We investigate high-fidelity multiple beam splitting in Hermitian and non-Hermitian symmetric coupled waveguides with one input and 2N output waveguide channels. In Hermitian systems, we realize adiabatically light splitting in resonant case based on the stimulated Raman adiabatic passage (STIRAP) and arbitrary proportion from the middle waveguide to outer waveguides in propagation coefficients mismatch case using shortcuts to adiabaticity (STA) technique. In non-Hermitian systems with even waveguides being dissipative, the compact and robust beam splitting can be achieved by eliminating the non-adiabatic coupling via the non-Hermitian STA method. We further verify the feasibility of our theoretical predictions by means of the beam propagation method (BPM). The suggested multiple beam splitters open new opportunities for the realization of on-chip high-bandwidth photonics with high fidelity in short distances.
Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the atomic scale wavelength of the electron. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo PT ) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array…
We study the self interference effect of a resonator coupled with a bent waveguide at two separated ports. Such interference effects are shown to be similar for the cases of standing-wave and traveling-wave resonators, while in the system of two separated resonators indirectly coupled via a waveguide, the coupling forms and the related interference effects depend on which kind of resonators is chosen. Due to the self interference, controllable optical responses including tunable linewidth and frequency shift, and optical dark state can be achieved. Moreover, we consider a self-interference pho…
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 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 …
We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-PT -- symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra -- and inter-cell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-PT -symmetric configurations, brok…
We investigate the effects of disorder on single particle time-evolution and two-particle correlations in an array of evanescently coupled waveguides with position-dependent tunneling rates. In the clean limit, the energy spectrum of such an array is widely tunable. In the presence of a Hermitian on-site or tunneling disorder, we find that the localization of a wave packet is highly sensitive to this energy spectrum. In particular, for an input confined to a single waveguide, we show that the fraction of light localized to the original waveguide depends on the tunneling profile. We compare the…
A non-Hermitian coupled waveguide system with periodically varying parameters, in which the Berry curvature is analogous to a hyperbolic magnetic monopole or antimonopole, is investigated. It is shown to have a purely imaginary Berry connection, and is consequently influenced by a geometric multiplier. It is possible for this multiplier to induce net gain or loss in the system, corresponding to the existence of the antimonopole or monopole in parameter space, respectively. For the right choice of parameters, the system will display an apparent non-adiabatic change in behaviour, which implies a…
One-dimensional structures of non-Hermitian plasmonic metallic nanospheres are studied in this paper. For a single sphere, solving Maxwell's equations results in quasi-stationary eigenmodes with complex quantized frequencies. Coupled mode theory is employed in order to study more complex structures. The similarity between the coupled mode equations and the effective non-Hermitian Hamiltonians governing open quantum systems allows us to translate a series of collective phenomenon emerging in condensed matter and nuclear physics to the system of plasmonic spheres. A nontrivial physics emerges as…
We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs.
We study an one-dimensional non-Hermitian lattice with complex hopping rates, which can be realized by a quasi-one-dimensional sawtooth-type Hermitian lattice after adiabatic elimination with proper conditions. By means of synthetic magnetic fluxes, the imaginary parts of the complex hopping rates can be modulated by additional phase, thus a non-reciprocal structure arises. With this lattice, one can realize robust unidirectional transport for both single-site and Gaussian excitations, which is immune to defects and backscattering. Furthermore, we proposed a sandwich structure based on the non…
We evaluate the sensing properties of plasmonic waveguide sensors by calculating their resonant transmission spectra in different regions of the non-Hermitian eigenmode space. We elucidate the pitfalls of using modal dispersion calculations in isolation to predict plasmonic sensor performance, which we address by using a simple model accounting for eigenmode excitation and propagation. Our transmission calculations show that resonant wavelength and spectral width crucially depend on the length of the sensing region, so that no single criterion obtained from modal dispersion calculations alone …
Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a t…
The surface plasmon-polaritons (SPPs) switch is the key element of the integrated devices in optical computation and terahertz (THz) communications. In this paper, we propose a novel design of THz SPPs switch based on quantum engineering. Due to the robustness of coherent quantum control technique, our switch is very robust against with perturbations of geometrical parameters and presents a good performance at on-state (and off-state) from 0.5 THz to 0.7 THz. The on-state and off-state of our device can be controlled by the external voltage. We believe this finding will be the great improvemen…
A judicious design of gain and loss leads to counterintuitive wave phenomena that are inaccessible by conservative systems. Notably, such designs can give rise to laser-absorber modes and anisotropic transmission resonances. Here, we analyze the emergence of these phenomena in an optical scatterer with sinusoid gain-loss modulation that is subjected to monochromatic oblique waves. We derive an analytical solution to the problem, with which we show how the scatterer parameters, and specifically the modulation phase and incident angle, constitute a real design space to access these phenomena.
