Unidirectional Invisibility Research Articles

Angular excitation of exceptional points and pseudospetra of photonic lattices

Abstract Optical parity-time ( PT ) symmetry has triggered a plethora of theoretical and experimental studies, and as a result non-Hermitian photonics is one of the frontiers of optics today. From unidirectional invisibility and coherent perfect absorbers to wireless power transfer and ultrasensitive sensors, non-hermiticity led to numerous important applications that rely on gain-loss synthetic structures. In particular, one such structure is that of complex photonic lattices that may exhibit exceptional points (EPs) around which the corresponding sensitivity is increased by orders of magnitude. Here, we investigate a new multiparametric family of non-Hermitian lattices that respects PT -symmetry, and examine their spectral sensitivity in terms of pseudospectra, as well, the angular excitation of the underlying EPs.

Tracking exceptional points above the lasing threshold

Recent studies on exceptional points (EPs) in non-Hermitian optical systems have revealed unique traits, including unidirectional invisibility, chiral mode switching and laser self-termination. In systems featuring gain/loss components, EPs are commonly accessed below the lasing threshold, i.e., in the linear regime. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning impedes the formation of EPs, here we demonstrate that such detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the EP. Furthermore, we find that the pump imbalance at lasing EPs varies with the total pump power, enabling their continuous tracking. This work uncovers the unstable nature of EPs above laser threshold in coupled semiconductor lasers, offering promising opportunities for the realization of self-pulsing nanolaser devices and frequency combs.

Broadband directional invisibility

The discovery of unidirectional invisibility and its broadband realization in optical media satisfying spatial Kramers–Kronig relations are important landmarks of non-Hermitian photonics. We offer a precise characterization of a higher-dimensional generalization of this effect and find sufficient conditions for its realization in the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions. More specifically, given a positive real number α and a continuum of unit vectors Ω, we provide explicit conditions on the interaction potential (or the permittivity and permeability tensors of the scattering medium in the case of electromagnetic scattering) under which it displays perfect (non-approximate) invisibility whenever the incident wavenumber k does not exceed α (i.e., k∈(0,α]) and the direction of the incident wave vector ranges over Ω. A distinctive feature of our approach is that it allows for the construction of potentials and linear dielectric media that display perfect directional invisibility in a finite frequency domain.

Tunable unidirectional reflectionless propagation in non-hermitian graphene-based metasurface

In this paper, we propose an graphene-based non-Hermitian metasurface and numerically investigate a tunable unidirectional reflectionless phenomenon for the THz region. The metasurface is composed of cascaded square graphene patch and its complementary structure separated by a thin dielectric layer. By simply selecting the thickness of the dielectric layer, the backward reflection for our structure is zero, and the corresponding forward reflection is about 35% at 31.15 THz. The coupled mode theory and the non-Hermitian scattering matrix are used to show that unidirectional reflectionless is responsible for the exceptional point. The Fermi energy of the graphene can actively tune the one-way zero reflection frequency. By varying the Fermi energy from 0.56 eV to 0.64 eV, a spectral blue shift of one-way zero reflection from 29.6 THz to 32.2 THz is obtained, maintaining the same structure. We believe that the proposed scheme will provides more flexible opportunities to realize unidirectional invisibility, diode-like device, on-chip sensors and filters.

Perfect light absorber with a PT phase transition via coupled topological interface states

Recently, the concepts of parity–time (PT) symmetry and band topology have inspired many novel ideas for light manipulation in their respective directions. Here we propose and demonstrate a perfect light absorber with a PT phase transition via coupled topological interface states (TISs), which combines the two concepts in a one-dimensional photonic crystal heterostructure. By fine tuning the coupling between TISs, the PT phase transition is revealed by the evolution of absorption spectra in both ideal and non-ideal PT symmetry cases. Especially, in the ideal case, a perfect light absorber at an exceptional point with unidirectional invisibility is numerically obtained. In the non-ideal case, a perfect light absorber in a broken phase is experimentally realized, which verifies the possibility of tailoring non-Hermiticity by engineering the coupling. Our work paves the way for novel effects and functional devices from the exceptional point of coupled TISs, such as a unidirectional light absorber and exceptional-point sensor.

Dynamic cloaking of a diamond-shaped hole in elastic plate

Invisibility cloaks for flexural waves have mostly been examined in a continuous-wave regime, while invisibility is likely to deteriorate for short pulses. Here, we propose the practical realization of a unidirectional invisibility cloak for flexural waves based on an area-preserving coordinate transformation. Time-resolved experiments reveal how the invisibility cloak deviates a pulsed plane wave from its initial trajectory and how the initial wavefront perfectly recombines behind the cloak, leaving the diamond-shaped hole invisible, notwithstanding the appearance of a forerunner. Three-dimensional full-elasticity simulations support our experimental observations.

