Self-modulation Oscillations Research Articles

Modulation instability of an electromagnetic wave interacting with a counterpropagating electron beam under condition of cyclotron resonance absorption.

In this paper, transmission of a monochromatic wave through a counterpropagating electron beam under the condition of cyclotron resonance absorption is studied by theoretical analysis and numerical simulation. Conditions of the modulation instability (MI) are analyzed. The MI strongly affects the regimes of transmission. We also derive explicit periodic stationary solutions expressed in terms of elliptic Jacobi functions, as well as bright- and dark-soliton solutions. Analysis of these solutions allows obtaining threshold values of the driving power and frequency for the different regimes of transmission, such as cyclotron absorption, multifrequency self-modulation oscillations, and stationary single-frequency propagation. The theoretical predictions are verified by numerical simulation. In this way, we obtain the conditions at which a continuous-wave driving signal disintegrates into a close-to-periodic train of microwave soliton pulses.

Frequency of self-modulation oscillations in a solid-state coupled-cavity ring laser

Self-modulation oscillations of the intensity of a solid-state coupled-cavity ring laser are theoretically investigated. The results obtained analytically show that external optical coupling allows the frequency of self-modulation oscillations to be varied in a wide range (from a few kilohertz to hundreds of megahertz). Using coupled cavities, it is possible to significantly weaken the influence of the coupling of counterpropagating waves through backscattering on the self-modulation frequency and to increase the scale factor that determines the dependence of the self-modulation frequency on the rotation velocity.

Self-modulation oscillations in a solid-state coupled-cavity ring laser

We propose a theoretical model describing the radiation dynamics in a solid-state coupled-cavity ring laser. Based on the numerical simulation conducted within the framework of this model, we investigate antiphase harmonic oscillations of counterpropagating wave intensities. It is shown that the amplitudes and frequencies of self-modulation oscillations in cases of in-phase and antiphase cavity couplings differ significantly. In the case of antiphase coupling, a new possibility of increasing the scale factor with increasing perimeter of the additional cavity is found. The dependence of the frequency of self-modulation oscillations on the optical nonreciprocity produced in the main cavity by a constant magnetic field is studied experimentally. Comparison of experimental and theoretical results shows good agreement between theory and experiment.

Application of the model of coupled oscillators in the analysis of the nonlinear excitation of hypersound in a ferrite plate under ferromagnetic resonance. Part 1. Basic equations

The excitation of hypersonic oscillations by ac magnetic field is considered in the framework of the problem of the magnetostriction microwave transducer using a model of coupled oscillators. Two regimes of the development of forced oscillations corresponding to an increase and decrease in the amplitude in time are separated by a bifurcation point. Two criteria of bifurcation are proposed to determine the critical values of the coupling constant and resonance frequency. The bifurcation point between the regimes is equivalent to the point of reorientation of the magnetization vector. It is demonstrated that the cubic nonlinearity plays the main role in the limitation of the exponential growth of the amplitude of forced oscillations. Frequency response functions (FRFs) of the coupled oscillations are considered at several excitation levels. It is demonstrated that the quadratic approximation provides the analysis of FRF with respect to magnetic oscillations with an accuracy of no worse than 2% if the ac-field amplitude is no greater than 0.7 of the saturation magnetization. The applicability of the quadratic approximation in the analysis of the self-sustained self-modulation process is considered. It is demonstrated that the model system fully characterizes the development of envelopes of both regular and chaotic self-modulation oscillations and the amplitude difference relative to the solution to the complete system is no greater than 20%. The calculations based on the model of coupled oscillators in the quadratic approximation allow a two-fold decrease in the computer resources and a decrease in the computation time by two orders of magnitude.

Synchronisation and desynchronisation of self-modulation oscillations in a ring chip laser under the action of a periodic signal and noise

The effect of pump noise on the synchronisation of self-modulation oscillations in a solid-state ring laser with periodic pump modulation is studied numerically and experimentally. It is found that, in contrast to desynchronisation that usually occurs under action of noise in the case of 1/1 synchronisation of self-oscillations by a periodic signal, the effect of noise on 1/2 synchronisation may be positive, namely, at a sufficiently low intensity, pump noise is favourable for synchronisation of self-oscillations, for narrowing of their spectrum, and for increasing the signal-to-noise ratio.

