Spectral Stability Research Articles

Low‐Threshold Multiwavelength Plasmonic Nanolasing in an “H”‐Shape Cavity

AbstractMultiwavelength plasmonic nanolasers are central to the quest for ultradense and versatile photonic integrations. However, the insufficient optical feedback and mode selection strategies result in a high lasing threshold and multi‐mode operation with limited spectral purity and stability. Here, a multiwavelength near‐infrared plasmonic nanolaser with high mode purity by leveraging a nontrivial “H”‐shape plasmonic cavity is demonstrated. The nanolaser is constructed by inserting InGaAs/GaAs multi‐quantum‐disk (MQD) nanowires into a metallic Fabry‐Perot cavity consisting of a pair of Ag nanowires positioned on an ultrasmooth Au film. The design is endowed with strong optical feedback to enhance the energy transfer between the exciton and plasmon, rendering a significant reduction of the lasing threshold. More importantly, the “H”‐shape cavity is featured with a large flexibility in tuning the resonance wavelength, where multiwavelength lasing with the virtues of single‐mode is realized at room temperature. The results make a crucial step toward near‐infrared multiwavelength plasmonic nanolasers and open up exciting opportunities for applications such as ultracompact photonic integrated circuits and high‐throughput biochemical sensing.

Linear stability analysis of second-mode attenuation via porous carbon-matrix ceramics

Effects of porous carbon-fiber-reinforced carbon-matrix ceramics (C/C) on the stability of second-mode waves on a 7°-half-angle cone were investigated for Reynolds numbers Rem=2.43×106–6.40×106 m−1 at the freestream Mach number of M∞=7.4, for both sharp and 2.5-mm-round nose tips. A broadband time-domain impedance boundary condition was used to model the effects of the C/C porosity on the flow dynamics leveraging direct ultrasonic benchtop experiments and homogenous absorber theory. A spectral linear stability solver based on orthogonal Laguerre functions, naturally vanishing in the free stream, was used to predict linear spatial growth rates, which are in agreement with independent pulsed axisymmetric direct-numerical simulations. The latter were carried out with the quasi-spectral viscosity closure—a dynamic quasi-spectral procedure capable of deactivating the sub-filter scale stresses in the absence of turbulent break down—verifying its suitability to carry out transitional calculations without affecting ultrasonic wave dynamics. The effectiveness of a porous C/C surface is shown to decrease drastically with static pressure and its presence is shown to decrease the second-mode growth rates in regions where it is unstable as well as increasing the attenuation rates in regions where it is stable.

The EnMAP imaging spectroscopy mission towards operations

EnMAP (Environmental Mapping and Analysis Program) is a high-resolution imaging spectroscopy remote sensing mission that was successfully launched on April 1st, 2022. Equipped with a prism-based dual-spectrometer, EnMAP performs observations in the spectral range between 418.2nm and 2445.5nm with 224 bands and a high radiometric and spectral accuracy and stability. EnMAP products, with a ground instantaneous field-of-view of 30m×30m at a swath width of 30km, allow for the qualitative and quantitative analysis of surface variables from frequently and consistently acquired observations on a global scale. This article presents the EnMAP mission and details the activities and results of the Launch and Early Orbit and Commissioning Phases until November 1st, 2022. The mission capabilities and expected performances for the operational Routine Phase are provided for existing and future EnMAP users.

Convergence behaviour of inverse differential quadrature method for analysis of beam and plate structures

Modelling of structures like beams and plates for advanced engineering applications is a tedious task considering the complexity of the kinematical assumptions governing their behaviour. A fundamental requirement in understanding the behaviour of these engineering structures is providing accurate numerical solutions to the high-order system of partial differential equations derived from the kinematic assumptions. To circumvent error accumulation arising from the numerical differentiation of high-order systems, the inverse differential quadrature method (iDQM) was recently proposed, and it is increasingly gaining attention due to its associated spectral convergence and numerical stability. To fully exploit the merits of iDQM for wider applications, this study establishes an understanding of sensitivity of static, buckling, and free vibration iDQM-based solutions of beam and plate structures to the choice of basis functions and grid distributions. Moreover, the computational complexity imposed by the full preconditioning required to transform the inherently underdetermined iDQM system to a square system suitable for eigenvalue analyses is addressed by proposing two novel subsystem preconditioning methods. From the ensuing comprehensive convergence analysis, it is shown that iDQM can be generalised for a specific class of polynomials that exhibit spectral convergence and negligible sensitivity to grid distributions. For other classes of polynomials that offer ill-conditioned coefficient matrices, iDQM can be applied to problems in which the desired accuracy can be achieved with few grid points. Finally, the study highlights the excellent computational gains offered by subsystem preconditioning methods for obtaining numerically stable eigenvalue solutions with high-order accuracy.

