Unidirectional Amplification Research Articles

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect.

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Here, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.

Phase and detuning control of the unidirectional reflection amplification based on the broken spatial symmetry.

In order to achieve the tunable unidirectional reflection amplification in a uniform atomic medium that is of vital importance to design high-quality nonreciprocal photonic devices, we propose a coherent closed three-level Δ-type atomic system by applying a microwave field, and a strong coupling field of linear variation along the x direction to control a probe field. In our scheme, the linearly increased coupling field destroys the spatial symmetry of probe susceptibility and effectively suppresses the reflection of one side; the microwave field constructs closed loop transitions to amplify the probe field and causes phase changes. The numerical simulation indicates that the unidirectional reflection amplification is sensitive to the relative phase ϕ and the coupling detuning Δc. Our results will open a new route toward harnessing optical non-reciprocity, which can provide more convenience and possibilities in the experimental realization.

Perfect non-reciprocal reflection amplification in closed loop coherent gain atomic system

High-performance non-reciprocal photonic devices can improve the efficiency of optical quantum manipulation, information processing, and quantum simulation effectively. The enhanced optical signal can simultaneously amplify the weak signal output by the quantum system and isolate the sensitive quantum system from the back-scattered external noise, which is the core technology of high-performance photonic devices. In our previous work (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1364/OE.499738">2023 <i>Opt. Express</i> <b>31</b> 38228</ext-link>), we have achieved dynamic control of unidirectional reflection amplification based on four-wave mixing gain and the use of coupling field intensity varying linearly with position. In this work, we design a simple three-level closed loop coherent gain atomic system, setting the intensity of coupling field to be varying with position step shape to break the spatial symmetry of probe susceptibility, and achieving perfect non-reciprocal reflection light amplification. In contrast, the stepped variation of coupling field intensity is easier to adjust in experiment, greatly reducing the difficulty in the experiment. Specifically, the system introduces phase modulation. By changing the phase, the frequency region of probe gain and absorption can be switched, which makes the modulation of reflection amplification more flexible.

Spatial susceptibility modulation and controlled unidirectional reflection amplification via four-wave mixing.

Control of unidirectional light propagation is of paramount importantance to optical signal processing and optical communication. Especially, the amplified optical signal can isolate noise well that may provide more applications. In this work, we propose a dynamically modulated regime to realize unidirectional reflection amplification in a short and dense uniform atomic medium, and all atoms are driven into four-level double-Λ type by two coupling fields with linearly varied intensities along x direction and two weak probe fields. Based on four-wave mixing resonance and the broken spatial symmetry, the complete nonreciprocal reflection (unidirectional reflection) can be amplified with reflectivity more than 2.0, even to 6.0. In addition, the width, height, and position of the unidirectional reflection bands can be tunable. Thus, our regime is feasible and may inspire further applications in all-optical networks that require controllable unidirectional light amplification.

Realization of the unidirectional amplification in a cavity magnonic system

We experimentally demonstrate the nonreciprocal microwave amplification using a cavity magnonic system, consisting of a passive cavity (i.e., the split-ring resonator), an active feedback circuit integrated with an amplifier, and a ferromagnetic spin ensemble (i.e., a yttrium–iron–garnet sphere). Combining the amplification provided by the active circuit and the nonreciprocity supported by the cavity magnonics, we implement a nonreciprocal amplifier with the functions of both unidirectional amplification and reverse isolation. The microwave signal is amplified by 11.5 dB in the forward propagating direction and attenuated in the reverse direction by −34.7 dB, giving an isolation ratio of 46.2 dB. Such a unidirectional amplifier can be readily employed in quantum technologies, where the device can simultaneously amplify the weak signal output by the quantum system and isolate the sensitive quantum system from the backscattered external noise. Also, it is promising to explore more functions and applications using a cavity magnonic system with a real gain.

