point to enable the redistribution of losses in a multi-mode photonic waveguide. Consequently, our multi-mode waveguide offers low propagation losses for fundamental mode while other higher order modes experience prohibitively high losses. Furthermore, we show an application of this non-Hermitian waveguide platform in designing power-efficient thermo-optic phase shifters with significantly faster response times than conventional silicon-based thermo-optic phase shifters. Our device achieves a propagation loss of less than 0.02 dB μm−1 for our non-Hermitian waveguide-based phase shifters with high performance efficiency of P π ⋅ τ = 19.1 mW μs. In addition, our phase shifters have significantly faster response time (rise/fall time), τ ≈ 1.4 μs, compared to traditional silicon based thermo-optic phase shifters.

Selecting mode by the complex Berry phase in non-Hermitian waveguide lattices

Bloch oscillations (BOs) in a parity-time (PT)-symmetric Su–Schrieffer–Heeger (SSH) waveguide array are theoretically investigated. We show that the BOs are amplified or damped even for the systems to exhibit entirely real energy bands. The amplified and damped BOs stem from the complex Berry phase and closely relate to the topological properties of the lattice. For the topological nontrivial lattice, the amplification and attenuation of BOs are much more prominent than the trivial case and the output Bloch mode can be selected. Furthermore, we propose an experimental scheme and perform a numerical simulation based on a bent waveguide array. Our work uncovers the impact of the topological properties on the dynamics of the bulk Bloch modes and unveils a horizon in the study of non-Hermitian physics. The mode selection induced by the complex Berry phase may also find application in integrated photonic devices such as the mode filter.

Mode-cleaning in antisymmetrically modulated non-Hermitian waveguides

Abstract We demonstrate all-optical spatial mode-cleaning in non-Hermitian waveguides. The effect is accounted by a unidirectional coupling among the modes resulting from a simultaneous modulation of the refractive index and the gain/loss along graded index multimodal waveguides. Depending on the spatial delay between the real and imaginary part of the potential modulation, higher or lower order modes are favored, which in latter case eventually leads to an nearly-monomode propagation. In this way, for any arbitrary initial field distribution an antisymmetric non-Hermitian modulation results in an effective mode-cleaning. The effect is demonstrated analytically, based on coupled mode theory in 1D waveguides, and numerically proven by solving the wave propagation equation with the antisymmetric non-Hermitian potential. The proposal is also generalized to the more involved case of 2D waveguides, leading to a significant reduction of the beam quality factor and improvement of beam spatial quality.

Non-reciprocal transmission in a non-Hermitian waveguide quantum electrodynamics system with non-reciprocal hopping

Non-reciprocal transmission in a non-Hermitian waveguide quantum electrodynamics system with non-reciprocal hopping

Non-Hermitian Waveguide Cavity QED with Tunable Atomic Mirrors.

Optical mirrors determine cavity properties by means of light reflection. Imperfect reflection gives rise to open cavities with photon loss. We study an open cavity made of atom-dimer mirrors with a tunable reflection spectrum. We find that the atomic cavity shows anti-PT symmetry. The anti-PT phase transition controlled by atomic couplings in mirrors indicates the emergence of two degenerate cavity supermodes. Interestingly, a threshold of mirror reflection is identified for realizing strong coherent cavity-atom coupling. This reflection threshold reveals the criterion of atomic mirrors to produce a good cavity. Moreover, cavity quantum electrodynamics with a probe atom shows mirror-tuned properties, including reflection-dependent polaritons formed by the cavity and probe atom. Our Letter presents a non-Hermitian theory of an anti-PT atomic cavity, which may have applications in quantum optics and quantum computation.

Controlled unidirectional reflectionlessness by coupling strength in a non-Hermitian waveguide quantum electrodynamics system

Unidirectional reflectionlessness is investigated in a waveguide quantum electrodynamics system that consists of a cavity and a [Formula: see text]-type three-level quantum dot coupled to a one-dimensional plasmonic waveguide. Analytical expressions of transmission and reflection coefficients are derived and discussed for both resonant and off-resonant couplings. By appropriately modulating the coupling strength, phase shift and Rabi frequency, unidirectional reflectionlessness is observed at the exceptional points (EPs). And unidirectional coherent perfect absorption is exhibited at the vicinity of the EP. These results might find applications in designing quantum devices of photons, such as optical switches and single-photon transistors.

