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Phase-locked photonic wire lasers by π coupling
The term photonic wire laser is now widely used for lasers with transverse dimensions much smaller than the wavelength. As a result, a large fraction of the mode propagates outside the solid core. In this paper, we propose and demonstrate a scheme to form a coupled cavity by taking advantage of this unique feature of photonic wire lasers. In this scheme, we used quantum cascade lasers with antenna-coupled third-order distributed feedback grating as the platform. Inspired by the chemistry of hybridization, our scheme phase-locks multiple such lasers by π coupling. With the coupled-cavity laser, we demonstrated several performance metrics that are important for various applications in sensing and imaging: a continuous electrical tuning of ~10 GHz at ~3.8 THz (fractional tuning of ~0.26%), a good level of output power (~50–90 mW of continuous-wave power) and tight beam patterns (~10 0 of beam divergence).
Phase locking of multi-helicity neoclassical tearing modes in tokamak plasmas
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Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system
We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
Fundamental Behavior of ENSO Phase Locking
El Niño–Southern Oscillation (ENSO) events tend to peak at the end of the calendar year, a phenomenon called ENSO phase locking. This phase locking is a fundamental ENSO property that is determined by its basic dynamics. The conceptual ENSO recharge oscillator (RO) model is adopted to examine the ENSO phase-locking behavior in terms of its peak time, strength of phase locking, and asymmetry between El Niño and La Niña events. The RO model reproduces the main phase-locking characteristics found in observations, and the results show that the phase locking of ENSO is mainly dominated by the seasonal modulation of ENSO growth/decay rate. In addition, the linear/nonlinear mechanism of ENSO phase preference/phase locking is investigated using RO model. The difference between the nonlinear phase-locking mechanism and linear phase-preference mechanism is largely smoothed out in the presence of noise forcing. Further, the impact on ENSO phase locking from annual cycle modulation of the growth/decay rate, stochastic forcing, nonlinearity, and linear frequency are examined in the RO model. The preferred month of ENSO peak time depends critically on the phase and strength of the seasonal modulation of the ENSO growth/decay rate. Furthermore, the strength of phase locking is mainly controlled by the linear growth/decay rate, the amplitude of seasonal modulation of growth/decay rate, the amplitude of noise, the SST-dependent factor of multiplicative noise, and the linear frequency. The asymmetry of the sharpness of ENSO phase locking is induced by the asymmetric effect of state-dependent noise forcing in El Niño and La Niña events.
Active phase locking of thirty fiber channels using multilevel phase dithering method
An active phase locking of a large-scale fiber array with thirty channels has been demonstrated experimentally. In the experiment, the first group of thirty phase controllers is used to compensate the phase noises between the elements and the second group of thirty phase modulators is used to impose additional phase disturbances to mimic the phase noises in the high power fiber amplifiers. A multi-level phase dithering algorithm using dual-level rectangular-wave phase modulation and time division multiplexing can achieve the same phase control as single/multi-frequency dithering technique, but without coherent demodulation circuit. The phase locking efficiency of 30 fiber channels is achieved about 98.68%, 97.82%, and 96.50% with no additional phase distortion, modulated phase distortion I (±1 rad), and phase distortion II (±2 rad), corresponding to the phase error of λ/54, λ/43, and λ/34 rms. The contrast of the coherent combined beam profile is about 89%. Experimental results reveal that the multi-level phase dithering technique has great potential in scaling to a large number of laser beams.
Phase locking of vortex cores in two coupled magnetic nanopillars
Phase locking dynamics of the coupled vortex cores in two identical magnetic spin valves induced by spin-polarized current are studied by means of micromagnetic simulations. Our results show that the available current range of phase locking can be expanded significantly by the use of constrained polarizer, and the vortices undergo large orbit motions outside the polarization areas. The effects of polarization areas and dipolar interaction on the phase locking dynamics are studied systematically. Phase locking parameters extracted from simulations are discussed by theoreticians. The dynamics of vortices influenced by spin valve geometry and vortex chirality are discussed at last. This work provides deeper insights into the dynamics of phase locking and the results are important for the design of spin-torque nano-oscillators.
