External Resonator Research Articles

Einstein–Podolsky–Rosen conditional squeezing for next generation Gravitational-Wave detectors

Frequency-dependent squeezing (FDS) represents a well established way to address quantum noise (QN) in Gravitational-Wave (GW) Earth-based detectors, such as LIGO, Virgo, and KAGRA. This technique is realized with the use of an external detuned optical resonator, the filter cavity. The experiment we present here is a table-top prototype that will probe a cheaper, more compact and more flexible strategy for broadband QN reduction (Ma et al., 2017). This scheme is based on two-mode Einstein–Podolsky–Rosen (EPR) entangled squeezed light, and it works without any filter cavity. The EPR-entangled beams will propagate in a small-scale suspended interferometer with high-finesse arm-cavities. This experiment aims at validating the EPR conditional squeezing at audio frequencies, suited for GW detection, implementing also innovative optical techniques.

Effects of extreme temperature environments on nonlinear vibrations of the cable-stayed functionally graded beam

A cable-stayed functionally graded beam (CSFGB) model is proposed for the first time to study nonlinear behaviors of the system exposed to extreme temperatures. To this end, the in-plane one-to-one internal resonance between the global mode (FGB's mode) and the local mode (cable's mode) is explored under the condition of external primary resonance. First, governing differential equations of the system considering temperature effects are derived by using Hamilton's principle. To obtain the modal function of the FGB, the in-plane eigenvalue problem is solved through the separation-of-variables method. Subsequently, ordinary differential equations (ODEs) are yielded according to Galerkin discretization. The method of multiple time scales is then applied to deal with the ODEs and derive the modulation equations. Based on the above theoretical solutions, the frequency-/force-response curves at three different temperatures are delineated via Newton-Raphson method and the continuation of fixed points. Meanwhile, the time histories and phase portraits are also provided by directly integrating the ODEs. The results show that temperature changes have a significant influence on nonlinear characteristics of the system.

Modeling and Vibration Analysis of Carbon Nanotubes as Nanomechanical Resonators for Force Sensing.

Carbon nanotubes (CNTs) have attracted considerable attention as nanomechanical resonators because of their exceptional mechanical properties and nanoscale dimensions. In this study, a novel CNT-based probe is proposed as an efficient nanoforce sensing nanomaterial that detects external pressure. The CNT probe was designed to be fixed by clamping tunable outer CNTs. By using the mobile-supported outer CNT, the position of the partially clamped outer CNT can be controllably shifted, effectively tuning its resonant frequency. This study comprehensively investigates the modeling and vibration analysis of gigahertz frequencies with loaded CNTs used in sensing applications. The vibration frequency of a partially clamped CNT probe under axial loading was modeled using continuum mechanics, considering various parameters such as the clamping location, length, and boundary conditions. In addition, the interaction between external forces and CNT resonators was investigated to evaluate their sensitivity for force sensing. Our results provide valuable insights into the design and optimization of CNT-based nanomechanical resonators for high-performance force sensing applications.

Narrow bandwidth spectral beam combining of cm bar in a short external resonator based on rhombic prism combinations

A novel narrow bandwidth spectral beam combining structure of cm bar with a short external resonator based on rhombic prism combinations is proposed and demonstrated. A pair of rhombic prism combinations are employed between the LDA and the transform lens in the external resonator, which consists of a rectangular quartz plate in the middle and two quartz rhombic prisms on either side in opposite orientations in each combination. The beam emitted from a standard cm bar is segmented and rearranged, and spectral beam combining is carried out along the slow axis. A spectral bandwidth of about 5.46 nm is obtained by employing a transform lens with a short focal length of 150 mm, which is only about 1/3 of that of the conventional spectral beam combining, and a narrow spectral bandwidth of 1.14 nm is obtained when a 5x de-magnifying telescope is employed in the above external resonator, the distance between LDA and diffraction grating is 500 mm while that between LDA and output coupler is 650 mm. This novel structure provides a compact external resonator scheme for narrow bandwidth spectral beam combining.