(Ann. Phys. 5/2023)

Annalen der PhysikVolume 535, Issue 5 2370009 Cover PictureFree Access (Ann. Phys. 5/2023) First published: 12 May 2023 https://doi.org/10.1002/andp.202370009AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Non-Hermitian Systems Proximity encirclement of exceptional points in non-Hermitian waveguides is investigated by Ming-Xuan Shi and co-workers in article number 2200456, to investigate the dynamics of this mechanism in multistate systems. A Schrödinger-like equation is used to describe the wave dynamics of the dynamic system, and the results are also presented in the form of wave-scattering simulations, some of which are seen in the cover image. Their results will contribute to the development of novel non-Hermitian photonic devices. Volume535, Issue5May 20232370009 RelatedInformation

Diverse lateral shifts of beams in non-Hermitian waveguide arrays.

Non-Hermitian systems have attracted considerable attention in optics due to the rich physics introduced by the existence of real spectra and exceptional points (EPs), which is exploited in lasers, optical sensors and on-chip manipulations of light. Here, focusing on the dynamics of beams in non-Hermitian waveguide arrays supporting a ring of EPs (exceptional ring) and 3rd-order EPs, we theoretically demonstrate that the center of energy of a beam prepared around an eigenstate of the waveguide array near EPs could exhibit non-zero shifts in the lateral direction during its propagation. When the initial state of the beam prepared around an eigenstate inside (outside) the exceptional ring with the imaginary (real) eigenvalue, the lateral shifts of the beams are manifested by the non-oscillating (Zitterbewegung-like) motions, which are robust to the perturbations of coupling coefficients between waveguides. Remarkably, the amplitude of the non-oscillating shift is dependent on a non-Hermitian Berry connection (U(1) gauge invariance). It contradicts the conventional wisdom that the Berry connection cannot induce the dynamic effect. Furthermore, near the high-order EPs, the initial-state-dependent lateral shifts of the beams present diversity, such as multifrequencies and destructive interferences. The counterintuitive lateral shifts of the beams stem from the non-orthogonal nature of eigenstate of the non-Hermitian systems, which may open a gateway towards the non-Hermitian beam dynamics and manipulations of beams.

Tunable unidirectional reflectionless propagation in non-Hermitian graphene plasmonic waveguide system

In this paper, a non-Hermitian graphene plasmonic waveguide system is proposed in the mid-infrared region. The proposed structure consists of two resonators and a graphene waveguide, which are attached to the SiO2 substrate. Based on the far-field coupling between the two stub plasmonic resonators, the single-band unidirectional reflectionless phenomenon of fundamental edge plasmonic mode in the non-Hermitian waveguide system has been theoretically studied. It can be found that when plasmonic mode is incident from one side, the reflection is 0, but from the other side, the reflection is 26.212%, so an exceptional point (EP) appears. Furthermore, the EP blueshifts with increasing Fermi level, and is unchanged under different relaxation times. All the simulation results are conducted by finite element method. Therefore, our findings pave a new way for the development of terahertz sensors, diodes, and so on.

Discrete optical propagation in one-dimensional synthetic mesh lattice

Synthetic mesh lattice (SML) with temporally controlled potential is a versatile platform for realizing wave dynamics associated with physical areas of optics and quantum physics. Here, discrete optics in one-dimensional synthetic photonic lattice is investigated systematically, in which the light behavior is highly analogous to that in evanescently coupled one-dimensional discrete waveguides. Such a synthetic dimension is constructed with position-dependent periodic effective gauge fields based on the Aharonov–Bohm effect arising from the phase accumulation of the fiber loops. By tuning the phase accumulation and coupling coefficient of the coupler, the band translation and gap property can be modulated, which further results in the impulse and tailored Gaussian wave packet responses as well as Talbot recurrences. In addition, Bloch oscillations and Anderson localization can also be obtained when the phase accumulations are linearly changed and weakly modulated in a random manner, respectively. The periodic effective gauge fields configuration in our protocol enables SML to be a research platform for one-dimensional dynamically modulated elements or even non-Hermitian waveguides.

Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

Non-Hermitian multimode interference.

Multimode interference (MMI) and self-imaging are important phenomena of diffractive optics with major applications in signal processing, beam shaping, and optical sensing. Such phenomena generally arise from interference of normal modes in lossless dielectric guiding structures; however, the impact of spatially inhomogeneous optical gain and loss, which break mode orthogonality and symmetries, has been overlooked. Here we consider MMI in non-Hermitian optical systems, either graded-index or coupled optical waveguide structures, and reveal distinctive features, such as the absence of mirror images and strong sensitivity of self-imaging to perturbations, making MMI in non-Hermitian waveguides of interest in optical sensing.