Simulations of ENSO Phase-locking in CMIP5 and CMIP6
The characteristics of El-Niño-Southern Oscillation (ENSO) phase-locking in observations and CMIP5 and CMIP6 models are examined in this study. Two metrics based on the peaking month histogram for all El Niño and La Niña events are adopted to delineate the basic features of ENSO phase-locking in terms of the preferred calendar month and strength of this preference. It turns out that most models are poor at simulating the ENSO phase-locking, either showing little peak strengths or peaking at the wrong seasons. By deriving ENSO’s linear dynamics based on the conceptual recharge oscillator (RO) framework through the seasonal linear inverse model (sLIM) approach, various simulated phase-locking behaviors of CMIP models are systematically investigated in comparison with observations. In observations, phase-locking is mainly attributed to the seasonal modulation of ENSO’s SST growth rate. In contrast, in a significant portion of CMIP models, phase-locking is co-determined by the seasonal modulations of both SST growth and phase-transition rates. Further study of the joint effects of SST growth and phase-transition rates suggests that for simulating realistic winter peak ENSO phase-locking with the right dynamics, climate models need to have four key factors in the right combination: (1) correct phase of SST growth rate modulation peaking at the fall; (2) large enough amplitude for the annual cycle in growth rate; (3) amplitude of semi-annual cycle in growth rate needs to be small; and (4) amplitude of seasonal modulation in SST phase-transition rate needs to be small.
Phase-locked laser array through global antenna mutual coupling
Here, phase locking of an array of lasers is a highly effective way in beam shaping, to increase the output power, and to reduce lasing threshold. In this work, we present a novel phase-locking mechanism based on "antenna mutual coupling" wherein laser elements interact through far-field radiations with definite phase relations. This allows long-range global coupling among array elements to achieve robust 2-dimensional phase-locked laser array. The new scheme is ideal for lasers with deep sub-wavelength confined cavity such as nanolasers, where the divergent beam pattern could be used to form strong coupling among elements in the array. We experimentally demonstrated such a scheme using sub-wavelength short-cavity surface-emitting lasers at terahertz frequency. More than 37 laser elements are phase-locked to each other, delivering up to 6.5 mW single-mode radiations at ~3 terahertz, with maximum 450-mW/A slope efficiency and near diffraction limit beam divergence.
Phase locking of moving magnetic vortices in bridge-coupled nanodisks
In this paper, phase locking dynamics of vortices induced by spin transfer torque in bridge-coupled nanodisks are studied by micromagnetic simulations. In the presence of the bridge coupling, the required time for the phase locking is dramatically reduced, and the phase difference between the two vortices keeps at a nonzero value after the phase locking. Moreover, the phase difference is affected significantly by bridge coupling, Oersted field distribution, nanodisk size, as well as in-plane bias magnetic field. In addition, the coupled gyrotropic frequency of vortices depends linearly on the perpendicular magnetic field. This systematic study of phase locking parameters, especially the phase difference, is important for the applications of vortex-based spin-torque nano-oscillators.
The Phase-Locking of Tropical North Atlantic and the Contribution of ENSO
The Tropical North Atlantic (TNA) is characterized by significant interannual variability in sea surface temperature (SST), which is phase-locked to the boreal spring. In this study, the phase-locking of TNA is investigated by adopting a linear stochastic-dynamical model (SDM) using seasonally modulated TNA feedbacks together with the seasonal modulation of ENSO forcing. In the observations, the role of local TNA feedbacks and ENSO forcing in TNA phase-locking are equivalently important with both preferring the peak of TNA variability to appear in the boreal spring. Besides, the seasonal modulation of TNA feedbacks and ENSO forcing strength are both mainly controlled by thermodynamic processes. In most climate models, the contribution of ENSO on TNA phase-locking is weaker than that in observations. The strength of ENSO-related TNA phase-locking is highly correlated with the relationship between ENSO and TNA, which is mainly determined by the amplitude of ENSO and its teleconnection patterns.
State diagram of magnetostatic coupling phase-locked spin-torque oscillators
The state diagram of magnetostatic coupling phase-locked spin torque oscillator (STO) with perpendicular reference layer and planar field generation layer (FGL) is studied by the macrospin model and the micromagnetic model. The state diagrams of current densities are calculated under various external fields. The simulation shows that there are two phase-lock current density regions. In the phase-locked STOs in low current region I, the spin configuration of FGL is uniform; in high current region II, the spin configuration of FGL is highly nonuniform. In addition, the results with different STOs separation L{sub s} are compared, and the coupling between two STOs is largely decreased when L{sub s} is increased from 40 nm to 60 nm.