Frequency-domain multiplexing of SNSPDs with tunable superconducting resonators

This work culminates in a demonstration of an alternative frequency-domain multiplexing (FDM) scheme for superconducting nanowire single-photon detectors (SNSPDs) using the kinetic inductance parametric up-converter (KPUP) made out of NbTiN. There are multiple multiplexing architectures for SNSPDs that are already in use, but FDM could prove superior in applications where the operational bias currents are very low, especially for mid-infrared and far-infrared SNSPDs. Previous FDM schemes integrated the SNSPD within the resonator, while, in this work, we use an external resonator, which gives more flexibility to optimize the SNSPD architecture. The KPUP is a DC-biased superconducting λ/2 resonator that is sensitive to current perturbations. When coupled to an SNSPD, the KPUP can be used to read out current pulses on a few μA scale. The KPUP is made out of NbTiN, which has a large kinetic inductance and a high operating temperature. Meanwhile, the SNSPD is made from WSi, which is a popular material for broadband SNSPDs. A software-defined radio platform and a graphics processing unit are used to read out the KPUP and SNSPD array. Frequency-domain multiplexed SNSPDs have applications in astronomy, remote sensing, exoplanet science, dark matter detection, and quantum sensing.

A novel 3D metal printing in‐line bandpass filter with multiple controllable transmission zeros

AbstractIn this paper, a novel three‐pole bandpass filter with a pair of controllable transmission zeros (TZs) is proposed first. The proposed structure is based on asymmetric dual‐postresonators and two external resonators. The fundamental mode and the first higher mode of the asymmetric dual‐postresonators are used as the nonresonant mode and the resonant mode separately. The nonresonant mode generates direct source to load negative coupling, thus providing one TZ located below the passband. The asymmetric dual‐postresonators and one of the external resonators R3 form a magnetically coupled cascaded triplet unit to produce the other TZ above the passband. Therefore, these two TZs are independently controlled. Moreover, the filter has a good quality factor (), of around 2700, compact size and an excellent out‐of‐band performance. For further suppressing the harmonic response and improving the processing accuracy, a six‐pole bandpass filter with harmonic suppression is designed and fabricated by using metal 3D printing technology. The measured result matches well with the simulated one, which verifies the accuracy of the method.

External and internal resonances of thin-walled curved beams under three-directional moving harmonic loads

This paper deals with the internal and external resonances of simply supported curved beams subjected to three-directional harmonic moving loads. Firstly, based on the differential transformation methods and the Glerkin methods, the analytical solutions are newly proposed for vertical, torsional, radial and axial response of thin-walled curved beams under three-directional harmonic moving loads. Then, in the proposed analytical solutions, this study attains the conditions for the external resonance for in-plane and out-of-plane vibrations by letting the denominator of the proposed analytical solutions equal to zero. Besides, the semi-analytical solution for the internal resonance of curved beams is first proposed in this paper by the coincidence of both two mentioned-above resonant frequencies of beams. The internal resonance will occur when the beam is designed with the critical length for the given cross-section. The derived condition for the internal resonance can offer a basis for structural design to avoid the resonant appearance. All the analytical solutions are in good agreement with the results addressed in existing literature and numerical ones obtained from the finite element method (FEM). The results reveal that the corresponding motion of curved beams diverges, reaching a maximum value during the duration of the harmonic moving loads, when in the external resonance. Moreover, under the internal resonance condition, the curved beams are in repetitive transition between the out-of-plane mode and the in-plane mode without any external energy input. Additionally, in this scenario, the excitation frequency can coincide with the two resonance frequencies of beams resulting in simultaneous occurrences of out-of-plane and in-plane resonances on curved beams. The aim of this study highlights the potential resonant appearances on beams and provide reference in the design phase to avoid the internal resonance appearance and ensure the safety of structures.

Multiphysics analysis of chip and resonator designs for increased damage threshold of external cavity high-power laser diodes.

We present a detailed analysis of multiphysics simulation results to evaluate the threshold for catastrophic optical damage (COD) of high-power laser diodes under misaligned external optical feedback. Three different chip designs are investigated: the non-injecting mirror concept, the non-absorbing mirror concept and the introduction of an additional energy barrier within the waveguide near the front facet. Furthermore, a modification of the external resonator that promises a lower sensitivity towards misalignments is considered. The dependence of the COD threshold on the additional design parameters (bandgap change, modification length, focal length) and the impact of the different approaches on electro-optical efficiency as well as beam quality are analyzed. Compared to the initial design, the different chip design concepts promise an increase of the achievable output power by 8%, 27% and 27% respectively, whereas the modified resonator fully prevents feedback-induced failure.

