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It is shown that the concept of topological phase transitions can be used to design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio.

The nonlinear inertial amplifier base isolators (NIABI) for dynamic response mitigation of structures are introduced in this paper. The nonlinear inertial amplifiers are installed inside the core of the traditional base isolators (TBI) to upgrade their vibration reduction capacity. The equivalent linearization method applies to linearize each element from highly nonlinear equations of motion of nonlinear NIABI to derive the optimal closed-form solutions for nonlinear NIABI. Therefore, H 2 and H ∞ optimization methods are applied to derive the exact closed-form expressions for optimal design parameters of NIABI, linearized NIABI, and TBI analytically. Initially, the dynamic responses of the structures isolated by the NIABI, linearized NIABI, and TBI are obtained through the transfer function formation. Thus, the dynamic response reduction capacities of H 2 and H ∞ optimized NIABI are significantly 38.55 % and 65.14 % superior to the H 2 and H ∞ optimized TBI. In addition, the nonlinear dynamic responses of the isolated structures are also derived analytically through the harmonic balancing method. Therefore, the dynamic response reduction capacities of H 2 and H ∞ optimized nonlinear NIABI are significantly 44.51 % , 39.80 % , 35.81 % and 90.10 % , 77.49 % , 67.66 % superior to the H 2 and H ∞ optimized TBI, inertial amplifier base isolator (IABI), linearized version of nonlinear inertial amplifier base isolator (linearized NIABI). The effectiveness of the optimum NIABI has been studied further by a numerical study using the Newmark-beta method with near-field earthquake base excitations (pulse records). Accordingly, the displacement and acceleration response reduction capacities of the optimum NIABI are 14.47 % and 22.23 % superior to the optimum TBI. The overall result shows that the nonlinearity of the inertial amplifiers increases the dynamic response reduction capacity of the traditional base isolators and inertial amplifier base isolators. All of the results are mathematically accurate and suitable for practical applications.

In recent decades, quasi-zero stiffness (QZS) vibration isolation systems with nonlinear characteristics have aroused widespread attention and strong research interest due to their enormous potential in low-frequency vibration isolation. This work comprehensively reviews recent research on QZS vibration isolators with a focus on the principle, structural design, and vibration isolation performance of various types of QZS vibration isolators. The negative-stiffness mechanism falls into two categories by different realization methods: passive and active/semi-active negative-stiffness mechanisms. Representative design, performance analysis, and practical application are elaborated for each category. The results show that passive vibration isolation systems have excellent low-frequency vibration isolation performance under specific payload and design parameters, whereas active/semi-active vibration isolation systems can better adapt to different environmental conditions. Finally, the development trends and challenges of QZS vibration isolators are summarized, and the solved and unsolved problems are highlighted. This review aims to give a comprehensive understanding of the QZS vibration isolation mechanism. It also provides guidance on designing new QZS vibration isolators for improving their vibration isolation performance and engineering applicability.

This paper proposes a novel bi-state nonlinear vibration isolator (BS-NVI) consisting of a linear mass–spring–damper and several permanent magnets (PMs). The working state of the BS-NVI can be monostable or bistable depending on the relative position of the PMs. The theoretical model of the BS-NVI is established. The transmissibility of the BS-NVI is derived according to the harmonic balance method. Both the simulation and experimental efforts are performed to study the nonlinear dynamics and vibration isolation performance of the BS-NVI. The results demonstrate that the monostable isolator acts like a quasi-zero-stiffness isolator and exhibits the hardening-spring-liked characteristic. With the change in the relative position of the PMs, the transmissibility and the peak frequency are decreased. However, the bistable isolator undergoes the interwell and intrawell oscillations with the change in the excitation amplitude and frequency. The motion of the bistable isolator can be periodic or chaotic. Due to the snap-through action, the transmissibility of the bistable isolator could be smaller than 1 in part of the resonance region.

Most existing quasi-zero stiffness (QZS) isolators with excellent vibration isolation performance in the low-frequency range are designed to attenuate vibration transmission only in one direction, but vibration suppression in multi-direction is more useful and expected in engineering practice. Hence, a novel 3-degree-of-freedom (3-DOF) passive vibration isolation unit with enhanced QZS effect in a large stroke is designed based on the X-shaped mechanism. The 3-DOF vibration isolation unit exhibits beneficial nonlinear stiffness and damping properties, and it can provide excellent ultra-low-frequency vibration isolation performance in three directions simultaneously. Combining two such isolation units can of course lead to more DOF vibration isolation. The effects of several design parameters such as spring stiffness, lengths of the rods, static equilibrium positions, spring connection parameters, damping coefficients and excitation amplitudes on vibration isolation performance are analyzed in detail. Some comparisons of the static characteristics and vibration isolation performance with a spring–mass–damper (SMD) isolator and an existing typical QZS isolator are carried out. The results reveal that (a) the proposed 3-DOF vibration isolation unit can have much enhanced QZS range with larger loading capacity in the vertical and horizontal directions and HSLD stiffness in the rotational direction; (b) when the excitation amplitudes are large, the novel vibration isolation unit exhibits beneficial nonlinear properties in all three directions without jumping and bifurcation phenomena; (c) compared with the typical QZS isolator, the X-shaped mechanism enables the proposed isolation unit to possess excellent vibration isolation performance in three directions simultaneously with guaranteed stable equilibrium; (d) the new 3-DOF isolator includes only 4 bars in the entire mechanism due to the special and totally new arrangement of the X-shaped mechanism without any guiding sliders, leading to more compact designs of multi-DOF vibration isolation systems of high performance, definitely demanded by engineering practices.