Enhanced spectral emission of CN in laser-induced PMMA plasmas by deposition of nanoparticles

Laser-induced breakdown spectroscopy (LIBS) has good capability for detecting molecular spectroscopy. Currently, little research has been done on enhancing this capability by depositing nanoparticles on the surface of samples. In this paper, a pulsed Nd:YAG laser with a wavelength of 1064 nm was utilized to excite polymethyl methacrylate (PMMA) targets and generate PMMA plasmas, and five spectral peaks (0−0), (1−1), (2−2), (3−3), and (4−4) of B2Σ+ − X2Σ+ (Δν = 0) transitions of CN molecules were obtained. The CN molecule was produced by the chemical reaction (C + N → CN) between the C atoms in PMMA targets and the N2 in the air. The effect of nanoparticles on the spectral intensity and spectral stability of CN molecules was studied. And the vibration temperature of CN molecules was calculated by fitting the CN spectra. The results showed that nanoparticles could improve the spectral intensity, stability, and vibrational temperature of the CN molecules, revealing the potential of nanoparticles for enhancing signal intensity and improving analytical sensitivity in molecular LIBS.

Thirty‐two‐tupling frequency millimeter‐wave generation based on eight Mach–Zehnder modulators connected in parallel

AbstractA new method is proposed to generate a 32‐tupling frequency millimeter wave (MMW) with eight Mach–Zehnder modulators (MZMs) connected in parallel. Theoretical analyses and simulation experiments are conducted. The optical sideband suppression ratio (OSSR) of the obtained ±16th order optical sidebands are 61.54 dB and 61.42 dB, and the radio frequency spurious suppression ratios (RFSSRs) of the generated 32‐tupling frequency MMW are 55.52 dB and 55.27 dB based on the theoretical analysis and simulation experiments, respectively; these outcomes verified the feasibility of the new method. The main parameters used to affect the stability of the generated signal are the modulation index and extinction ratio of MZM. Their effects on the OSSR and RFSSR of the generated signals are investigated when they deviate from their designed values. Compared with the other proposed methods for the generation of 32‐tupling frequency MMW by MZM, our method has the best spectral purity and stability, and it is expected to have important MMW over fiber applications.

High side-mode suppression ratio with a Vernier effect single-mode laser using triple coupled microrings

The development of single-mode lasers with a high side-mode suppression ratio (SMSR) is challenging but highly desirable for integrated photonics devices and long-distance communications due to their high spectral purity and stability. Here, we demonstrate a single-mode laser with a high side-mode suppression ratio based on size-mismatched triple-coupled microrings. With the exact engineering of several key parameters of the structure like air gap and radii of microrings for controlling the free spectral range (FSR), a predominant mode is selected to lase in amplified spontaneous emission (ASE) of the gain material and all side and high order modes are suppressed by Vernier effect. In this work, we show that a single-mode operation is efficiently generated with an improved side-mode suppression ratio of over 20 dB in a three-ring-coupled microcavity laser. The single-frequency output persists for a wide power range. The theoretical calculations and numerical simulations’ results confirm the validity of the experimental results. Our structural engineering creates new opportunities in a variety of frontier applications in single-mode lasers and high-quality sensors.

Suppressing Ion Migration of Mixed‐Halide Perovskite Quantum Dots for High Efficiency Pure‐Red Light‐Emitting Diodes

AbstractPerovskite‐based light‐emitting diodes (PeLEDs) with a mixed halide composition can be used to obtain the “pure red” emission, i.e., in the 620–650 nm range, required for high‐definition displays. However, fast halide ion migration induces phase separation in these materials under electric fields, resulting in poor spectral stability and low efficiency. Herein, a method for producing mixed halide CsPbI3‐xBrx quantum dots (QDs) is reported in which ion migration is suppressed. The mixed halide composition is first achieved by anion exchange between CsPbI3 QDs and hydrobromic acid (HBr), during that the bromine ions efficiently passivate the iodine vacancies of the QDs. The original oleic acid ligands are then exchanged for 1‐dodecanethiol (1‐DT), which suppresses halide ion migration via the strong binding of the sulfhydryl group with the QD surface. PeLEDs based on these QDs exhibit a pure‐red electroluminescence (EL) peak at 637 nm, a maximum external quantum efficiency (EQE) of 21.8% with an average value of 20.4%, a peak luminance of 2653 cd m−2, and low EQE decease with increasing luminance. The EL spectrum of these devices is stable even at 6.7 V and they have an EQE half‐life of 70 min at an initial luminance of 150 cd m−2.