Dual-loop parity-time symmetric system with a rational loop length ratio.

By exploring the relationship between the gain/loss and the coupling coefficient, parity-time (PT) symmetry has been well explored in the photonics and optoelectronics fields to achieve unique functions, such as sidemode suppression, non-reciprocal light propagation, and unidirectional invisibility. In general, a PT-symmetric system has an architecture with two identical coupled resonators or loops. In this Letter, we explore the possibility of implementing a PT-symmetric system having an architecture with one resonator having a loop length that is a rational number of times the length of the other resonator, to increase the sidemode suppression ratio. A theoretical analysis is performed, which is validated by a proof-of-concept experiment in which a fiber ring laser having two loops with a length ratio being a rational number of 200/3, supporting single-longitudinal-mode lasing at 1555.88 nm, is demonstrated. Thanks to the non-identical loop lengths, the sidemode suppression ratio is increased, which is 53.2 dB in the experiment.

Double exceptional points in grating coupled metal-insulator-metal heterostructure.

In this work we theoretically study the exceptional points and reflection spectra characteristics of a grating coupled metal-insulator-metal heterostructure, which is a non-Hermitian system. Our results show that by selecting suitable geometrical parameters with grating periodicity @150 nm, that satisfy zero reflection condition, double exceptional points appear in a mode bifurcation regime. Furthermore, the thickness of partition metal layer between two cavities plays an important role in controlling the reflection properties of the heterostructure. There is a clear mode splitting when the partition layer allows strong coupling between the two cavity modes. Conversely, in weak coupling regime the mode splitting becomes too close to be distinguished. Moreover, the vanishing of reflection leads to unidirectional reflectionless propagation, which is also known as unidirectional invisibility. With grating periodicity ≥400nm, the transmissions for forward and backward incident directions are no longer the same due to the generation of diffraction. High contrast ratio (≈1) between the two incident directions leads to asymmetric transmission. This work lays the basis for designing double exceptional points and asymmetric transmission in coupled non-Hermitian photonics system. The proposed heterostructure can be a good candidate for new generation optical communications, optical sensing, photo-detection, and nano-photonic devices.

Unidirectional invisibility in a PT-symmetric structure designed by topology optimization.

This study designs a piecewise homogeneous dielectric structure with parity-time (PT) symmetry that realizes the unidirectional invisibility of a perfect electric conductor in two dimensions. We apply topology optimization and design a PT-symmetric material that minimizes the total scattering cross section for a given plane wave to achieve unidirectional invisibility. A rigorous mode-matching finite element method is used to perform all computations. The designed PT-symmetric structure suppressed plane-wave scattering by approximately 99% for the given incident direction, whereas the reversed incident wave experienced 83 times larger scattering intensity. The proposed method provides a novel approach, to the best of our knowledge, to promote various applications of PT symmetry.

Step-wise constant-amplitude waves in non-Hermitian disordered media

Multi-reflection interference of sound waves is ubiquitous in our daily life, and suppressing any such distortions of a wave’s free propagation and achieving counter-directional adaptation is a challenging task, with many applications in acoustics. Here, we propose a non-Hermitian Fabry–Perot resonance unit, which demonstrates unidirectional invisibility in opposite directions at the so-called exceptional points by adjusting its geometric configuration and intrinsic acoustic parameters. Then, we extend the principle and design a waveguide containing six inclusion–membrane pairs in which a unique property of step-wise constant-amplitude waves in two opposite directions has been realized, irrespective of whether the distribution of inclusions is periodic or random. Our method breaks through the limitation of the impedance, amount, position of the inclusions, and the incident direction of the waves, revealing potential applications in acoustic sensing, noise control engineering, and other related wave disciplines.

Truncation-dependent PT phase transition for the edge states of a two-dimensional non-Hermitian system

We consider a bulk system supporting parity and time reversal ($PT$) symmetry, and investigate how the $PT$ phase transition of edge states is influenced by different truncations of the system. As an example, we study a two-dimensional $PT$-symmetric Su--Schrieffer--Heeger lattice with non-Hermitian onsite potentials. We find that when the truncation preserves certain symmetries of the bulk lattice, the edge states can remain in the $PT$-unbroken phase when the non-Hermitian onsite potentials are less than a nonzero critical value. On the other hand, when the truncation removes such symmetries, edge states with complex eigen-energies are observed for infinitesimal non-Hermitian onsite potentials. We develop an analytic theory to account for such behaviors. Our results are important in the manipulation of the gain and loss behaviors of edge states in non-Hermitian systems, with potential applications in the study of topological lasers, quantum sensors, and unidirectional invisibility.

