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In this paper, we propose an improved closed form large injection perturbation analytical model for accurately studying the phase-locking dynamics and frequency pulling phenomenon in optoelectronic oscillator (OEO) for radio frequency (RF) signal injection. We provide formulas for the lock-range, and the beat frequency, which are general and accurate in estimating the degree of phase perturbation in unlocked-driven OEO under weak as well as strong injection signal level. We also give closed form expressions for the spectral components of the unlocked-driven oscillator. It is shown that our model is capable of predicting the phase-locking and estimating the frequency pulling of RF driven OEO under weak and strong injection signal level. The accuracy of the proposed model is verified by the simulations.

The matrix reconstruction technique can effectively estimate the direction-of-arrival (DOA) of coherent signals with a relatively small computational complexity. However, the existing methods are affected by the phase perturbation or the fact that the eigenvalue ratio of the signal subspace to noise subspace is linearly related to the square of input signal-to-noise ratio (SNR). This results in a significant decrease in the DOA estimation performance for the cases with a low SNR. To address these problems, we propose a new method for DOA estimation of coherent signals based on the beamspace matrix reconstruction. The array is firstly divided into multiple subarrays, and the data received is transformed from the element space into the beamspace via beamforming, which can eliminate the phase perturbation caused by the mutual impact between the coherent signals and improve the SNR. Then, we add the output covariance matrices from several beam directions to realize the beamspace matrix reconstruction, this results in the eigenvalue ratio of the signal subspace to the noise subspace is the linear transformation of the input SNR in the beamspace domain, which can enhance the eigenvalue ratio of beamspace signal to noise at low SNRs. Finally, the DOAs can be resolved by combining it with the subspace-based methods. Theoretical analysis and simulation results verify the effectiveness of the proposed method at low input SNRs due to beamspace processing, even in the cases where the DOAs between the coherent signals are closely spaced and low snapshot number, our proposed method significantly provides better performance on estimation and resolution.

Practical orbital angular momentum (OAM)-based free-space optical (FSO) communications commonly experience serious performance degradation and crosstalk due to atmospheric turbulence. In this paper, we propose a wave-front sensorless adaptive optics (WSAO) system with a modified Gerchberg–Saxton (GS)-based phase retrieval algorithm to correct distorted OAM beams. We use the spatial phase perturbation (SPP) GS algorithm with a distorted probe Gaussian beam as the only input. The principle and parameter selections of the algorithm are analyzed, and the performance of the algorithm is discussed. The simulation results show that the proposed adaptive optics (AO) system can significantly compensate for distorted OAM beams in single-channel or multiplexed OAM systems, which provides new insights into adaptive correction systems using OAM beams.

We demonstrate the influence on mode features with introducing typical intracavity perturbation and results of aberrated wavefront compensation in a folded-type unstable resonator used in high energy lasers. The mode properties and aberration coefficient with intracavity misalignment are achieved by iterative calculation and Zernike polynomial fitting. Experimental results for the relation of intracavity maladjustment and mode characteristics are further obtained in terms of S-H detection and model wavefront reconstruction. It indicates that intracavity phase perturbation has significant influence on out coupling beam properties, and the uniform and symmetry of the mode is rapidly disrupted even by a slight misalignment of the resonator mirrors. Meanwhile, the far-field beam patterns will obviously degrade with increasing the distance between the convex mirror and the phase perturbation position even if the equivalent disturbation is inputted into such the resonator. The closed-loop device for compensating intracavity low order aberration is successfully fabricated. Moreover, Zernike defocus aberration is also effectively controlled by precisely adjusting resonator length, and the beam quality is noticeably improved.

