We propose a metallic-silicon system with a complex optical potential modulated along the length of the waveguide for a robust higher harmonic generation. For right moving fields when the strength of non-Hermiticity becomes equal to the real part of the optical potential, the dynamical equations associated with modal field amplitudes in our proposed system are described by a Jordan form Hamiltonian. This ultimately will allow for a unidirectional higher frequency generation which always has a maximum value for a specific length of the waveguide irrespective of the geometrical imperfections in the design of the waveguide. Furthermore, the phase of the generated higher harmonic mode becomes independent of the coupling between the fundamental frequency and higher harmonic one. Unlike other proposed spatiotemporal modulated systems when the system has a Jordan form Hamiltonian, the fundamental mode remains reciprocal while the harmonic generation is non-reciprocal. Consequently, while the proposed device cannot be used as an optical isolator it can be used for many other devices such as laser cavities, interferometry, and holographic processes.
Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is reversed. Here we show that the dynamical encircling of an EP in anti-PT-symmetric systems can also result in chiral dynamics if the starting/end point lies in the PT-broken phase, in contrast to PT-symmetric systems where chiral dynamics emerges if the starting/end point lies in the PT-unbroken phase. For many applications, such as signal processing using wavegu…
Dynamically encircling exceptional points (EPs) in two-dimensional Hamiltonian parameter space has enabled intriguing chiral dynamics in which the final state of the system depends on the encircling direction. Here, we show that full Hamiltonian parameter space can be described in a Riemann sphere, and those points on the parameter space boundary with the eigenstates of the system Hamiltonian being convergent, converge to the north vertex. We present that encircling one EP on the Riemann sphere leads to chiral response, and a continuous encircling trajectory passing through the north vertex ca…
We investigate the exceptional points (EPs) in a non-Hermitian system composed of a pair of graphene sheets with different losses. There are two surface plasmon polaritons (SPP) modes in the graphene waveguide. By varying the distance between two graphene sheets and chemical potential of graphene, the EPs appear as the eigenvalues, that is, the wave vectors of the two modes coalesce. The cross conversion of eigenmodes and variation of geometric phase can be observed by encircling the EP in the parametric space formed by the geometric parameters and chemical potential of graphene. At the same t…
We have observed the quench of the lasing at the exceptional point in the electronic circuit system by applying asymmetric gain in the coupled oscillator. Since there is the analogy between oscillation in laser and oscilation in the operational amplifier, when the system hits the exceptional point, oscillation stops. This phenomenon is also theoretically investigated.
Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise. Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly, like a state-flip or the accumulation of a geometric phase. Experiments dedicated to this issue could already successfully explore the topological structur…
Bianisotropy is a powerful concept enabling asymmetric optical response, including asymmetric reflection, absorption, optical forces, light trapping, and lasing. The physical origin of these asymmetric effects can be understood from magnetoelectric coupling and asymmetrical field enhancement. Here, we theoretically propose highly asymmetric second-harmonic generation (SHG) in bianisotropic AlGaAs metasurfaces. We show that around four orders of magnitude second-harmonic power difference for the forward and backward illuminations can be obtained by altering geometrical parameters that coincide …
We investigate a parity-time (PT) symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the PT phase transition. The system can reenter the exact PT-symmetric phase from a broken PT-symmetric phase with large non-Hermiticity. Two-state coalescence may have one or two defective eigenstates. The topology of exceptional points is reflected by the magnetic flux independent phase rigidity scaling exponents. The topology changes when exceptional points coincide. The geometric phases accumulate when encircling the exceptional points and var…