Giant boundary layer induced by nonreciprocal coupling in discrete systems

Nonreciprocally coupled systems present rich dynamical behavior such as unidirectional amplification, fronts, localized states, pattern formation, and chaotic dynamics. Fronts are nonlinear waves that may connect an unstable equilibrium with a stable one and can suffer a convective instability when the coupling is nonreciprocal. Namely, a state invades the other one, and due to boundary conditions, the front stops and creates a boundary layer. Unexpectedly, in nonreciprocal coupled systems, we observe arbitrarily large boundary layers in the convective regime when the condition at the fixed edge does not match the equilibrium value. We analytically determine the boundary layer size using map iterations; these results agree with numerical simulations. On the other hand, if one of the boundary conditions matches the unstable equilibrium state, the boundary layer size diverges; however, due to the computer numerical truncation, it is finite in numerical simulations. Our result shows that, in nonreciprocally coupled systems, this mismatch in the boundary condition is relevant in controlling the boundary layer size, which exhibits a logarithm scaling with the mismatch value.

Insect-scale jumping robots enabled by a dynamic buckling cascade

Millions of years of evolution have allowed animals to develop unusual locomotion capabilities. A striking example is the legless-jumping of click beetles and trap-jaw ants, which jump more than 10 times their body length. Their delicate musculoskeletal system amplifies their muscles' power. It is challenging to engineer insect-scale jumpers that use onboard actuators for both elastic energy storage and power amplification. Typical jumpers require a combination of at least two actuator mechanisms for elastic energy storage and jump triggering, leading to complex designs having many parts. Here, we report the new concept of dynamic buckling cascading, in which a single unidirectional actuation stroke drives an elastic beam through a sequence of energy-storing buckling modes automatically followed by spontaneous impulsive snapping at a critical triggering threshold. Integrating this cascade in a robot enables jumping with unidirectional muscles and power amplification (JUMPA). These JUMPA systems use a single lightweight mechanism for energy storage and release with a mass of 1.6 g and 2 cm length and jump up to 0.9 m, 40 times their body length. They jump repeatedly by reengaging the latch and using coiled artificial muscles to restore elastic energy. The robots reach their performance limits guided by theoretical analysis of snap-through and momentum exchange during ground collision. These jumpers reach the energy densities typical of the best macroscale jumping robots, while also matching the rapid escape times of jumping insects, thus demonstrating the path toward future applications including proximity sensing, inspection, and search and rescue.

Unidirectional amplification in optomechanical system coupling with a structured bath.

Nonreciprocity plays an indispensable role in quantum information transmission. We theoretically study the unidirectional amplification in the non-Markovian regime, in which a nanosphere surrounded by a structured bath is trapped in a single (dual)-mode cavity. The global mechanical response function of the nanosphere is markedly altered by the non-Markovian structured bath through shifting the effective frequency and magnifying the response function. Consequently, when there is a small difference in the transmission rate within the regime of Markovian, the unidirectional amplification is achieved in the super-Ohmic spectral environment. In the double-optomechanical coupling system, the phase difference between two optomechanical couplings can reverse the transmission direction. Meanwhile, the non-Markovian bath still can amplify the signal because of the XX-type coupling between nanosphere and its bath.

Non-Hermitian chiral phononics through optomechanically induced squeezing.

Imposing chirality on a physical system engenders unconventional energy flow and responses, such as the Aharonov-Bohm effect1 and the topological quantum Hall phase for electrons in a symmetry-breaking magnetic field. Recently, great interest has arisen in combining that principle with broken Hermiticity to explore novel topological phases and applications2-16. Here we report phononic states with unique symmetries and dynamics that are formed when combining the controlled breaking of time-reversal symmetry with non-Hermitian dynamics. Both of these are induced through time-modulated radiation pressure forces in small nano-optomechanical networks. We observe chiral energy flow among mechanical resonators in a synthetic dimension and Aharonov-Bohm tuning of their eigenmodes. Introducing particle-non-conserving squeezing interactions, we observe a non-Hermitian Aharonov-Bohm effect in ring-shaped networks in which mechanical quasiparticles experience parametric gain. The resulting complex mode spectra indicate flux-tuning of squeezing, exceptional points, instabilities and unidirectional phononic amplification. This rich phenomenology points the way to exploring new non-Hermitian topological bosonic phases and applications in sensing and transport that exploit spatiotemporal symmetry breaking.