On the influence of an energy harvesting device on a dynamical system

This article studies the motion of a three degrees-of-freedom (DOF) dynamical system, which consists of two parts, a dynamic part, and an electromagnetic harvesting device. The composition of the system depends on the magnet oscillating in the coil of this device. An electric potential is exerted because of the electromotive force to obtain energy harvesting (EH). Lagrange's equations (LE) are used to derive the system’s equations of motion (EOM), which are solved analytically up to a third-order of approximation using the multiple-scales method (MSM). These solutions are considered novel, in which the mentioned method is applied to a novel dynamical system. The gained are confirmed through comparison with the numerical solutions of the EOM to reveal a high degree of consistency. To establish the system’s solvable conditions and modulation equations (ME), three scenarios of primary external resonance are investigated simultaneously. Certain diagrams of time histories for the amplitudes and phases of the examined dynamical system are plotted to show their behaviors at any given instance of time. The Routh–Hurwitz criteria (RHC) are used to establish the stability and instability regions in light of the graphs of resonance response curves. The presence of an energy harvester in dynamic devices helps us to convert vibrational motion into electrical energy that can be exploited in several applications in a variety of daily tasks, including structural and environmental monitoring, military applications, space exploration, and remote medical sensing.

Amplified spontaneous emission from a liquid crystalline phase: anisotropic property and active modulation.

Amplified spontaneous emission (ASE) is considered to be a primary indication of optical gain in active media without an external resonator. Molecular materials with ASE are expected to be one of the suitable light sources for specific applications such as optical coherent tomography owing to their low coherence and flexible tunability. Concentration quenching of emissive excited states has been a critical issue to boost the quantum efficiency of molecular materials in their condensed phases. The rod-like design of molecules with excited state intramolecular proton transfer (ESIPT) has been demonstrated to overcome this issue in highly-concentrated molecularly-doped systems, as represented by C4alkyne-HBT (2-(4-(1-hexynyl)-2-hydroxyphenyl)-benzothiazole). We designed an ESIPT molecule-doped liquid crystalline (LC) system for optical amplification via the ASE regime with its wide tunability of emission intensity. Detailed ASE behaviour and optical gain of a LC blend of C4alkyne-HBT and 4-pentyl-4'-cyano biphenyl (5CB) was evaluated to afford a maximum optical gain of 16.5 cm-1 with an estimated ASE threshold of optical pumping at 0.6-0.7 mJ cm-2. Although most ASE studies focus on homogeneous solutions, solids, or crystalline states, ASE from a soft-flexible LC phase is quite limited and advantageous for the design of an external optical resonator/cavity structure. Optical excitation parallel and perpendicular to the director resulted in the strong modulation of the ASE. By using the benefits of a LC phase, the ASE was actively modulated under the external electric field by the reorientation of the molecular dipole moment.

Spatially Structured Optical Pump for Laser Generation Tuning.

The goal and essential parameter of laser light conversion is achieving emitted radiation of higher brightness. For many applications, the laser beam must have the highest available beam quality and highest achievable power. However, lasers with higher average power values usually have poorer beam quality, limiting the achievable brightness. Here, we present a method for improving the beam quality by using a spatially structured optical pump for a membrane external cavity laser resonator. An increase in brightness is achieved under fixed focusing conditions just by changing the pump intensity profile. A controllable output laser mode can be achieved by using a dynamically changing pump pattern.

Vibration suppression of pipe conveying fluid using a nonlinear absorber in longitudinal direction

The article outlines the design of a nonlinear absorber that features cubic stiffness. The absorber was created for a pipe conveying fluid and was based on the internal resonance mechanism. To create the nonlinear absorber, a sliding mass oscillator was attached along to the pipe conveying fluid. Nonlinear equations were derived using Hamilton's principle. The flowing fluid was considered both as a constant value and a fluctuating term. To investigate the nonlinear behavior of the coupled pipe-absorber system, the direct multiple scales method was used. By selecting appropriate values of mass and stiffness for the absorber, the natural frequency of the absorber was tuned in three cases: 1–1, 2–1, and 3–1 internal resonance ratios between the natural frequency of the absorber and the first natural frequency of the pipe. The goal of the mechanism was to transfer energy from the pipe to the absorber, and the design was successful in achieving this. A saturation phenomenon was detected in the force modulation response at the three-to-one internal resonance. The results showed a reduction in amplitudes in both frequency and force response curves under the external primary resonance and pulsating flowing fluid in the supercritical regime. The nonlinear absorber has a good performance in a wide range of flow velocity and excitation. The accuracy of the results was verified using Galerkin and Finite difference methods.