We report a 1D planar optical waveguide with transverse distribution of inhomogeneous loss profile, which exhibits an exceptional point (EP). The waveguide hosts two leaky resonant modes; where the interaction between them in the vicinity of the EP is controlled by proper adjustment of the inhomogeneity in attenuation profile only. We study the adiabatic dynamics of propagation constants of the coupled modes by quasi-static encirclement of control parameters around the EP. Realizing such an encirclement with the inhomogeneous loss distribution along the direction of light propagation, we repor…
The dynamical encirclement around a second order exceptional point (EP) and corresponding chirality driven nonadiabatic modal dynamics have attracted enormous attention in the topological study of various non-Hermitian systems. However, dynamical encirclement around multiple second-order EPs in a multi-state system is yet to be explored. Here, exploiting an exclusive design of a planar gain-loss assisted three-mode supported optical waveguide with local Kerr-nonlinearity, we encounter multiple second-order EPs. Judiciously, choosing a specific parameter space by varying the unbalanced gain-los…
We show that second harmonic generation can be enhanced by Fano resonant coupling of asymmetric plasmonic metal nanostructures. We develop a theoretical model examining the effects of electromagnetic interaction between two metal nanostructures on the second harmonic generation. We compare the second harmonic generation efficiency of a single plasmonic metal nanostructure with that of two coupled ones. We show that second harmonic generation from a single metal nanostructure can be enhanced about 30 times by attaching a second metal nanostructure with a 10 times higher quality factor than that…
We introduce a nonlinear photonic system that enables asymmetric localization and unidirectional transfer of an electromagnetic wave through the second harmonic generation process. Our proposed scattering setup consists of a non-centrosymmetric nonlinear slab with nonlinear susceptibility $χ^{(2)}$ placed to the left of a one-dimensional periodic linear photonic crystal with an embedded defect. We engineered the linear lattice to allow the localization of a selected frequency $2ω_\star$ while frequency $ω_\star$ is in the gap. Thus in our proposed scattering setup, a left-incident coherent tra…
We use numerical simulations to demonstrate third-harmonic generation with near-unity nonlinear circular dichroism (CD) and high conversion efficiency ($ 10^{-2}\ \text{W}^{-2}$) in asymmetric Si-on-SiO$_2$ metasurfaces. The working principle relies on the selective excitation of a quasi-bound state in the continuum, characterized by a very high ($>10^5$) quality-factor. By tuning multi-mode interference with the variation of the metasurface geometrical parameters, we show the possibility of independent control of linear CD and nonlinear CD. Our results pave the way for the development of all-…
Exploiting scattering-matrix in a gain-loss assisted optical-microcavity, interplay between asymmetric-state-conversion and cavity-control parameters around exceptional points is analyzed; where occupying a least area by coupled states during switching, maximum conversion-efficiency with minimal asymmetry is achieved.
Non-Hermitian systems have recently attracted significant attention in photonics. One of the hallmarks of these systems is the possibility of realizing asymmetric mode switching and omnipolarizer action through the dynamic encirclement of exceptional points (EP). Here, we offer a new perspective on the operating principle of these devices, and we theoretically and experimentally show that asymmetric mode switching and omni-polarizer action can be easily realized with the same performance and limitations, using simple configurations that emulate the physics involved in encircling EPs without th…
Resonant metasurfaces have received extensive attention due to their sharp spectral feature and extraordinary field enhancement. In this work, by breaking the in-plane symmetry of silicon nanopillars, we achieve a sharp Fano resonance. The far-field radiation and near-field distribution of metasurfaces are calculated and analyzed to further uncover the resonant performance of metasurfaces. Moreover, the theoretical derivation and simulation exhibit an inverse quadratic dependence of Q-factors on asymmetry parameters, revealing that the resonance is governed by the symmetry-protected bound stat…
We show the abundance of Exceptional Points in the generic asymmetric configuration of two coupled diode lasers, under nonzero optical detuning and differential pumping. We pinpoint the location of these points with respect to the stability domains and the Hopf bifurcation points, in the solution space as well as in the space of experimentally controlled parameters.