We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenom…
By using the real-space method, switching of a single plasmon interacting with a hybrid nanosystem composed of a semiconductor quantum dot (SQD) and a metallic nanoparticle (MNP) coupled to one-dimensional surface plasmonic waveguide is investigated theoretically. We discussed that the dipole coupling between an exciton and a localized surface plasmon results in the formation of a hybrid exciton and the transmission and reflection of the propagating single plasmon could be controlled by changing the interparticle distance between the SQD and the MNP and the size of the nanoparticles. The contr…
We study the spontaneous emission rate of a dipole emitter in $\mathcal{PT}$-symmetric environment of two coupled waveguides using the reciprocity approach generalized to non-orthogonal eigenmodes of non-Hermitian systems. Considering emission to the guided modes, we define and calculate the modal Purcell factor composed of contributions of independent and interfering non-orthogonal modes leading to the emergence of cross-mode terms in the Purcell factor. We reveal that the closed-form expression for the modal Purcell factor within the coupled mode theory slightly alters for the non-Hermitian …
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
We show that a system of three parallel waveguides, among which the central one is dissipative, leads to an ultrabroadband power splitting associated with an overall 50% power loss. The present approach is reminiscent of non-Hermitian systems in quantum mechanics and does not require a perfect effective index matching between the external and the central waveguides. The present concept does not need any slow adiabatic evolution of the waveguide parameters and may therefore be realized over very short device lengths, especially in the case where the central waveguide is of the plasmonic type.
Parity-time (PT) symmetry in non-Hermitian optical systems promises distinct optical effects and applications not found in conservative optics. Its counterpart, anti-PT symmetry, subscribes another class of intriguing optical phenomena and implies complementary techniques for exotic light manipulation. Despite exciting progress, so far anti-PT symmetry has only been realized in bulky systems or with optical gain. Here, we report an on-chip realization of non-Hermitian optics with anti-PT symmetry, by using a fully-passive, nanophotonic platform consisting of three evanescently coupled waveguid…
We show that the time-averaged Poynting vector in parity-time (PT ) symmetric coupled waveguides is always positive and cannot explain the stopped light at exceptional points (EPs). In order to solve this paradox, we must accept the fact that the fields E and H and the Poynting vector in non-Hermitian systems are in general complex. Based on the original definition of the instantaneous Poynting vector, a formula on the group velocity is proposed, which agrees perfectly well with that calculated directly from the dispersion curves. It explains not only the stopped light at EPs, but also the fas…
Multi-mode interference (MMI) and self-imaging are important phenomena of diffractive wave optics with major applications in optical 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 with optical gain and loss, and reveal distinctive fea…
We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schrödinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an impor…
Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteris…
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We …
We construct localized beams that are located at the edge of a non-Hermitian Glauber Fock (NGF) lattice made of coupled waveguides and can propagate for a long distance without almost no diffraction. Specifically, we calculate the closed-form of the eigenstates at the exceptional point of a semi-infinite NGF lattice composed of waveguides which are coupled in a unidirectional manner. We use the closed-form solution to construct the non-diffracting beams in finite NGF lattices. We provide a numerical approach to find other lattices that are capable of supporting non-diffracting beams at an exce…
A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero …
We introduce non-Hermitian plasmonic waveguide-cavity systems with topological edge states (TESs) at singular points. The compound unit cells of the structures consist of metal-dielectric-metal (MDM) stub resonators side-coupled to an MDM waveguide. We show that we can realize both a TES and an exceptional point at the same frequency when a proper amount of loss is introduced into a finite three-unit-cell structure. We also show that the finite structure can exhibit both a TES and a spectral singularity when a proper amount of gain is introduced into the structure. In addition, we show that we…