We demonstrate the influence on mode features with typical intracavity astigmatism perturbation and results of aberrated wavefront in a folded-type unstable resonator usually used in high energy lasers. The mode properties are illuminated by numerical iterative calculation, and Zernike aberration polynomial fitting. Subtle beam features such as the first 35 order Zernike aberration coefficient, PSF and circle energy distribution in the far-field, and Strehl ratio with the intracavity astigmatism perturbation have been further achieved. The results show that such perturbation has significant influence on out coupling beam properties, and the uniform and symmetry of the mode is rapidly disrupted even by a slight intracavity astigmatism perturbation for the small Fresnel number unstable resonator. Moreover, some relevant higher order aberrations such as Zernike coefficient A3, A5 and A10 will also increase in the wavefront profiles. Based on the analysis, suggestions for the practical design and further possible aberration improvement strategies are proposed.

Eigenmode of resonators with asymmetric circular mirrors based on misalignment passive positive-branch unstable resonator is investigated in the paper. To do so, we use iterative algorithm to simulate the effect of intracavity phase perturbation on eigenmode structure properties of the passive confocal unstable resonator. On this basis, further experiment of output beam properties on a misaligned passive unstable laser resonator has been performed by adopting Hartmann–Shack (H–S) method and Zernike modal wavefront reconstruction. Wavefront distribution and the first 35-order Zernike coefficient included in the wavefront are obtained. The results show that intracavity tilt perturbation notablely affects outcoupled beam intensity distribution, and will also increase some high-order aberrations of beam phase properties. However, low-order Zernike tilt aberration is the main component with phase-tilted perturbation is introduced into resonator cavity. Defocus, low-order astigmatism and coma aberration will all be brought with the augument of phase tilt aberration, which will obviously degrade output beam quality. When intracavity compensating elements are adopted for optical aberration correction, the correction of tilt aberration should be considered first.

Some representative factors of intracavity perturbation will obviously degrade output power and beam mode properties for crystal passive Q-modulated solid-state lasers. In this paper, eigenmode of resonators using general asymmetric circular mirrors in solid-state lasers is briefly discussed, moreover, experiment analysis of the output beam quality on a passive Q-switched zig-zag slab Nd:YAG laser has been presented by adopting Hartmann–Shack (H–S) method and Zernike mode reconstruction theory. In this way, the PV and RMS errors of the wavefront aberration, each order Zernike aberrations can be acquired accurately, distribution of circle energy in far-field and other beam evaluation factors can also be obtained by further calculation, so beam mode properties and quality can be analyzed comprehensively. Experimental results illuminate that wavefront aberration of the laser is concentrated in the frontal 10 ranks of Zernike aberration, mainly including the defocus Z3, the low-order astigmatism Z5, the coma aberration Z6 and the spherical aberration Z10 because of the crystal thermal effect and the intracavity phase perturbation.

An approximate strong injection perturbation mathematical model to analyze the frequency pulling and non-linear dynamics in radio frequency (RF) signal driven optoelectronic microwave oscillator (OEO) is presented here. The formulas regarding the lock-range, the beat frequency and the average frequency are derived, which help to estimate the amount of phase perturbation in pulled (unlocked-driven) OEO more accurately considering both weak and strong RF signal injection. The analytical expressions for the spectral components of the pulled OEO are also given to predict the frequency pulling phenomenon of the pulled OEO. It is presented that our proposed analytical model has the capability to accurately determine the phase-locking and assessing the frequency pulling of RF driven single-loop OEO when injected by weak and strong RF signal. The verification of the accuracy of the proposed model is also done by the experiments.

Clock signal distribution networks have been studied since the 1960s in the search of topologies and parameters that can optimize performance. The problem can be viewed as the mutual synchronization of coupled oscillators, a field being extensively investigated. However, the majority of these investigations consider a linear coupling factor, unlike in the case of time signal distribution systems, wherein nonlinear coupling terms appear. The latter complicates the analysis, mainly because the nodes are phase-locked loops. In the literature pertaining to telecommunications, this problem is studied using linear analysis and is supported by corrections provided by the experimental work. In this paper, a different approach to this problem is presented: here, it is considered that the basic unit of a fully connected time distribution network is a triangular ring of phase-locked loops. The stability of equilibrium states is derived, starting with a delay-free analytical model for the spatial phase and frequency errors. Perturbations of the equilibrium, step, ramp, and accidental phase modulation are included in the model, producing results reflecting the performance of the entire loop.

