Low-frequency Relaxation Oscillations Research Articles

Relaxation oscillations in a bipolarised Nd : YAG laser with a Fabry – Perot cavity

Based on the model of a bipolarised laser, which takes into account real orientations of absorbing and emitting dipoles of active centres in the unit cell of an Nd : YAG single crystal, we have shown that the appearance of low-frequency relaxation oscillations requires the participation of both competing pump channels through linearly and circularly polarised dipole transitions.

Dynamical properties of total intensity fluctuation spectrum in two-mode Nd:YVO4 microchip laser**Project supported by the Beijing Higher Education Young Elite Teacher Project, China (Grant No. YETP0086), the Tsinghua University Initiative Scientific Research Programme, China (Grant No. 2012Z02166), and the Special-funded Programme on National Key Scientific Instruments and Equipment Development of China (Grant No. 2011YQ04013603).

We investigate the total intensity fluctuation spectrum of the two-longitudinal- mode Nd:YVO4 microchip laser (ML). We find that low-frequency relaxation oscillation (RO) peaks still appear in the total intensity fluctuation spectrum, which is different from a previous research result that the low-frequency RO peaks exist in the spectrum of the individual mode but compensate for each other totally in the total intensity fluctuation spectrum. Taking the spatial hole-burning effect into account, one and two-mode rate equations for Nd:YVO4 ML laser are established and studied. Based on the theoretical model, we find that when the gains and losses for two longitudinal models are different, a low-frequency RO peak will appear in the total intensity fluctuation spectrum, while when they share the same gain and loss, the total spectrum will behave like that of a single mode laser. Theoretical simulation results coincide with experimental results very well.

High and low frequency relaxation oscillations in a capacitive discharge plasma

Both high and low frequency relaxation oscillations have been observed in an argon capacitive discharge connected to a peripheral grounded chamber through a slot with dielectric spacers. The oscillations, observed from time-varying optical emission of the main discharge chamber, show, for example, a high frequency (46 kHz) relaxation oscillation at 100 mTorr, with an absorbed power near the peripheral breakdown, and a low frequency (2.7–3.7 Hz) oscillation, at a higher absorbed power. The high frequency oscillation is found to ignite a plasma in the slot, but usually not in the periphery. The high frequency oscillation is interpreted by using an electromagnetic model of the slot impedance, combined with the circuit analysis of the system including a matching network. The model is further developed by using a parallel connection of variable peripheral capacitance to analyse the low frequency oscillation. The results obtained from the model are in agreement with the experimental observations and indicate that a variety of behaviours are dependent on the matching conditions.

Low-Frequency Relaxation Oscillations in Capacitive Discharge Processes

Low-frequency (2.72–3.70Hz) relaxation oscillations at 100 m Torr at higher absorbed power were observed from time-varying optical emission of the main discharge chamber and the periphery. We interpret the low frequency oscillations using an electromagnetic model of the slot impedance with parallel connection variational peripheral capacitance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations, and indicate a variety of behaviours dependent on the matching conditions.

Breakage of the induced mode synchronization in a solid state laser and the anomalous effect of spontaneous noise level on the synchronization bandwidth

The process of optical pulse formation in a solid state laser in the regime of induced mode synchronization and the development of breakage upon frequency detuning are considered based on a numerical solution of the Maxwell-Bloch equation. It is established that breakage of the sequence and shape of laser pulses in the course of an increase in the frequency detuning begins with the appearance of a periodic modulation of the pulse sequence envelope by low-frequency relaxation oscillations. These oscillations transform into regular spikes, which follow the scenario of period doubling that leads to a chaotic regime. It is also established that an optimum level of spontaneous noise exists at which the synchronization bandwidth is maximum, while the duration of pulses is minimum at a fixed loss modulation amplitude. This scheme of synchronization breakage was qualitatively confirmed in experiments on a YAG:Nd laser (λ = 1.06 μm) with cavity loss modulation at an intermode beat frequency.

