Self-pulsing Phenomenon Research Articles

Numerical study of the self-pulsing of DC discharge: from corona to parallel-plate configurations

We present here an investigation of the self-pulsing phenomenon of negative corona and parallel-plate discharge in argon within one frame of a one-dimensional fluid model in cylinder–cylinder electrode geometry. The transition from corona to parallel-plate discharge is obtained by changing the inner and outer radii of the electrodes. The model reproduces the self-pulsing waveform well and provides the spatiotemporal behaviors of the charged particles and electric field during the pulse. The self-pulsing shows a common feature that occurs in various configurations and that does not depend on a specific electrode structure. The self-pulsing is the transformation between a weak-current Townsend mode and a large-current normal glow mode. The behavior of the positive ions is the dominant factor in the formation of the pulse.

Self-Pulsations in Terahertz Quantum Cascade Lasers under Strong Optical Feedback: The Effect of Multiple Reflections in the External Cavity.

We have recently reported the self-pulsation phenomenon under strong optical feedback in terahertz (THz) quantum cascade lasers (QCLs). One important issue, however, we left open: the effect of multiple round trips in the external cavity on the laser response to feedback. Our current analysis also casts additional light on the phenomenon of self-pulsations. Using only one external cavity round trip (ECRT) in the model has been the common approach following the seminal paper by Lang-Kobayashi in 1980. However, the conditions under which the Lang-Kobayashi model, in its original single-ECRT formulation, is applicable has been rarely explored. In this work, we investigate the self-pulsation phenomenon under multiple ECRTs. We found that the self-pulsation waveform changes when considering more than one ECRT. This we attribute to the combined effect of the extended external cavity length and the frequency modulation of the pulsation frequency by the optical feedback. Our findings add to the understanding of the optical feedback dynamics under multiple ECRTs and provide a pathway for selecting the appropriate numerical model to study the optical feedback dynamics in THz QCLs and semiconductor lasers in general.

An analog electronic emulator of non-linear dynamics in optical microring resonators

The microring resonator is a ubiquitous building block of optical integrated circuits. Owing to its unique non-linear properties, it appears well-suited as a node in the realization of photonic networks, such as spiking neural networks. However, experimental investigation requires complex setups, incurring considerable device fabrication times and costs. Inherent physical constraints limit the ranges of the parameters determining the timescales and strengths of the non-linear behaviors. Moreover, on-the-fly changes to these parameters and node couplings are not easily realizable. On the other hand, numerical simulations are computationally heavy, particularly for large networks, and do not entirely replace measurement on a physical apparatus. To mitigate this problem, we introduce and realize an analog electronic emulator that implements dynamics, attempting to reproduce the self-pulsing phenomenon in an optical microresonator. It can be readily constructed with off-the-shelf components, and is well-suited for building complex networks. The circuit is explicitly based on a mathematical model of the microresonator, subject to some approximations, parameter adjustments and rescalings. Initial results comparing experimental data from the emulator and a representative silicon photonic device plus numerical simulations suggest a satisfactory level of agreement in the temporal dynamics and response to parametric sweeps when scaled for the different response times. This work exemplifies the relevance of explicitly establishing correspondences between physical systems having widely different features but governed by similar dynamics.

Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period x one-period cells. This technique avoids cumulative numerical errors as well as efficiently saves computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically-driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.

An investigation into self-pulsing behavior in an Er-doped ring laser

We observe a strong self-pulsing phenomenon in an all-fiber Er-doped ring laser. With an increase in the pump power, the generated pulse gradually evolves from a sine-wave pulse to a typical mode-locking pulse train. The self-mode-locked laser pulse obtained has a pulse-repetition rate in the megahertz region and a maximum average output power of around 1 mW. The self-pulsing evolving dynamics can be analyzed using coupled-wave rate equations by simultaneously considering the interaction of two adjacent Er-ions and the reabsorption loss of the ground-state energy levels.

Comparison between Trichel pulse in negative corona and self-pulsing in other configurations

We present here a comparison study on self-pulsing phenomena in negative corona, hollow cathode discharges (HCD) and parallel-plate discharge in air. The voltage-current (V-I) curve, the waveforms of self-pulsed currents, and the time-resolved images of the pulsed discharge are measured under various operating conditions. It is experimentally evidenced that the Trichel pulse in a negative corona and the self-pulsing in HCD and/or parallel-plate discharge have similar features as well as spatial-temporal developing process. It is suggested that they should have a similar mechanism that the pulsing reflects the mode transition of discharge between the low-current Townsend and the high-current normal glow. The pulse rising corresponds to the breakdown and formation of temporal glow discharge in a background of low-current Townsend discharge, while the decay edge relates to the transition back to Townsend discharge. The pulse interval is the re-building process of the space charge layer of high density to ensure the glow breakdown.