Моделирование режимов генерации двух гиротронов с общим резонансным отражателем

The generation regimes of two gyrotrons with a common narrow-band resonant reflector were studied using numerical simulation in the approximation of a fixed field structure. The dependences of the output power and generation efficiency, frequency and phase of oscillations of each gyrotron on system parameters, such as the driving magnetic field, mutual detuning of the gyrotrons’ eigen frequencies and the phase delay of the reflected wave, have been calculated. Using the example of gyrotrons at a frequency of 28 GHz with an output power of up to 10 kW, the possibility of stabilizing the radiation frequency of two gyrotrons when part of their power is reflected from an external high-Q resonator was demonstrated. It is shown that even if the eigen frequencies of the gyrotron resonators and the delay phases of the reflected wave do not coincide, it is possible to obtain frequency-stable states in which the phase difference of the gyrotrons does not depend on time and on the initial conditions, while the radiation power of each gyrotron exceeds the power of autonomous generation.

Исследование возможности стабилизации частоты двух гиротронов при воздействии отражения от внешнего высокодобротного резонатора

The possibility of frequency stabilization of two gyrotrons with similar parameters when part of their radiation is reflected from an external high-Q cavity is shown analytically, and the stability of stabilized states is investigated. Analysis of stationary states in which the generators radiate coherently shows that the radiation frequency can be stabilized if the quality factor of the external resonator is high enough. In this case, changing the parameters of the system leads to significantly smaller changes in the generation frequency than in the absence of reflections: in a fairly wide range of parameters, the gyrotron radiation frequency can be kept within the band of the external resonator. As the eigen frequencies of gyrotron resonators increase and decrease, hysteresis and jumps in the radiation frequency can be observed. A study of stability at the optimal delay phase shows that frequency-stabilized states are stable. When the deviation from these states is small, the disturbances in the amplitudes of the gyrotrons decrease most quickly. At the next stage, over a longer period of time, stationary values of the gyrotron phases are settled. At the last, longest stage, stationary values of the amplitude and phase of the external resonator are formed.

Analysis and Design of Injection-Locked Oscillators Coupled to an External Resonator

This work investigates the nonlinear dynamics of an injection-locked power oscillator inductively coupled to an external resonator. This allows a high-efficiency power transfer while ensuring a constant oscillation frequency versus the coupling factor, unlike free-running implementations. The investigation focuses on the impact of the external-resonator elements on the locking range, output power, efficiency, and phase noise. The aim is to derive a strategy for an optimum selection of these elements. Initially, the effect of the coupled resonator is theoretically studied using a simple oscillator model, based on a cubic nonlinearity. For practical oscillators, two kinds of analysis methods, compatible with the use of commercial harmonic-balance (HB) simulators, are presented. The first one is semianalytical and is based on the extraction of a phase-dependent nonlinear admittance function from HB simulations. The system response is predicted in a flexible and computationally efficient manner, but coupling effects are considered at the fundamental frequency only. The second set of methods is fully based on HB and relies on the combination of a nonlinear immittance function and a Thevenin/Norton equivalent. The impact of the external resonator on the stability properties is analyzed through bifurcation detection. The phase-noise spectrum is predicted with a semianalytical formulation that demonstrates the benefit of the injection-locked operation. For validation, the methods have been applied to a Class-E oscillator at 13.56 MHz.

Wavelength Conversion of Multi-Joule Energy 532 nm Pulse Bursts via a Potassium Gadolinium Tungstate Raman Laser

In this study, pulse bursts at 559, 589, and 621 nm, with a record energy of ~10 J, are generated using a KGW Raman laser with an external resonator, while pumping at 532 nm. The pulse bursts have a 10 ms duration, and consist of 78 subpulses with a duration of <10 ns, at 8 kHz. The maximum energy of the bursts is restricted only by the characteristics of the Nd: YAG laser used as the 532 nm pump source, and can be increased.

GHz Figure‐9 Er‐Doped Optical Frequency Comb Based on Nested Fiber Ring Resonators

AbstractThe field of optical‐frequency‐combs (OFCs) has seen significant progress in recent years due to the advance of mode‐locked fiber lasers with low‐noise performance and long‐term reliability. With the emergence of applications, OFCs with repetition rates close to GHz have become highly sought after. However, generating GHz fiber‐based combs with low noise remains a significant challenge. In this study, a GHz figure‐9 Er‐doped OFC based on a nested fiber ring resonator is presented. By matching the free‐spectral range (FSR) of external and internal optical resonators, an 11‐fold increase in repetition rate from 82 MHz to 907 MHz is achieved. Notably, it is demonstrated that a single pulse operation with long‐term FSR matching can be achieved without any active feedback control. The comb offset frequency is detected using f‐to‐2f technique to ensure high coherence between pulses, which is distinguished from harmonic mode‐locking. The results show that the nested resonators are capable of generating GHz ultrafast OFC pulses with low phase noise via a more flexible cavity design than conventional short‐cavity solutions. This work provides a valuable contribution to the field of ultrafast laser and optical metrology, which demonstrates the potential of nested‐resonators for generating low noise OFCs with boosted repetition rate.