A novel three sub‐step explicit time integration method for wave propagation and dynamic problems

AbstractA novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A demonstrative dispersion analysis for wave propagation is presented to acquire optimal algorithm parameter value for finite element analysis of wave propagation problems. Numerical tests demonstrate that new method show desirable algorithm accuracy and convergence for dynamic problems. Especially, for highly nonlinear problems, the new method can provide very accurate and stable solutions.

Uncovering the Origins of Instability in Dynamical Systems: How Can the Attention Mechanism Help?

The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics.

Manipulating Local Lattice Distortion for Spectrally Stable and Efficient Mixed‐halide Blue Perovskite LEDs

AbstractMixed‐halide perovskites are considered the most straightforward candidate to realize blue perovskite light‐emitting diodes (PeLEDs). However, they suffer severe halide migration, leading to spectral instability, which is particularly exaggerated in high chloride alloying perovskites. Here, we demonstrate energy barrier of halide migration can be tuned by manipulating the degree of local lattice distortion (LLD). Enlarging the LLD degree to a suitable level can increase the halide migration energy barrier. We herein report an “A‐site” cation engineering to tune the LLD degree to an optimal level. DFT simulation and experimental data confirm that LLD manipulation suppresses the halide migration in perovskites. Conclusively, mixed‐halide blue PeLEDs with a champion EQE of 14.2 % at 475 nm have been achieved. Moreover, the devices exhibit excellent operational spectral stability (T50 of 72 min), representing one of the most efficient and stable pure‐blue PeLEDs reported yet.

Manipulating Local Lattice Distortion for Spectrally Stable and Efficient Mixed-halide Blue Perovskite LEDs.

Mixed-halide perovskites are considered the most straightforward candidate to realize blue perovskite light-emitting diodes (PeLEDs). However, they suffer severe halide migration, leading to spectral instability, which is particularly exaggerated in high chloride alloying perovskites. Here, we demonstrate energy barrier of halide migration can be tuned by manipulating the degree of local lattice distortion (LLD). Enlarging the LLD degree to a suitable level can increase the halide migration energy barrier. We herein report an "A-site" cation engineering to tune the LLD degree to an optimal level. DFT simulation and experimental data confirm that LLD manipulation suppresses the halide migration in perovskites. Conclusively, mixed-halide blue PeLEDs with a champion EQE of 14.2 % at 475 nm have been achieved. Moreover, the devices exhibit excellent operational spectral stability (T50 of 72 min), representing one of the most efficient and stable pure-blue PeLEDs reported yet.

Spectral stability and dynamics of solitary waves in a coupled nonlinear left-handed transmission line

Spectral stability and dynamics of solitary waves in a coupled nonlinear left-handed transmission line

Spectral stability of near-extremal spacetimes

It has been suggested that the spectrum of quasinormal modes of rotating black holes is unstable against additional potential terms in the perturbation equation, as the operator associated with the equation is non-self-adjoint. We point out that a bilinear form has been constructed previously to allow a perturbation analysis of the spectrum, which was applied to study the quasinormal modes of weakly charged Kerr-Newman black holes [Phys. Rev. D 91, 044025 (2015)]. The proposed spectral instability should be restated as instability against potential terms that have an infinitesimal ``energy'' norm that is specifically defined by the type of inner products introduced by Jaramillo et al. and preserving the physical meaning of energy. We argue that it is necessary to address the stability of all previous mode analysis results to reveal their susceptibility to energetically infinitesimal perturbations. In particular, for near-extremal Kerr spacetime, we show that the spectrum of zero-damping modes, which have slow decay rates, is unstable (with order unity fractional change in decay rates) with fine-tuned modification of the potential. The decay rates are, however, always positive with energetically infinitesimal perturbations. If finite potential modifications are allowed near the black hole, it is possible to find superradiantly unstable modes, i.e., a ``black hole bomb'' without an explicit outer shell. For the zero-damping modes in near-extremal Reissner-Nordstr\"om--de Sitter black holes, which are relevant for the breakdown of strong cosmic censorship, we find that the corresponding spectrum is stable under energetically infinitesimal perturbations.

On-Demand Reconfigurable Incoherent Optical Matrix Operator for Real-Time Video Image Display

For emerging application fields such as autonomous driving and computing vision, which demands the real-time response of massive information, advanced image processing techniques on artificial neural networks (ANNs) are crucial. However, with increasing task complexity, the electrical hardware limited by the well-known von Neumann bottleneck is inadequate to meet these extreme requirements in computing speed and computing power. We propose an incoherent optical matrix operator by dynamically manipulating the parameters of the lightwave in terms of the wavelength, time and space to implement the on-demand reconfiguration both in the optical perceptron and optical convolutional processor. For the optical perceptron, it is conducted to perform the case-sensitive classification of 52 English letters. Furthermore, by adjusting the spectral characteristics and output ports, an optical convolution processor is constructed to realize multitask convolution processing for both the image and real-time video. Based on multikernels parallel computing in an optical convolutional layer coupled with an electrically fully connected layer, a convolutional neural network is built to recognize ‘0–9’ handwritten digital images from the Modified National Institute of Standards and Technology (MNIST) database. Owing to the excellent performance of the incoherent beam in terms of the spectral purity, wavelength stability and side-mode suppression ratio, the experimental classification accuracy up to 96.01% greatly matches the theoretical value of 96.67%. Moreover, incoherent information processing is synchronous with data transmission, which releases the requirement of the global clock in digital counterparts. The high-fidelity incoherent convolution processor offers a novel computing framework that serves the next-generation ANN platform.