Unidirectional amplification with acoustic non-Hermitian space\u2212time varying metamaterial

Space−time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion, and non-reciprocal transmission. The non-Hermitian space−time varying systems combining non-Hermiticity and space−time varying capability, have been proposed to realize wave control like unidirectional amplification, while its experimental realization still remains a challenge. Here, based on metamaterials with software-defined impulse responses, we experimentally demonstrate non-Hermitian space−time varying metamaterials in which the material gain and loss can be dynamically controlled and balanced in the time domain instead of spatial domain, allowing us to suppress scattering at the incident frequency and to increase the efficiency of frequency conversion at the same time. An additional modulation phase delay between different meta-atoms results in unidirectional amplification in frequency conversion. The realization of non-Hermitian space−time varying metamaterials will offer further opportunities in studying non-Hermitian topological physics in dynamic and nonreciprocal systems.

Nonreciprocity in Bianisotropic Systems with Uniform Time Modulation.

Physical systems with material properties modulated in time provide versatile routes for designing magnetless nonreciprocal devices. Traditionally, nonreciprocity in such systems is achieved exploiting both temporal and spatial modulations, which inevitably requires a series of time-modulated elements distributed in space. In this Letter, we introduce a concept of bianisotropic time-modulated systems capable of nonreciprocal wave propagation at the fundamental frequency and based on uniform, solely temporal material modulations. In the absence of temporal modulations, the considered bianisotropic systems are reciprocal. We theoretically explain the nonreciprocal effect by analyzing wave propagation in an unbounded bianisotropic time-modulated medium. The effect stems from temporal modulation of spatial dispersion effects which to date were not taken into account in previous studies based on the local-permittivity description. We propose a circuit design of a bianisotropic metasurface that can provide phase-insensitive isolation and unidirectional amplification.

Tunable unidirectional compact acoustic amplifier via space-time modulated membranes

Space-time modulation has recently attracted considerable attention as it enables new possibilities in wave manipulation and control. Here we propose a tunable unidirectional acoustic amplifier based on a space-time modulated membrane system. The transfer matrix method is applied to design this system and optimize the modulation parameters for the realization of unidirectional amplification. Efficient one-way amplification of acoustic waves is demonstrated theoretically and numerically within a frequency range from 2260 to 2520 Hz, with overall dimension being less than $1/3$ of the corresponding wavelength. Across this operation band, the amplification factor in the positive direction varies smoothly from 3.0 to 5.8, while the transmitted wave energy in the negative direction does not change significantly. Our work identifies a feasible approach to realize a tunable unidirectional acoustic amplifier via space-time modulated membranes, which offers a design platform for a number of applications in sensing, imaging, and communication.

Dual-gate transistor amplifier in a multimode optomechanical system.

We present a dual-gate optical transistor based on a multimode optomechanical system, composed of three indirectly coupled cavities and an intermediate mechanical resonator pumped by a frequency-matched field. In this system, two cavities driven on the red mechanical sidebands are regarded as input/ouput gates/poles and the third one on the blue sideband as a basic/control gate/pole, while the resonator as the other basic/control gate/pole. As a nonreciprocal scheme, the significant unidirectional amplification can be resulted by controlling the two control gates/poles. In particular, the nonreciprocal direction of the optical amplification/rectification can be controlled by adjusting the phase differences between two red-sideband driving fields (the pumping and probe fields). Meanwhile, the narrow window that can be analyzed by the effective mechanical damping rate, arises from the extra blue-sideband cavity. Moreover, the tunable slow/fast light effect can be observed, i.e, the group velocity of the unidirectional transmission can be controlled, and thus the switching scheme of slow/fast light effect can also utilized to realize both slow and fast lights through opposite propagation directions, respectively. Such an amplification transistor scheme of controllable amplitude, direction and velocity may imply exciting opportunities for potential applications in photon networks and quantum information processing.