Inverse design of invisibility cloaks using the optical theorem

We develop and apply an optimization method to design unidirectional invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object which, by the optical theorem, is equivalent to the total cross section. The use of the optical theorem circumvents the need to evaluate and integrate the scattering amplitude over an angle at each iteration, and thus provides a simpler, more computationally efficient objective function to optimize structures. We implement the approach using gradient descent optimization and present several gradient-permittivity unidirectional cloaks that reduce scattering by metallic targets of different sizes and shapes.

Parity–time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time (PT) symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain. Here, we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits. By judiciously adjusting the resistances and inductances in the external circuits, we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility. Moreover, the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits, which represents the active control that makes the acoustic manipulation more convenient. Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Non-Hermitian topological whispering gallery.

In 1878, Lord Rayleigh observed the highly celebrated phenomenon of sound waves that creep around the curved gallery of St Paul's Cathedral in London1,2. These whispering-gallery waves scatter efficiently with little diffraction around an enclosure and have since found applications in ultrasonic fatigue and crack testing, and in the optical sensing of nanoparticles or molecules using silica microscale toroids. Recently, intense research efforts have focused on exploring non-Hermitian systems with cleverly matched gain and loss, facilitating unidirectional invisibility and exotic characteristics of exceptional points3,4. Likewise, the surge in physics using topological insulators comprising non-trivial symmetry-protected phases has laid the groundwork in reshaping highly unconventional avenues for robust and reflection-free guiding and steering of both sound and light5,6. Here we construct a topological gallery insulator using sonic crystals made of thermoplastic rods that are decorated with carbon nanotube films, which act as a sonic gain medium by virtue of electro-thermoacoustic coupling. By engineering specific non-Hermiticity textures to the activated rods, we are able to break the chiral symmetry of the whispering-gallery modes, which enables the out-coupling of topological 'audio lasing' modes with the desired handedness. We foresee that these findings will stimulate progress in non-destructive testing and acoustic sensing.

Non-Hermitian metasurfaces for the best of plasmonics and dielectrics

Materials and their geometry make up the tools for designing nanophotonic devices. In the past, the real part of the refractive index of materials has remained the focus for designing novel devices. The absorption, or imaginary index, was tolerated as an undesirable effect. However, a clever distribution of imaginary index of materials offers an additional degree of freedom for designing nanophotonic devices. Non-Hermitian optics provides a unique opportunity to take advantage of absorption losses in materials to enable unconventional physical effects. Typically occurring near energy degeneracies called exceptional points, these effects include enhanced sensitivity, unidirectional invisibility, and non-trivial topology. In this work, we leverage plasmonic absorption losses (or imaginary index) as a design parameter for non-Hermitian, passive parity-time symmetric metasurfaces. We show that coupled plasmonic-photonic resonator pairs, possessing a large asymmetry in absorptive losses but balanced radiative losses, exhibit an optical phase transition at an exceptional point and directional scattering. These systems enable new pathways for metasurface design using phase, symmetry, and topology as powerful tools.

Unidirectional invisibility of an acoustic multilayered medium with parity-time-symmetric impedance modulation

Non-Hermitian scattering systems respecting parity-time symmetry exhibit unidirectional invisibility or reflectionlessness at an exceptional point of the scattering matrix. In this study, we investigate the scattering properties of a one-dimensional acoustic parity-time-symmetric multilayered medium. Parity-time symmetry is defined by a spatial small-amplitude square-wave modulation of the medium parameters in the complex plane. Such a multilayered medium has been demonstrated to reach an exceptional point and support unidirectional invisibility for balanced real and imaginary part modulations of the refractive index. Through the analysis of interference within the medium, we show that the complex modulation of acoustic impedance instead of the refractive index governs the exceptional point of the scattering matrix and determines the occurrence of the unidirectional invisibility. This unidirectional invisibility is further investigated for more general cases of complex parameter distribution including unequal modulation amplitudes and rectangular wave modulation. Our study provides an intuitive physical picture of the occurrence of unidirectional invisibility induced by an exceptional point in acoustic wave systems. Moreover, this study could facilitate the design and practical realization of acoustic parity-time-symmetric structures.

Chirped pulse propagation in a quasi-PT-symmetric medium with a broadband exceptional-point condition.