Reciprocal waveguide coupled mode theory

Mode coupling is a common phenomenon in waveguides. The mode coupling among different guided modes in fiber-optic communication can cause crosstalk, and the mode coupling of guided mode and radiated mode can reduce the power of the guided mode. Application of mode coupling can guide the design of optical devices such as couplers and beam splitters with specific functions, which have been widely used in fiber optic communication and fiber sensing. So it is important to analyze how waveguide modes are coupled. The coupled-mode theory is a common method of studying mode coupling in waveguides. It provides not only an intuitive picture of how the photonic modes are hybridized, but also a quantitative assessment of how the hybridization among those relevant modes evolves. In recent years, non-Hermitian waveguides, represented by parity-time symmetrical structures, have become a research hotspot. However the conventional coupled-mode theory no longer works in this case. In this review, we briefly summarize the development history of coupled-mode theory and introduce the representative work in reciprocal waveguide coupled-mode theory in detail. Then the relationship among several coupled-mode theories is analyzed and their applications are briefly introduced.

Dynamically encircling exceptional points in a three-mode waveguide system

Dynamically encircling exceptional points (EPs) in non-Hermitian systems has attracted considerable attention recently, but all previous studies focused on two-state systems, and the dynamics in more complex multi-state systems is yet to be investigated. Here we consider a three-mode non-Hermitian waveguide system possessing two EPs, and study the dynamical encircling of each single EP and both EPs, the latter of which is equivalent to the dynamical encircling of a third-order EP that has a cube-root behavior of eigenvalue perturbations. We find that the dynamics depends on the location of the starting point of the loop, instead of the order of the EP encircled. Compared with two-state systems, the dynamical processes in multi-state systems exhibit more non-adiabatic transitions owing to the more complex topological structures of energy surfaces. Our findings enrich the understanding of the physics of multi-state non-Hermitian systems and may lead to the design of new wave manipulation schemes.

Distinct outcomes by dynamically encircling an exceptional point along homotopic loops

We study a two-state non-Hermitian waveguide system that carries an exceptional point (EP). It is commonly believed that dynamically encircling an EP exhibits a chiral behavior when the starting point of the loop lies in the branch cut with eigenmodes being symmetric and antisymmetric modes. We show here that such statement is conditional; i.e., the dynamics can in fact be nonchiral for specially designed loops with the starting point in the branch cut. In particular, we find that for two homotopic loops (i.e., loops that can be transformed continuously from one to another without crossing any EP), the outcomes can be completely different even if the two loops share the same starting state, enclose the same EP, and encircle the EP in the same direction. Our findings greatly enrich the understanding of the physics in dynamical processes of EP encircling in non-Hermitian systems.

Adiabatic transfer of surface plasmons in non-Hermitian graphene waveguides

We investigate the energy transfer of surface plasmon polaritons (SPPs) based on adiabatic passage in a non-Hermitian waveguide composed of three coupled graphene sheets. The SPPs can completely transfer between two outer waveguides via the adiabatic dark mode as the waveguides are lossless and the coupling length is long enough. However, the loss of graphene can lead to breakdown of adiabatic transfer schemes. By utilizing the coupled mode theory, we propose three approaches to cancel the nonadiabatic coupling by adding certain gain or loss in respect waveguides. Moreover, the coupling length of waveguide is remarkably decreased. The study may find interesting application in optical switches on a deep-subwavelength scale.

Optical Force Enhancement Using an Imaginary Vector Potential for Photons.

The enhancement of optical forces has enabled a variety of technological applications that rely on the optical control of small objects and devices. Unfortunately, optical forces are still too small for the convenient actuation of integrated switches and waveguide couplers. Here we show how the optical gradient force can be enhanced by an order of magnitude by making use of gauge materials inside two evanescently coupled waveguides. To this end, the gauge materials inside the cores should emulate imaginary vector potentials for photons pointing perpendicularly to the waveguide plane. Depending on the relative orientation of the vector potentials in neighboring waveguides, i.e., pointing away from or towards each other, the conventional attractive force due to an even mode profile may be enhanced, suppressed, or may even become repulsive. This and other new features indicate that the implementation of complex-valued vector potentials with non-Hermitian waveguide cores may further enhance our control over mode profiles and the associated optical forces.

General coupled mode theory in non-Hermitian waveguides.

In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.