Influence of beam-loaded effects on phase-locking in the high power microwave oscillator
Owing to the power limitation of a single device, much more attentions are focused on developing high power microwave (HPM) oscillators that can be phase-locked to the external signal in the recent HPM researches. Although the phase-locking is proved to be feasible in the conventional devices (such as magnetrons), challenges still exist in the HPM devices due to beam-loaded effects, which are more obvious in HPM devices because of its high current and the low Q-factor of the device. A simple structured HPM oscillator (Bitron) is introduced to study such effects on the phase-locking in the HPM oscillator. The self-consistent analysis is carried out to study such effects together with particle in cell simulations. Then the modified Adler equation is established for the phase-locking HPM oscillator. Finally, conditions for the phase-locking in the HPM oscillator are given.
Dynamics of ENSO Phase–Locking and Its Biases in Climate Models
Here, the contributions of different oceanic feedbacks to the El Niño–Southern Oscillation (ENSO) phase-locking are examined by deriving ENSO dynamics based on the recharge-discharge framework. In observations, the significant winter preference of the ENSO peak is determined by a strong seasonal modulation of SST growth rate, which is controlled by the zonal advective and thermodynamic feedbacks. However, the majority of climate models fail to simulate ENSO phase-locking because the contribution of zonal advective feedback to the seasonal modulation of the SST growth rate is much smaller compared to observations. The weak annual cycle of the SST-current coupling coefficient and small annual mean of the negative climatological zonal SST gradient are two factors contributing to the weak-biased seasonality of zonal advective feedback. Further analysis shows that the Niño3.4 SSTA has better phase-locking performance than Niño3 SSTA in the climate models due to the better simulation of zonal advection feedback in the Niño3.4 region.
Study of phase-locking of optoelectronic microwave oscillators considering amplitude perturbation
This paper presents a detailed study of the phase-locking phenomenon in single-loop optoelectronic microwave oscillators considering strong radio frequency (RF) signal injection. The analyses are made in terms of the lock-range, beat frequency and the spectral components of the unlocked-driven oscillator in presence of amplitude perturbation. An approximate expression for the amplitude perturbation of the oscillator is derived and the influence of amplitude perturbation on the phase-locking dynamics is analysed. The influence of external RF signal on the frequency pulling of the unlocked-driven optoelectronic oscillator (OEO) is also studied. It is shown that the unlocked-driven OEO output signal has a very non-symmetrical sideband distribution about the carrier. Also, analytical technique for studying the response characteristics of a phase-locked OEO to pure continuous wave amplitude modulated signal is presented. The simulation findings are also given in partial support of the conclusions of the analysis.
An X-band phase-locked relativistic backward wave oscillator
For the purpose of coherent high power microwave combining at high frequency band, an X-band phase-locked relativistic backward wave oscillator is presented and investigated. The phase-locking of the oscillator is accomplished by modulation of the electron beam before it reaches the oscillator. To produce a bunched beam with an acceptable injected RF power requirement, an overmoded input cavity is employed to provide initial density modulation. And a buncher cavity is introduced to further increase the modulation depth. When the beam enters the oscillator, the modulation depth is enough to lock the frequency and phase of the output microwave generated by the oscillator. Particle-in-cell simulation shows that an input power of 90 kW is sufficient to lock the frequency and phase of 1.5 GW output microwave with locking bandwidth of 60 MHz.
High-power phase-locked quantum cascade laser array emitting at λ ∼ 4.6 μm
A phase-locked quantum cascade laser (QCL) array consisting of one hundred elements that were integrated in parallel was achieved at λ ∼ 4.6 μm. The proposed Fraunhofer’s multiple slits diffraction model predicted and explained the far-field pattern of the phase-locked laser array. A single-lobed far-field pattern, attributed to the emission of an in-phase-like supermode, is obtained near the threshold (I{sub th}). Even at 1.5 I{sub th}, greater than 73.3% of the laser output power is concentrated in a low-divergence beam with an optical power of up to 40 W.