Quantization of the Low-Frequency Variability of the Double-Gyre Circulation

AbstractThe low-frequency dynamics of the double-gyre wind-driven circulation in large midlatitude oceanic basins is investigated. It is shown that for quasigeostrophic models linear (Rayleigh) friction is necessary to obtain realistic recirculation gyres and elongated jet streams with small meridional-to-zonal aspect ratio. It is also found that the use of either no-slip or free-slip boundary conditions does not change the drastic effects of bottom drag on the large scales. These long oceanic jets are alternatively destabilized and restabilized through successive (subcritical) supercritical symmetry-breaking bifurcations that are linked to the (non) existence of stationary Rossby waves. These waves are strongly localized along the oceanic front and are thus hardly affected by the basin geometry. Numerical and analytical results show that these waves are “quantized” with respect to the length of the jet, and an explicit dispersion relation is given. Numerical computations of branches of steady states, together with linear and nonlinear analysis, indicate that two classes of regimes characterize the low-frequency dynamics of the flow. The first class corresponds to supercritical regimes, which are associated with oceanic jets that have been destabilized by undamped stationary Rossby waves. In particular, these regimes allow the formation of gyre modes responsible for low-frequency relaxation oscillations of the jet. The second class corresponds to subcritical regimes, which are either quiescent or dominated by high-frequency instabilities and are characterized by jets that do not allow the formation of both stationary Rossby waves and gyre modes. Each of these regimes is characterized by typical spatial and time scales that are both quantized. The number n of “bumps” of the jet, which is related to the zonal wavenumber of the stationary Rossby waves, is used to distinguish between these regimes either in their supercritical or subcritical phase. For instance, the supercritical n = 2 regime is associated with a class of interdecadal gyre modes that extend up to 3000 km in the zonal direction. The quantization of the low-frequency dynamics and the existence of these regimes are also found to survive severe modifications of the basin geometry. These quantized regimes suggest that the low-frequency dynamics in turbulent regimes is likely to be autosimilar to the low-frequency dynamics found in a weakly nonlinear “ground” regime corresponding to n = 0.

Anomalies, symmetries, and asymmetries in the relaxation oscillation spectra of multimode standing-wave solid-state lasers

When the laser medium only partially fills the cavity of a multimode solid-state laser, there are significant changes in the spectral profile of the emission, the intensity fluctuation power spectra, and modulation transfer functions in comparison with lasers which have media that entirely fill the cavity. These effects are computed according to several approximate models for the multimode interactions and compared with experimental measurements. Symmetries and asymmetries in the multimode optical spectrum have corresponding features in the relaxation oscillation spectra. Changes in the laser cavity detuning and laser excitation lead to relatively abrupt changes in some variables (modal intensities, low-frequency relaxation oscillations) while the total intensity and largest relaxation oscillation frequency vary as they would for a single-mode laser.

A 1.55-μm solid-state laser source for DWDM applications

We describe the design and operation of a 1550-nm diode pumped Er,Yb:glass laser with >130 mW of output power and a free running linewidth of /spl sim/22 kHz. Due to the low frequency relaxation oscillation, near shot limited relative intensity noise performance is obtained throughout the radio frequency (RF) range of interest for cable television and dense wavelength division multiplexed (CATV/DWDM) applications. For long-haul spans an intracavity lithium niobate phase modulator allows for chirping of the linewidth to bandwidths and at rates sufficient to defeat stimulated Brillouin scattering (SBS). For certain applications, the high output power can eliminate the need for an erbium-doped fiber amplifier (EDFA).

Disappearance of relaxation oscillation frequencies in a multimode solid-state laser

Abstract We study analytically the Tang, Statz and deMars rate equations describing a solid-state Fabry-Perot laser. When the modes have equal gains, there is a critical number of lasing modes, above which the low-frequency relaxation oscillations responsible for antiphase dynamics disappear. These results are generalized to include unequal modal gains resulting from a Lorentzian gain profile.

Dependence of the frequency of low-frequency relaxation oscillations of a solid-state ring laser on the polarisation

An investigation is reported of the dependence of the frequency of low-frequency relaxation oscillations of the radiation power of solid-state ring lasers on the nature of the polarisation of the counterpropagating optical waves and on the ring cavity parameters. It is shown that the maximum frequency of antiphase low-frequency oscillations corresponds to the linear collinearly oriented polarisations of the counterpropagating waves. An increase in the ellipticity of the counterpropagating waves reduces the frequency of the antiphase oscillations and this frequency tends to zero for orthogonal circular polarisations of these waves.