Dynamical parametric encirclement around an Exceptional Point (EP) and corresponding asymmetric state transfer phenomenon have attracted considerable attention recently. In this context, beyond the reported time-asymmetric state dynamics around a second-order EP (EP2) in a two-level system, the investigation of similar state dynamics around a third-order EP (EP3) in a multi-state system, having comparably complex topology with rich physics, is lacking. Here, we report a fabrication-feasible few-mode planar optical waveguide with a customized gain-loss profile and investigate the effect of dyna…
Asymmetric microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing. We define asymmetric microcavities on topologically curved surfaces, where the geodesic light trajectories completely reconstruct the cavity mode features. The quality factors of the lossy chaotic and island modes in flat cavities can be increased by up to ~200 times by the space curvature. Strong and weak coupling between modes of very different origins occur when the space curvature brings them into resonance, leading to a fine tailoring of the cavity phot…
We demonstrate to image asymmetric molecular orbitals via high-order harmonic generation in a one-color inhomogeneous field. Due to the broken inversion symmetry of the inhomogeneous field in space, the returning electrons with energy in a broad range can be forced to recollide from only one direction for all the orientation angles of molecules, which therefore can be used to reconstruct asymmetric molecular orbitals. Following the procedure of molecular orbital tomography, the highest occupied molecular orbital of CO is satisfactorily reconstructed with high-order harmonic spectra driven by t…
The existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically. The frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three. The frozen mode regime is characterized by vanishing group velocity and enhanced field amplitude, which can be very attractive in various applications including dispersion engineering, lasers, and delay lines. Useful and simple design equations that lead to realizati…
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…
Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenom…
A novel mechanism of asymmetric frequency conversion is investigated in nonlinear dispersive devices driven parametrically with a biharmonic pump. When the relative phase between the first and second harmonics combined in a two-tone pump is appropriately tuned, nonreciprocal frequency conversion, either upward or downward, can occur. Full directionality and efficiency of the conversion process is possible, provided that the distribution of pump power over the harmonics is set correctly. While this asymmetric conversion effect is generic, we describe its practical realization in a model system …
Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We show that a slow enough variation of parameters, even away from the system's exceptional point, can also lead to a robust asymmetric state exchange. To study this process, we consider a prototypical two-level non-Hermitian Hamiltonian with a constant coupling between elements. Closed form solutions are obtained when the amplification/attenuation coefficient…
We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $χ^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the up-converted radiation rate in such a system can be greatly enhanced---by up to two orders of magnitude---compared to typical Purcell factors achievable in non-degenerate cavities, for both monochromatic and broadband emitters. We provide a proof-of-concept demonstration by studying an inverse-designed 2D photonic-crystal slab that supports an EP formed out of a Dirac c…
The enhanced electric field at plasmonic resonances in nanoscale antennas can lead to efficient harmonic generation, especially when the plasmonic geometry is asymmetric on either inter-particle or intra-particle levels. The planar Archimedean nanospiral offers a unique geometrical asymmetry for second-harmonic generation (SHG) because the SHG results neither from arranging centrosymmetric nanoparticles in asymmetric groupings, nor from non-centrosymmetric nanoparticles that retain a local axis of symmetry. Here we report forward SHG from planar arrays of Archimedean nanospirals using 15 fs pu…
We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and double-hump soliton profiles, and multihump structures. Exploiting the linear stability analysis and direct simulations, we prove that these localized states are exceptional stable in the respective finite band gaps. The model applies to Bose-Einstein condensates loaded onto optical lattices, and in optics with period potentials, e.g., the photonic crystals and…
Chiral exceptional points (CEPs) have been shown to emerge in traveling wave resonators via asymmetric back scattering from two or more nano-scatterers. Here, we provide a new perspective on the formation of CEPs based on the coupled oscillator model. Our approach provides an intuitive understanding for the modal coalescence that signals the emergence of CEPs, and emphasizes the role played by dissipation throughout this process. In doing so, our model also unveils an otherwise unexplored connection between CEPs and other types of exceptional points associated with parity-time symmetric photon…