Drift Performance and Chromatic Thermal Response of a Temperature Stabilized Solid-etalon Calibrator

Etalon-based calibrators have rapidly gained popularity over the past decade in the field of high-precision radial velocity and high-resolution spectroscopy studies. Solid etalons are compact, pressure insensitive, commercially available alternatives to customized air spaced Fabry–Perot etalons. For tight-budget projects and weight-constricted missions, calibration system built from solid etalon is an interesting option to explore. For those, achievable spectral stability becomes the biggest question due to increased thermal sensitivity of the cavity material. Here, the design and performance of a low-cost solid-etalon calibrator is presented. A dual-loop temperature control system keeps the temperature fluctuations to within 1 mK rms when fully stabilized. Drift performance was tracked simultaneously with a laser frequency comb and the chromatic thermal response is measured through temperature tuning. The results indicate that a thermally controlled solid-etalon system can demonstrate sufficient short-term stability (<1 m s−1) for precise wavelength calibration in combination with a hollow-cathode lamp, and the measured drift and chromatic thermal response agree with theoretical predictions. Such systems are plausible candidates for cost-effective calibration of m s−1 level precision radial velocity instruments with improvement in thermal isolation, optimization in data processing, and long-term testing in the foreseeable future.

Results on the Spectral Stability of Standing Wave Solutions of the Soler Model in 1-D

We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle\psi,\beta \psi\rangle_{\mathbb{C}^2}) \beta$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-i\omega t} \phi_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies $\omega$ such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition $\langle\phi_0,\beta \phi_0\rangle_{\mathbb{C}^2} > 0$ characterizes groundstates analogously to the Schr\"odinger case.

On the stability of ring relative equilibria in the N-body problem on with Hodge potential

AbstractIn this paper, we study the stability of the ring solution of the N-body problem in the entire sphere $\mathbb {S}^2$ by using the logarithmic potential proposed in Boatto et al. (2016, Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 472, 20160020) and Dritschel (2019, Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 377, 20180349), derived through a definition of central force and Hodge decomposition theorem for 1-forms in manifolds. First, we characterize the ring solution and study its spectral stability, obtaining regions (spherical caps) where the ring solution is spectrally stable for $2\leq N\leq 6$ , while, for $N\geq 7$ , the ring is spectrally unstable. The nonlinear stability is studied by reducing the system to the homographic regular polygonal solutions, obtaining a 2-d.o.f. Hamiltonian system, and therefore some classic results on stability for 2-d.o.f. Hamiltonian systems are applied to prove that the ring solution is unstable at any parallel where it is placed. Additionally, this system can be reduced to 1-d.o.f. by using the angular momentum integral, which enables us to describe the phase portraits and use them to find periodic ring solutions to the full system. Some of those solutions are numerically approximated.

Spectral stability of the critical front in the extended Fisher-KPP equation

We revisit the existence and stability of the critical front in the extended Fisher-KPP equation, refining earlier results of Rottschäfer and Wayne (J Differ Equ 176(2):532–560, 2001) which establish stability of fronts without identifying a precise decay rate. Our main result states that the critical front is marginally spectrally stable, with essential spectrum touching the imaginary axis but with no unstable point spectrum. Together with the recent work of Avery and Scheel (SIAM J Math Anal 53(2):2206–2242, 2021; Commun Am Math Soc, 2:172–231, 2022), this establishes both sharp stability criteria for localized perturbations to the critical front, as well as propagation at the linear spreading speed from steep initial data, thereby extending front selection results beyond systems with a comparison principle. Our proofs are based on far-field/core decompositions which have broader use in establishing robustness properties and bifurcations of invasion fronts.

Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity

This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effects due to a Bohm potential. It is shown that, if the shock amplitude is sufficiently small, then the profiles are spectrally stable. This analytical result is consistent with numerical estimations of the location of the spectrum [43]. The proof is based on energy estimates at the spectral level, on the choice of an appropriate weighted energy function for the perturbations involving both the dispersive potential and the nonlinear viscosity, and on the montonicity of the dispersive profiles in the small-amplitude regime.