Researchers show that optical isolators based on nonlinearity cannot provide complete isolation for arbitrary backwards propagating noise, revealing limitations for their practical application. Motivated by the demands of integrated and silicon photonics, there is significant interest in optical isolators in on-chip integrated systems. Recent works have therefore explored nonlinear optical isolators and demonstrated non-reciprocal transmission contrast when waves are injected in forward or backward directions 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . However, whether such nonlinear isolators can provide complete isolation under practical operating conditions remains an open question. Here, we analytically prove and numerically demonstrate a dynamic reciprocity in nonlinear optical isolators based on Kerr or Kerr-like nonlinearity. We show that, when a signal is transmitting through, such isolators are constrained by a reciprocity relation for a class of small-amplitude additional waves and, as a result, cannot provide isolation for arbitrary backward-propagating noise. This result points to an important limitation on the use of nonlinear optical isolators for signal processing and for laser protection.

Emerging technologies based on tailorable photon–phonon interactions promise new capabilities ranging from high-fidelity information processing to non-reciprocal optics and quantum state control. However, many existing realizations of such light–sound couplings involve unconventional materials and fabrication schemes challenging to co-implement with scalable integrated photonic circuitry. Here, we demonstrate direct acousto-optic modulation within silicon waveguides using electrically driven surface acoustic waves (SAWs). By co-integrating electromechanical SAW transducers with a standard silicon-on-insulator photonic platform, we harness silicon’s strong elasto-optic effect to create travelling-wave phase and single-sideband amplitude modulators from 1 to 5 GHz, with index modulation strengths comparable to electro-optic technologies. Extending this non-local interaction to centimetre scales, we demonstrate non-reciprocal modulation with operation bandwidths of >100 GHz and insertion losses of <0.6 dB. This acousto-optic platform is compatible with complementary metal–oxide–semiconductor fabrication processes and existing silicon photonic device architectures, opening the door to flexible, low-loss modulators and non-magnetic optical isolators and circulators in integrated photonic circuits.Direct acousto-optic modulation within complementary metal–oxide–semiconductor compatible silicon photonic waveguides using electrically driven surface acoustic waves is demonstrated. Non-reciprocal operation bandwidths of >100 GHz and insertion losses of <0.6 dB are obtained.

Patterned chiral liquid crystals operate as configurable optical elements. Reflective metasurfaces based on metallic 1 , 2 , 3 and dielectric 4 , 5 nanoscatterers have attracted interest owing to their ability to control the phase of light. However, because such nanoscatterers require subwavelength features, the fabrication of elements that operate in the visible range is challenging. Here, we show that chiral liquid crystals 6 , 7 with a self-organized helical structure enable metasurface-like, non-specular reflection in the visible region. The phase of light that is Bragg-reflected off the helical structure can be controlled over 0–2π depending on the spatial phase of the helical structure; thus planar elements with arbitrary reflected wavefronts can be created via orientation control. The circular polarization selectivity and external field tunability of Bragg reflection open a wide variety of potential applications for this family of functional devices, from optical isolators to wearable displays.

Semi-active vibration isolators have attracted considerable attention due to their high reliability and excellent vibration isolation performance. Most of the existing adjustable stiffness components can only be adjusted in the positive stiffness range. However, the bearing stability requires that the stiffness should not be too low, which limits the vibration isolation frequency band. To extend the isolation frequency band to low frequencies, an electromagnetic negative stiffness mechanism (ENSM) which can be continuously adjusted in the positive and negative stiffness range is proposed, and a semi-active control algorithm is proposed for it. The configuration of the coils and magnets in the ENSM is optimized, and the stiffness adjustable range and energy efficiency are improved. A double-layer vibration isolator with an ENSM in parallel is designed, and its nonlinear dynamic characteristics are analyzed. The suboptimal control method based on linear quadratic regulator (LQR) is introduced into the nonlinear vibration isolator by feedback linearization method. The input current of the ENSM is controlled according to the relative displacement and electromagnetic force model to generate the required control force. The simulation results show that extending the adjustable stiffness to the negative stiffness range can reduce the stiffness adjustment range required for vibration isolation. The vibration test results show that the ENSM can extend the isolation frequency band while maintaining the bearing stability, and the semi-active control of the ENSM can suppress resonance and further improve the vibration isolation performance.

This paper researches the nonlinear behavior of a nonlinear torsional vibration isolator (NTVI) which is composed of flexible rod element and electromagnetic element. And the NTVI has a quasi-zero stiffness (QZS) characteristic. Firstly, a statics model of the QZS-NTVI and the parameter relationship between the nonlinear electromagnetic element and the flexible rod are established; the effects of geometric parameters on the QZS behavior and restoring torque are described. Then, the statics model approximated by the Taylor series is incorporated into the dynamic model of QZS-NTVI. The stability of the harmonic solution is analyzed, and the amplitude–frequency response and the torque transmissibility curves under different geometric parameters are derived according to the harmonic balance method. Furthermore, numerical analysis effort is performed to study the nonlinear behavior of QZS-NTVI. The results show that the QZS-NTVI exhibits super-harmonic and sub-harmonic resonances and undergoes the periodic and chaotic motions alternatively with the change in the excitation amplitude and the angular frequency. Finally, both the simulation and experimental efforts are performed to validate the statics model of the flexible rod and to study the vibration isolation performance and nonlinear behavior of QZS-NTVI. The results demonstrate that the vibration isolation performance of QZS-NTVI notably outperforms the linear system, as well as nonlinear behavior with frequency jump.