Synchronisation of self-oscillations in a solid-state ring laser with pump modulation in the region of parametric resonance between self-modulation and relaxation oscillations

The synchronisation of the self-modulation oscillation frequency in a Nd : YAG ring laser by an external periodic signal modulating the pump power in the region of parametric resonance between self-modulation and relaxation oscillations is studied theoretically and experimentally. The characteristic features of synchronisation processes in lasers operating in the self-modulation regime of the first kind and in the regime with a doubled self-modulation period are considered. Two bistable branches of synchronisation of self-modulation oscillations are found by numerical calculation. The experimental data agree well with the numerical simulation results for one of these branches, but the other branch of bistable self-modulation oscillations was not observed experimentally.

Bistability of self-modulation oscillations in an autonomous solid-state ring laser

Bistable self-modulation regimes of generation for a ring YAG : Nd chip laser with the counterpropagating waves asymmetrically coupled via backward scattering are simulated numerically. Two branches of bistable self-modulation regimes of generation are found in the domain of the parametric resonance between the self-modulation and relaxation oscillations. The self-modulation regimes observed in earlier experiments pertain to only one of the branches. Possible reasons for such a discrepancy are considered, related to the influence of technical and natural noise on the dynamics of solid-state ring lasers.

Self-modulation oscillation regimes in fibre lasers with microoptomechanical resonance structures

Self-modulation oscillation regimes are studied in erbium fibre lasers with intracavity microoptomechanical structures (microoscillators) of different types, namely, based on silicon structures and consisting of special waveguide segments. Optical excitation of acoustomechanical vibrations of microoscillators is accomplished using photothermal effect or light pressure. Under the conditions of resonance interaction, i.e., when the eigenfrequencies of microoscillators coincide with the frequencies of relaxation oscillations or with those of intermode beats, the dependences of self-oscillation characteristics on the system parameters are found and the stability of the self-modulation frequency within 10-4 — 10-6 is obtained at relatively low (40 — 300) Q-factors of microoscillators. The possibility to construct multivariate (multichannel) fibreoptical sensors of physical quantities with frequency division of measurement channels is demonstrated.

Quasi-periodic synchronisation of self-modulation oscillations in a ring chip laser by an external periodic signal

The synchronisation of periodic self-modulation oscillations in a ring Nd:YAG chip laser under an external periodic signal modulating the pump power has been experimentally investigated. A new quasi-periodic regime of synchronisation of self-modulation oscillations is found. The characteristic features of the behaviour of spectral and temporal structures of synchronised quasi-periodic oscillations with a change in the external signal frequency are studied.

Quasi-periodic regime of self-modulation oscillations with a periodic low-frequency envelope in a ring chip laser

The dynamics of a ring chip Nd:YAG laser radiation in an external static magnetic field inducing an optical nonreciprocity of the resonator is studied experimentally. The amplitude and frequency nonreciprocities of the ring cavity induced by this magnetic field varied with moving the magnet with respect to the active element of the chip laser. A previously unknown quasi-periodic self-modulation lasing regime in which the self-modulation intensity oscillations of counterpropagating waves have an antiphase low-frequency envelope is found. The temporal and spectral characteristics of radiation are studied and the conditions of the appearance of this lasing regime are determined.

Nonisochronism of the self-modulation oscillation frequency in a solid-state ring laser

The dependence of the frequency of self-modulation oscillations of the first kind in a solid-state ring laser on its parameters is studied theoretically and experimentally. It is shown that the nonisochronism takes place: the self-modulation oscillation frequency depends on the intracavity field intensity. The influence of the amplitude — phase coupling on the nonlinear frequency shift of self-modulation oscillations, depending on the excess of the pump over the threshold, is studied. Comparison of the experimental results with theoretical data made it possible to determine the amplitude—phase coupling coefficient.

Stochastic effects during the action of the pump noise on bistable self-modulation oscillations in a solid-state ring laser

Nonlinear radiation dynamics of a solid-state ring laser is studied in the region of laser parameters corresponding to the parametric resonance between the self-modulation and relaxation oscillations. Bistable regions are found in which, apart from the self-modulation regime of the first kind, a stable quasi-periodic self-modulation regime exists. Temporal and spectral emission parameters of counterpropagating waves are considered in the bistable self-modulation generation regimes. The effect of noise on the bistable self-modulation oscillations is studied. It is shown that during the interaction of noise, spectral peaks split at relaxation and self-modulation frequencies.