The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a crucial quantity near exceptional points in non-Hermitian systems, where it diverges in a way that fully controls the description of wavepacket trajectories. The quantum metric behaviour is responsible for a constant acceleration with a fixed direction, and for a non-vanishing constant velocity with a controllable direction. Both contributions are independe…
We study controllable single photon scattering in a one-dimensional waveguide coupling with an additional cavity by second order nonlinear materials in a non-cascading configuration, where the additional cavity is embedded with two-level atom and filled with Kerr-nonlinear materials. Considering the second order nonlinear coupling, we analyze the transmission properties of the three different coupling forms as follows: (i) The two-level atom is excited without the Kerr-nonlinearity. (ii)The Kerr-nonlinearity is excited without the two-level atom. (iii) Both of the two-level atom and Kerr-nonli…
We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy condition, yet unexplored in the contest of gain and loss. We demonstrate the concept of Parity-Time ($\cal{PT}$)-symmetry in coupled uniform waveguides with balanced and symmetric gain and loss and how this condition is associated with a second order EPD. We show that by introducing gain into naturally lossy structures provides for the conditions whereby exc…
Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a…
Non-Hermitian systems, which contain gain or loss, commonly host exceptional point degeneracies rather than the diabolic points found in Hermitian systems. We present a class of non-Hermitian lattice models with symmetry-stabilized diabolic points, such as Dirac or Weyl points. They exhibit non-Hermiticity-induced phenomena previously existing in the Hermitian regime, including topological phase transitions, Landau levels induced by pseudo-magnetic fields, and Fermi arc surface states. These behaviors are controllable via gain and loss, with promising applications in tunable active topological…
A localized non-Hermitian potential can operate as a coherent perfect absorber or as a laser for nonlinear waves. The effect is illustrated for an array of optical waveguides, with the central waveguide being either active or absorbing. The arrays situated to the left and to the right from the center can have different characteristics. The result is generalized to setups with the central waveguide carrying additional nonlinear dissipation or gain and to the two-dimensional arrays with embedded one-dimensional absorbing or lasing sub-arrays.
We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental rea…
Electromagnetic waves propagating, at finite speeds, in conventional wave-guiding structures are reflected by discontinuities and decay in lossy regions. In this Letter, we drastically modify this typical guided-wave behavior by combining concepts from non-Hermitian physics and topological photonics. To this aim, we theoretically study, for the first time, the possibility of realizing an exceptional point between \emph{coupled topological modes in a non-Hermitian non-reciprocal waveguide}. Our proposed system is composed of oppositely-biased gyrotropic materials (e.g., biased plasmas or graphe…
Unifying quantum mechanics and special relativity, the Dirac equation describes the behaviour of relativistic quantum particles, including imaginary-mass particles with faster-than-light speeds (e.g., tachyon). However, experimental searches for such particles remain negative so far. Fortunately, there are possibilities to investigate the relativistic quantum effects by quantum simulations using a controllable system. However, these simulations are mostly explored in closed physical systems that hinders the demonstration of imaginary-mass particles, whereas the general open framework would pro…
Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow…
We study the breaking of reciprocity in non-Hermitian coupled photonic waveguides by the simultaneous action of the nonlinear effect of saturable absorption, and the presence of exceptional points. The nonlinear response of such a system is studied in depth, giving physical insight into the operational principles and fundamental limitations, while producing analytical and semi-analytical results for the transmission and nonreciprocal intensity range. We numerically validate the theoretical results and assess important performance metrics for the nonreciprocal operation of such a device. This n…
We show that the analogue of the geometric phase for non-Hermitian coupled waveguides with PT-symmetry and at least one periodically varying parameter can be purely imaginary, and will consequently result in the manifestation of an instability in the system. The instability peaks seen in the spectrum of the system's eigenstates after evolution along the waveguides can be directly mapped to the spectrum of the derivative of the geometric function. The instabilities are magnified as the exceptional point of the system is approached, and non-adiabatic effects begin to appear. As the system cannot…