A generic photonic coupler with active and lossy parts, gain saturation and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to undesirable unbounded modes and allow for bistable operation in specific regions of parametric space. Both stability and bistability are studied in the phase space of the system, where the basins of attraction of each state are identified, providing an accurate description of the dependence of the electric fields on the initial conditions. Continuous families of exce…
We demonstrate that a periodic waveguide comprising of uniform lossless segments together with discrete gain and radiating elements supports exceptional points of degeneracy (EPDs). We provide analytical expressions for all possible conditions that guarantee the occurrence of an EPD, i.e., the coalescence of eigenvalues and eigenvectors. We show that EPDs are not only achieved using symmetric gain and radiation periodic loading, but they are also obtained using asymmetric gain and radiation loss conditions. We illustrate the characteristics of the degenerate electromagnetic modes, showing the …
Institute for Quantum Science and Technology, University of Calgary（卡尔加里大学量子科学与技术研究所）；Department of Physics, University of Alberta（阿尔伯塔大学物理系）；National Research Council of Canada, Quantum and Nanotechnology Research Centre（加拿大国家研究委员会量子与纳米技术研究中心）；nanoFAB Centre, University of Alberta（阿尔伯塔大学纳米制造中心）
Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and optical systems. Here, exploiting a gain-loss assisted dual-mode optical waveguide that hosts a dynamical EP-encirclement scheme, we have explored enhanced nonreciprocal effect in the dynamics of light with onset of saturable nonlinearity in the optical medium. We propose a prototype waveguide-based isolation scheme with judicious tuning of nonlinearity leve…
The physics of exceptional point (EP) singularities, has been a key to a wide range of unique physical applications in open systems. In this context, the mutual interactions among four coupled states around a fourth-order EP (EP4) in a physical system is yet to be explored. Here, we investigate the unique features of an EP4 in a fabrication feasible planar optical waveguide with a multilayer gain-loss profile based on only two tunable parameters. A unique `fourth-order $β$-switching' phenomenon due to quasi-static gain-loss variation around EP4 has been explored. An exclusive chiral light dyna…
We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely $N^\text{th}$ order EP. Using symmetry considerations, we show an EP associated with an order system is very sensitive to the disorder. Specifically, if the EP associated with the ordered system occurs at the fixed degree of non-Hermiticity $γ_{EP}$, the disordered system will not have EP at the same $γ_{PT}$ which puts an obstacle in front of the observation and app…
Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this letter, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided…
Exceptional points (EPs), i.e., non-Hermitian degeneracies at which eigenvalues and eigenvectors coalesce, can be realized by tuning the gain/loss contrast of different modes in non-Hermitian systems or by engineering the asymmetric coupling of modes. Here we demonstrate a mechanism that can achieve EPs of arbitrary order by employing the non-reciprocal coupling of spinning cylinders sitting on a dielectric waveguide. The spinning motion breaks the time-reversal symmetry and removes the degeneracy of opposite chiral modes of the cylinders. Under the excitation of a linearly polarized plane wav…
An asymmetric \b{eta}-sheet structure of spider silk is said to induce optical second harmonic generation. In this paper, using an in-house non-scanning type femtosecond pulse laser second harmonic generation microscope, we characterized the behavior of the \b{eta}-sheet of spider silk under an applied external force. The orientation of the \b{eta}-sheets was more unidirectional when the silk was extended. One of the origins of the high mechanical strength of the dragline is suggested to be the physical arrangement of its \b{eta}-sheets.
The H1 photonic crystal cavity supports two degenerate dipole modes of orthogonal linear polarization which could give rise to circularly polarized fields when driven with a $π$/$2$ phase difference. However, fabrication errors tend to break the symmetry of the cavity which lifts the degeneracy of the modes, rendering the cavity unsuitable for supporting circular polarization. We demonstrate numerically, a scheme that induces chirality in the cavity modes, thereby achieving a cavity that supports intrinsic circular polarization. By selectively modifying two air holes around the cavity, the dip…
We investigate the influence of chirality on the PT-symmetric and PT-broken phase of PT-symmetric chiral systems. Starting from the point that transverse magnetic (TM) and transverse electric (TE) waves have different exceptional points, we show that with circularly polarized waves (which are linear combinations of TM and TE waves) mixed PT-symmetric phases can be realized and the extent of these phases can be highly controlled by either or both the chirality and the angle of incidence. Additionally, while the transmission of both TM and TE waves in non-chiral PT-symmetric systems is the same …