200-W short-pulse operation of photonic-crystal lasers based on simultaneous absorptive and radiative Q-switching.

Short-pulse high-peak-power lasers are crucial laser sources for various applications such as non-thermal ultrafine material processing and eye-safe high-resolution remote sensing. Realizing such operation in a single semiconductor laser chip without amplifiers or external resonators is expected to contribute to the development of compact, affordable laser sources for such applications. In this paper, we demonstrate short-pulse high-peak-power photonic-crystal surface-emitting lasers based on simultaneous absorptive and radiative Q-switching. The proposed device induces an instantaneous and simultaneous decrease in both absorptive and out-of-plane radiation losses due to saturable absorption and self-evolution of the photonic band, respectively, which results in drastic Q-switching operation of the device. Based on this concept, we experimentally demonstrate short-pulse generation with 200-W-class peak power and a pulse width of < 30 ps. In addition, via pulse compression with dispersion compensation, we achieve an even higher peak power of ∼300 W with a shorter pulse width of ∼10 ps.

Resonator Arrays for Linear Position Sensors

A contactless position sensor based on an array of magnetically coupled resonators and an external single coil cell is discussed for both stationary and dynamic applications. The simple structure allows the sensor to be adapted to the system in which it is installed and can be used to detect the positions of objects in motion that bear an external resonator coil that does not necessitate a supply. By exploiting the unique behaviour of the array input impedance, it is possible to identify the position of the external resonator by exciting the first array cell with an external voltage source and measuring the resulting input current. The system is robust and suitable for application in harsh environments. The sensitivity of the measured input impedance to the space variation is adjustable with the definition of the array geometry and is analysed. Different configurations of the array and external resonator are considered, and the effects of various termination conditions and the resulting factor of merit after changing the coil resistance are discussed. The proposed procedure is numerically validated for an array of ten identical magnetically coupled resonators with 15 cm side lengths. Simulations carried out for a distance of up to 20 cm show that, with a quality factor lower than 100 and optimal terminations of both the array and external coil, it is possible to detect the position of the latter.

Efficiency of non-operative management for pectus deformities in children using an X-ray-free protocol.

To explore the correlation between the Haller index (HI), the external depth of protrusion, and the external Haller index (EHI) for both pectus excavatum (PE) and carinatum (PC). To assess the variation of the HI during this first year of non-operative treatment for pectus deformities in children. From January 2018 to December 2022, all children treated for PE by vacuum bell and for PC by compression therapy at our institution were evaluated by external gauge, 3D scanning (iPad with Structure Sensor and Captevia-Rodin4D), and magnetic resonance imaging (MRI). The main objectives were to assess the effectiveness of the treatment during the first year and to compare the HI determined by MRI to the EHI evaluated with 3D scanning and external measurements. The HI determined by MRI was compared to the EHI evaluated with 3D scanning and external measurements at M0 and M12. 118 patients (80 PE and 38 PC) had been referred for pectus deformity. Of these, 79 met the inclusion criteria (median age 13.7 years, 8.6-17.8). There was a statistically significant difference in the external measurements of the depth for PE between M0 and M12: 23.0 mm ± 7.2 vs 13.8 mm ± 6.1, respectively; p < 0.05 and for PC 31.1 mm ± 10.6 vs 16.7 mm ± 8.9, respectively; p < 0.01. During this first year of treatment, the reduction in the external measurement increased more rapidly for PE compared with PC. We found a strong correlation between the HI by MRI and the EHI by 3D scanning for PE (Pearson coefficient = 0.910, p < 0.001) and for PC (Pearson coefficient = 0.934, p < 0.001). A correlation between the EHI by 3D scanning and the external measurements by profile gauge was found for PE (Pearson coefficient = 0.663, p < 0.001) but not for PC. Excellent results were observed as soon as the sixth month for both PE and PC. Measurement of protrusion is a reliable monitoring tool at clinical consultation but caution is required for PC as it does not appear to be correlated to the HI by MRI.