This paper is concerned with mixed far-field and near-field source localization in the presence of gain-phase perturbations. Under some mild assumptions, we propose a new mixed source localization algorithm with the partly calibrated symmetric uniform linear array. By constructing a special second-order statistical vector, the DOAs and powers of all sources are first estimated by the modified sparse total least square (M-STLS) algorithm after compensating gain errors. Based on the estimated DOAs, the phase errors are successively obtained by the least squares criterion and a discriminant function formed by using the MUSIC null spectrum property. Finally, the mixed sources are classified and the range of near-field sources are achieved via one-dimensional spectral search. Meanwhile, the stochastic Cramer-Rao bound (CRB) for the considered problem is also given. The proposed algorithm can lead to a good mixed source classification and localization result. Numerical simulations validate the effectiveness of the proposed algorithm.

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens–Fresnel diffraction integral. Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved.

The paper describes the basic concepts underlying the design of Multi-Conjugate Adaptive Optics systems. The paper takes into account mainly three papers. The first paper, published in 1988, is due to J. Beckers and it introduces the currently used multi-conjugation concept and quantifies the increase in FoV achieved applying this concept with respect to the single conjugate adaptive system. The second paper considered is due to M. Tallon and R. Foy. This paper, published in 1990, provides a quantitative method to estimate the 3D map of the atmospheric phase perturbation. This is the needed information to properly control the multi-conjugate system introduced by J. Beckers. Finally a third paper, published in 2000 and due to R. Ragazzoni et al. is considered, where the Layer Oriented scheme is described opening the multi-conjugate adaptive system field to natural guide stars. These three papers stimulated a lot of other contributions from several people and some of them are briefly discussed in the paper. To cite this article: S. Esposito, C. R. Physique 6 (2005).

Higher-harmonic FM oscillation of an Er-fiber laser is demonstrated and the constant amplitude output is used for generating a high repetition rate short pulse train by compression. Chirped, constant-amplitude FM light of 193-GHz width was generated, at 1.56 μm at a repetition rate of 7.3 GHz, by applying detuned phase perturbation of 131 kHz to the ring cavity. The output was compressed using a 2-km-long anomalous-dispersion fiber and this resulted in a stable train of 4.3-ps pulses and corresponded to a compression ratio of 32. The experimental results are found to be in good agreement with the calculated results.

The dynamic ergodic divertor is a new concept for distributing the power flux from the plasma to a large area target plate while keeping or even improving the particle removal capabilities of the toroidal pump limiter ALT-II. The transport in the ergodized boundary magnetic field shields the impurities from penetrating into the central plasma while the option of a radiative mantle should become even more efficient. To achieve the ergodization, a set of perturbation coils is oriented parallel to the field lines of a resonant layer (q=3 layer). A four phase perturbation current (up to 15 kA) is selected to impose the option of field rotation; the available frequencies are DC, 50 Hz and the band between 1 and 10 kHz. The low frequency option is chosen for smearing out the divertor strike point while the rotation high frequency option may give rise to a `temporal' ergodization in addition to the spatial one and may improve the plasma confinement and increase the disruption limit.

Spectral representations for the complex phase perturbations of weakly perturbed plane and spherical wave fields in free space are derived. These representations, which are analogous to the analogous to the angular spectrum representation of the optical field, are shown to lead to simple algebraic formulae relating the spatial Fourier transforms and spatial power spectra of the complex phase perturbation on any two parallel planes in free space.

Observations of simultaneous Q-switching and mode-locking have been made in a TEA CO2 laser when a low density underdense plasma was injected into the cavity. The plasma which was produced in an electromagnetic shock tube had a density ≈1017 cm-3. A likely mechanism for mode-locking is the time dependent plasma refractive index leading to phase perturbation.