Low frequency relaxation oscillations in class B lasers with feedback

Relaxation oscillations have been studied both theoretically and experimentally in a multimode YAG laser in the presence of a derivative feedback. In addition to the standard relaxation oscillations, discrete low frequency components are present in the noise spectrum of each individual mode but they compensate almost exactly in the total intensity. The influence of a combined derivative feedback involving both the total intensity and that of one selected mode on the behavior of the relaxation oscillations and nonlinear dynamics of the laser is investigated. It is shown that the compensation nature of the low frequency relaxation oscillations of the multimode class B lasers can be disturbed in this case and, as a consequence, the selected relaxation oscillations appear in the noise spectrum of the total intensity. A higher feedback level can induce a destabilization of the laser and eventually chaos. An excellent qualitative agreement between experiments and theory has been obtained.

The chaotic oscilloscope

In spite of its apparent simplicity, a system consisting of a high-frequency oscilloscope operated in the x–y mode and a photodiode, which detects the light emitted from the trace while feeding the signal back to the oscilloscope, exhibits extraordinary complex behavior. Scenarios involved are limit cycles evolving into chaos through the Feigenbaum bifurcation route and low-frequency relaxation oscillations that can be phaselocked to external signals. Regions of complete phase lock are observable in this case. Furthermore, the Feigenbaum oscillations can be superimposed upon the relaxation oscillations. The different scenarios will be illustrated and the underlying mechanisms discussed.

The relaxation oscillation in ramjet combustion

A mechanism of low frequency relaxation oscillation in ram jet combustion is proposed. Initial pressure disturbances induce combustion instability which results in periodic heat release. Acting as feedback, the periodic heat release boosts the pressure pulsations. The complex shock wave system separating the supersonic and subsonic flows may be replaced by a virtual normal shock which shifts back and forth in the diffuser duct in response to the pulsating pressure. The cold gas column expands or contracts like a buffer plug between the virtual normal shock and the flame front in accordance with the pulsating combustion downstream. This chain of actions and reactions results in a self excited nonlinear relaxation oscillation with irregular frequency. The proposed mechanism explains quite well the oscillograph obtained from rig testing of a 220 mm ram jet engine in a free jet of Mach No 1.94 from a blowdown tunnel.

Resonator configuration for the suppression of relaxation oscillations in a long-pulsed Nd:YAG laser

A resonator configuration which couples out the Gaussian TEM(00) mode was demonstrated to suppress lowfrequency relaxation oscillations in the output from a long-pulse Nd:YAG laser. Experimental measurements of the spatial and temporal beam quality, the spectral bandwidth, and the depth of amplitude modulation were made for this and several other Nd:YAG laser resonator designs. The result of these measurements indicates that this resonator configuration can be used to generate a high-quality (TEM(00)) long-pulse laser output which is nearly free from relaxation oscillations.

Simultaneous low-frequency relaxation and high-frequency microwave oscillation of a bulk GaAs c.w. oscillator

A new mode of operation of a Gunn-effect diode has been observed, where the bulk GaAs oscillator simultaneously generates a low-frequency relaxation oscillation and a microwave oscillation. This operational mode results from the dynamic path moving into and out of the negative-resistance region.

Relaxation Oscillation near the Threshold of Instability in Yttrium Iron Garnet

Coherent low-frequency relaxation oscillation in the amplitude of the z component of magnetization and the imaginary part of susceptibility has been observed in YIG at a microwave power level slightly above the threshold of instability. The relaxation time associated with the uniform mode has also been measured. The condition for coherent relaxation oscillation depends critically on the magnitude of the dc magnetic field. The low-frequency oscillation is interpreted to be the beat of two high-frequency components due to a split in the frequency of the k spin wave ωk±Δωk. It is also believed that the period of oscillation is controlled by the relaxation time associated with the uniform mode.