Optimal unidirectional amplification induced by optical gain in optomechanical systems

We propose a three-mode optomechanical system to realize optical nonreciprocal transmission with unidirectional amplification, where the system consists of two coupled cavities and one mechanical resonator which interacts with only one of the cavities. Additionally, the optical gain is introduced into the optomechanical cavity. It is found that for a strong optical input, the optical transmission coefficient can be greatly amplified in a particular direction and suppressed in the opposite direction. The expressions of the optimal transmission coefficient and the corresponding isolation ratio are given analytically. Our results pave a way to design high-quality nonreciprocal devices based on optomechanical systems.

Directional amplifiers in a hybrid optomechanical system

The unidirectional amplification of signals is of great importance in signal processing and communication. We propose a hybrid optomechanical system to achieve directional amplification between light fields with different frequencies, where three cavities are coupled to a common mechanical resonator. Two cavities function as an input cavity and an output cavity, respectively, while the third cavity is introduced to facilitate the unidirectional transfer between the input and output cavities. In our scheme, three tones are required to realize the directional amplifier without requiring any gain medium or additional mechanical driving. We find that under certain conditions, the amplifier can reach a large photon number gain with the quantum-limited added noise, with no limitation on the gain–bandwidth product. Furthermore, the directional amplification behavior is controllable by modulating the phase differences between the effective optomechanical couplings.

Nonreciprocal Phonon Laser

We propose nonreciprocal phonon lasing in a coupled cavity system composed of an optomechanical and a spinning resonator. We show that the optical Sagnac effect leads to significant modifications in both the mechanical gain and the power threshold for phonon lasing. More importantly, the phonon lasing in this system is unidirectional, that is the phonon lasing takes place when the coupled system is driven in one direction but not the other. Our work establishes the potential of spinning optomechanical devices for low-power mechanical isolation and unidirectional amplification. This provides a new route, well within the reach of current experimental abilities, to operate cavity optomechanics devices for such a wide range of applications as directional phonon switches, invisible sound sensing, and topological or chiral acoustics.

Nonreciprocal Gain in Non-Hermitian Time-Floquet Systems.

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non-Hermitian time-Floquet systems are capable of nonreciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect nonreciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the complex coupling between lossless resonators, promoting only upward frequency conversion, and leading to nonreciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.

Topological phases and edge states in a non-Hermitian trimerized optical lattice

Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled waveguide lattice are evaluated, the PT-symmetric phase of a PT-symmetric lattice can have different topologies; the edge states depend on the lattice size, boundary configuration, and competition between the coupling and degree of non-Hermiticity. The topologically nontrivial region extends in the presence of periodic gain and loss. The nonzero geometric phases accumulated by the Bloch bands indicate the existence of topologically protected edge states between the band gaps. The unidirectional amplification and attenuation zero modes appear above a threshold degree of non-Hermiticity, which facilitate the development of a robust optical diode.

Non-Hermitian interferometer: Unidirectional amplification without distortion

A non-Hermitian interferometer can realize asymmetric transmission in the presence of imaginary potential and magnetic flux. Here, we propose a non-Hermitian dimer with an unequal hopping rate by an interferometer-like cluster in the framework of tight-binding model. The intriguing features of this design are the wave-vector independence and unidirectionality of scattering, which amplifies wavepacket without distortion and absorbs incoherent wave without reflection. The absorption relates to the system spectral singularities, the dynamical behaviors of the spectral singularities are also investigated analytically and numerically.