Experimental study on self-pulsing in flow-induced atmospheric pressure plasma jet

In this paper, we present an experimental study on the self-pulsing phenomenon in a flow-induced atmospheric pressure plasma jet (APPJ) in a hollow electrode configuration driven by dc voltage supply. The current-voltage curve, the typical waveforms of current and voltage of self-pulsing, the time-resolved images, and the repetition frequency were measured under different experimental conditions. The results show that the APPJ of a hollow electrode can sustain in a stable, repeatable self-pulsing regime. The waveform of the pulsed current is very stable with nearly constant rising time and decay time at different discharge averaged currents. Although the pulsing frequency increases linearly with the averaged current and the gas flow rate, it decreases with the electrode gap. An equivalent electric circuit consisting of a capacitor and two resistors was used to model the self-pulsing discharge plasma. The simulation results and the time-resolved images recorded using an ICCD camera show that the pulsed process of the hollow electrode APPJ contains the evolutions of gas breakdown, discharge development, and decay of a glow plasma. A weak discharge is maintained during the time interval between two pulses, indicating that the self-pulsing in this APPJ is a mode transition between glow and weak discharge.

Self-pulsing in kilowatt level narrow-linewidth fiber amplifier with WNS phase-modulation.

The self-pulsing phenomenon in kilowatt level narrow-linewidth fiber amplifiers with white noise source (WNS) phase-modulation is observed experimentally. It possesses the obvious threshold of the pump power and prevents the narrow-linewidth fiber lasers from further power scaling. The experimental study shows that known explanations are not applicable here and indicates that occurrence of self-pulsing is closely related to Stimulated Brillouin Scattering (SBS) process. The theoretical discussion reveals that the spikes in the modulated spectrum are the critical factor that SBS threshold is lower than the theoretical estimation. The 1+1 dimensional SBS model analysis predicts that self-pulsing originates from forward second order Stokes pulses, which is in good qualitative agreement with the experimental data.

Extended and localized Hopf-Turing mixed-mode in non-instantaneous Kerr cavities.

We investigate the spatio-temporal dynamics of a ring cavity filled with a non-instantaneous Kerr medium and driven by a coherent injected beam. We show the existence of a stable mixed-mode solution that can be either extended or localized in space. The mixed-mode solutions are obtained in a regime where Turing instability (often called modulational instability) interacts with self-pulsing phenomenon (Andronov-Hopf bifurcation). We numerically describe the transition from stationary inhomogeneous solutions to a branch of mixed-mode solutions. We characterize this transition by constructing the bifurcation diagram associated with these solutions. Finally, we show stable localized mixed-mode solutions, which consist of time-periodic oscillations that are localized in space.

Self-pulsing in a low-current hollow cathode discharge: From Townsend to glow discharge

We investigate the self-pulsing phenomenon of a low current cavity discharge in a cylindrical hollow cathode in pure argon. The waveforms of pulsed current and voltage are measured, and the time-averaged and time-resolved images of hollow cathode discharge are recorded by using high-speed intensified charge coupled device camera. The results show that the self-pulsing is a mode transition between low-current stage of Townsend discharge and high-current stage of glow discharge. During the self-pulsing, the current rising time relates to the dissipation of space charges, and the decay time relates to the reconstruction of the virtual anode by the accumulation of positive ions. Whether or not space charges can form and keep the virtual anode is responsible for the discharge mode and hence plays an important role in the self-pulsing phenomenon in low current hollow cathode discharge.

Low-frequency, self-sustained oscillations in inductively coupled plasmas used for optical pumping

We have investigated very low frequency, on the order of one hertz, self-pulsing in alkali-metal inductively-coupled plasmas (i.e., rf-discharge lamps). This self-pulsing has the potential to significantly vary signal-to-noise ratios and (via the ac-Stark shift) resonant frequencies in optically pumped atomic clocks and magnetometers (e.g., the atomic clocks now flying on GPS and Galileo global navigation system satellites). The phenomenon arises from a nonlinear interaction between the atomic physics of radiation trapping and the plasma's electrical nature. To explain the effect, we have developed an evaporation/condensation theory (EC theory) of the self-pulsing phenomenon.

Self-pulsing of hollow cathode discharge in various gases

In this paper, we investigate the self-pulsing phenomenon of cavity discharge in a cylindrical hollow cathode in various gases including argon, helium, nitrogen, oxygen, and air. The current-voltage characteristics of the cavity discharge, the waveforms of the self-pulsing current and voltage as well as the repetition frequency were measured. The results show that the pulsing frequency ranges from a few to tens kilohertz and depends on the averaged current and the pressure in all gases. The pulsing frequency will increase with the averaged current and decrease with the pressure. The rising time of the current pulse is nearly constant in a given gas or mixture. The self-pulsing does not depend on the external ballast but is affected significantly by the external capacitor in parallel with the discharge cell. The low-current self-pulsing in hollow cathode discharge is the mode transition between Townsend and glow discharges. It can be described by the charging-discharging process of an equivalent circuit consisting of capacitors and resistors.