Nonlinear processes upon doubling the period of self-modulation oscillations in a solid-state ring laser

Nonlinear phenomena appearing in a solid-state ring laser upon approaching the period-doubling bifurcation point of self-modulation oscillations and inside the doubling region are studied theoretically and experimentally. The bifurcation appears due to the parametric interaction of self-modulation oscillations of the first kind with relaxation oscillations. It is found that the bifurcation diagrams, time dependences of the intensities and power spectrum can significantly differ for counterpropagating waves because of the amplitude nonreciprocity of the ring resonator and the inequality of the moduli of the feedback coefficients. It is shown that when the self-modulation period is doubled, the widths of spectral peaks corresponding the self-modulation frequency and the fundamental relaxation frequency decrease. Noise precursors of doubling bifurcation are studied. It is found that the distance between the peaks of noise precursors increases with increasing the noise intensity. It is demonstrated experimentally that the noise modulation leads to the bifurcation point displacement, which increases with increasing the noise.

Phase dynamics in the self-modulation oscillation regime in a solid-state ring laser

The dynamics of the phase difference of counterpropagating waves is studied theoretically and experimentally in the self-modulation oscillation regime in a solid-state ring laser. It is found that in the case of a small enough frequency nonreciprocity of the ring resonator, the phase difference of counterpropagating waves changes within a limited range, performing periodic oscillations with the intensity self-modulation frequency. The instant frequency difference of counterpropagating waves also changes periodically in time; however, its mean value is zero (the frequency locking for counterpropagating waves takes place). The width of the frequency locking region is measured. It is shown that the phase difference of the coupling coefficients considerably affects the phase dynamics. This opens up new possibilities for determining the phase difference of coupling coefficients of counterpropagating waves.

Influence of the difference in polarisations of counterpropagating waves on the dynamics of solid-state ring lasers

The influence of polarisations of counterpropagating waves on the dynamics of self-modulation oscillations of the first kind in solid-sate ring lasers is studied theoretically and experimentally. The characteristic features of amplitude and frequency characteristics of radiation and the spectra of relaxation oscillations appearing at different polarisations of counterpropagating waves are analysed. The obtained experimental results are well described by the vector model of a solid-state ring laser, which takes into account different polarisations of the ring resonator for counterpropagating waves.

Self-modulation lasing regimes in a fast-flow CO2 laser

Numerical simulation of self-modulation lasing regimes has been carried out for a CO2 laser with transverse flow of the active medium through an unstable resonator with inhomogeneous internal pumping. Two types of steady-state self-modulation oscillation differing in the feedback mechanism were observed. The type of lasing regime and the conditions of its realization depend both upon the pumping profile and upon the composition and pressure of the working mixture, which makes it generally possible to control temporal characteristics of lasing.

High-Dimensional Chaos in a Gyrotron

In this paper, nonstationary and chaotic dynamics of a gyrotron with a nonfixed field structure have been studied. We discuss the mechanism of transition to self-modulation and chaotic oscillations and present the plane of parameters with different kinds of regimes in a gyrotron. For chaotic attractors, the set of Lyapunov exponents has been calculated. We have estimated the dimensions of chaotic attractors from the Kaplan-Yorke formula and found it to be anomalously high. The explanation of this fact is based on the presence of a large number of high-Q eigenmodes in the gyrotron resonator operating near a critical frequency of the electrodynamic system

Self-modulation regimes of a phase-locked loop with the second-order filter

We study self-modulation oscillations of a phase-locked loop with the second-order filter. The regions in parameter space in which the modulated oscillations are generated and the properties of modulating oscillations are analyzed. Special attention is paid to studying chaotically modulated oscillations.

Controllable spectrum of an axial-mode gyrotron with external reflections

The feasibility of controlling the spectrum of multifrequency oscillations in a gyrotron by means of external reflections is studied. It is shown that, in self-modulation oscillation modes of operation, the radiation spectrum lines may come close to the resonance frequencies of a combined electromagnetic system including the reflector-limited part of the output waveguide. Under these conditions, the frequency separation of modes and, accordingly, the self-modulation period can be controlled by varying the position of the reflector. Theoretical results are corroborated by experiments with a 30-GHz relativistic gyrotron with an external reflector.

Effect of a magnetic field on self-modulation oscillations in a ring chip laser

The phase shift of self-modulation oscillations induced in a solid-state ring laser by an external magnetic field is studied theoretically and experimentally. It is found that the phase shift is caused by the amplitude nonreciprocity of the ring laser due to the Faraday effect in an active medium.