The boundary problem of dynamical Bragg diffraction of a chirped optical pulse in a dispersive quasi-PT-symmetric photonic crystal (PhC) in the Laue geometry ("on transmission") is solved by the analytical spectral method. It is shown that, in a quasi-PT-symmetric medium, in which an inhomogeneous spectral line width is much larger than the spectrum of investigated field, the exceptional-point (EP) condition is realized in a wide continuous frequency range, i.e., so-called broadband exceptional-point (BEP) condition takes place. If the Bragg condition is satisfied in a much narrower spectral range than the pulse spectrum, it leads to dramatic changes in the propagation dynamics and parameters of broadband chirped pulses in a quasi-PT-symmetric PhC. Indeed, for a positive Bragg angle of incidence in the case of diffraction in the Laue geometry, the entire spectrum of a broadband chirped pulse fulfills the BEP condition. The diffractionally reflected wave is absent in the BEP regardless of whether the Bragg condition is satisfied, and the pulse propagates as in a homogeneous conservative medium, i.e., without diffraction, gain and loss - unidirectional invisibility. When the sign of the angle of incidence changes, a unidirectional enhancement of the chirped diffracted pulse is observed in that part of it whose frequency simultaneously satisfies both the BEP condition and the Bragg condition. The rest part of the pulse, for which the Bragg condition is not satisfied, propagates as in the case of a positive angle of incidence - there is no diffracted wave. With a smooth change in the angle of incidence of the chirped pulse, a change in frequency that satisfies the Bragg condition occurs and, as a consequence, a smooth change appears in the frequency of the amplified output pulse, as well as in its duration and transverse size. It is also shown that the dispersion of the group velocity of the pulse is suppressed in the frequency range of the BEP condition. Therefore, all its frequency components propagate at a speed close to the speed of light in a conservative homogeneous medium.

Pseudo-Hermitian trimer: Asymmetric resonances and exceptional points

A pseudo-Hermitian (PH) system made up of three coupled waveguides (trimer) with an overall balanced gain and loss is investigated in a parity time (PT)-symmetric-like regime. Remarkably, the pseudo hermiticity parameter controls the asymmetric spatial field modulation between left and right propagating waves whereby, a complex coupling arises that induces an additional source of non-Hermiticity, which in the system acts as a relative gain/loss Hellmann-Feynman correction. In this situation, we show that, transmissionless backscatterings are observed for the PH-trimer in the non PT broken phase. Interestingly, the scattering properties of PH-trimer result in multiple lasing states with different mechanisms. In particular, we show that in the PT-symmetric case, the lasing modes associated to the coherent perfect-absorption (CPA), occur from the spectral singularity induced by the Hermitian chain coupling and give rise to unidirectional invisibility in the direction of incident wave. On the contrary, additional emerging lasing modes in a PH regime result from the scattering maxima resonance. We demonstrate that this specific cases suppress the CPA-laser phenomenon and rather exhibit exceptional points characterized by reflectionless but also the points of transmissionless. Numerical beam propagations realized to emphasize the results are in good agreement with the scattering investigation until gain/loss parameter is around it’s value giving resonance.

Stability Constraints on Practical Implementation of Parity-Time-Symmetric Electromagnetic Systems

Recently, several applications leveraging unconventional manipulation of electromagnetic radiation based on parity-time symmetry have been proposed in the literature. Typical examples include systems with unidirectional invisibility and asymmetric refraction. Such applications assume an inherent system stability and no occurrence of unbounded signal growth or unwanted self-oscillations. Here, a general instability issue of parity-time-symmetric systems is investigated, with particular emphasis on a recently proposed system based on resistive metasurfaces. Explicit closed-form stability criterion is derived, crosschecked and verified by both time-domain transient simulations and the measurements on an experimental demonstrator operating in a lower radiofrequency range. Results of this study lead to the conclusion that any parity-time-symmetric system is necessarily marginally stable. Finally, it is shown that such a marginally stable system may easily become unstable if not designed carefully.

Transfermatrix in scattering theory: a survey of basic properties and recent developments

We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials, Jost solutions, spectral singularities and their time-reversal, and unidirectional reflectionlessness and invisibility. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of time-independent scattering theory in one dimension. This formulation relates the transfer matrix and therefore the solution of the scattering problem for a given potential to the solution of the time-dependent Schrodinger equation for an effective non-unitary two-level quantum system. We provide a self-contained treatment of this formulation and some of its most important applications. Specifically, we use it to devise a powerful alternative to the Born series and Born approximation, derive dynamical equations for the reflection and transmission amplitudes, discuss their application in constructing exact tunable unidirectionally invisible potentials, and use them to provide an exact solution for single-mode inverse scattering problems. The latter, which has important applications in designing optical devices with a variety of functionalities, amounts to providing an explicit construction for a finite-range complex potential whose reflection and transmission amplitudes take arbitrary prescribed values at any given wavenumber.