Self-pulsing discharge of a plasma brush operated in atmospheric-pressure argon

A plasma brush excited by DC voltage is developed with argon as working gas in the ambient air. The time evolution of the discharge current, the light emission, and the sustaining voltage are analyzed under different conditions. The self-pulsing phenomenon of the discharge is observed with oscillated voltage and intermittent current. The self-pulsing frequency ranges from several tens hertz to several hundred hertz depending on the output power and the gas flow rate. It increases with the increasing of the gas flow rate, while it decreases as the output power increases. The phenomenon is explained qualitatively based on a spatially resolved measurement about the discharge.

Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects

Bistability (BS) and self-pulsation (SP) phenomena in silicon microring resonators (MRR) with intense CW light injection are studied. Several nonlinear optical effects including Kerr effect, two-photon absorption, free carrier absorption and free carrier dispersion are taken into account. The threshold optical intensity of BS and SP is derived from the coupled mode theory and a linear stability analysis method. The influences of MRR's parameters (carrier lifetime, linear loss and radius) and light injection conditions (input power, wavelength detuning) on the characteristics of SP (modulation depth and oscillating frequency) are analyzed and discussed. It is shown that, SP occurs only if the carrier lifetime ranges from several ps to several-hundred ps and the input light intensity is higher than 10⁶W/cm². The modulation depth of SP can be as large as 8dB and the associated oscillating frequency is in the range from several GHz to beyond 10 GHz.

Self-pulsing operating mode of hollow cathode discharge in noble gas

The self-pulsing phenomenon of hollow cathode discharge in a semi-cylindrical hollow cathode in noble gas is investigated in this paper. The current-voltage (I-V) characteristics and the time evolution of the current and voltage of self-pulsing are measured under different conditions. The results show that the pulse frequency ranges from a few to tens kilohertz depending on the pressure and the averaged current. It increases with the averaged current and decreases as the pressure rising. The external parallel capacitances have no influence on the self-pulsing frequency. It is supposed that the mode transition between pre-discharge and hollow cathode discharge may contribute to the self-pulse.

Design and performance analysis of a tunable and self-pulsation diode pumped double-clad D-shaped Yb<sup>3+</sup>-doped silica fiber laser

A wide range of applications have emerged for tunable ytterbium fiber lasers as single-frequency sources for spectroscopic applications, pumping source of Pr:ZBLAN amplifier, and Tm:ZBLAN upconversion laser, material processing, and military applications. In this paper, a 975-nm high power fiber coupled high power diode laser module of up to 5 W end pumping a ytterbium-doped multimode D-shaped fiber laser has been investigated. This used a Fabry-Pérot cavity with output coupler reflectivities of 80%, 60%, and Fresnel reflection of 4%. The output laser wavelength was tuned over a wide range of more than 50 nm, from 1041 to 1094 nm for cavity lengths from 1 to 10 m, respectively. An optical-to-optical slope efficiency of 45% was found for a 1-m cavity length, which increased to 60% for a 4-m cavity length. The maximum slope efficiency of 82.1% for a cavity length of 2 m was measured with the Fresnel reflection output coupler, and the measured lowest threshold pump power for this high gain cavity configuration was 130 mW. The threshold lasing pumping powers of 4.3, 4.5, and 4.7 W were dependent on the output coupler reflectivities of 80%, 60%, and Fresnel reflection of 4%, respectively. Also, self-pulsation phenomena were observed only at higher level pumping powers of more than 4 W and at longer cavity length.

Model and Characteristics of Self-Pulsing in ${\rm Tm}^{3+}$-Doped Silica Fiber Lasers

In this paper, a theoretical model, taking into account the phonon-assisted excited-state absorption process ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> → <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ), has been constructed to explain the self-pulsing (SP) phenomenon in the Tm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> -doped fiber lasers. Both numerical simulation and experimental investigation on the SP characteristics of ~2-μ.m Tm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> -doped fiber lasers have been carried out. The numerical simulation shows agreement with the experimental results. Furthermore, the impacts of output coupling, pump intensity, and Tm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> -ion doping concentration on the SP characteristics of the Tm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> -doped fiber lasers have been studied explicitly, and optimization of the SP features has been discussed. In addition, the potential applications of SP in fiber lasers or solid-state lasers have also been proposed.

Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers

Fiber laser resonator configurations have been analyzed theoretically on the basis of steady-state rate equations to optimize the laser conversion efficiency. Evolution of the pump- and signal powers and the saturated gain coefficient along the length of the laser medium has been simulated for high- and low-finesse resonators in forward- and backward pumping schemes. The corresponding fiber laser configurations have been setup to verify the results of simulation. Backward pumping configuration in an Yb-doped fiber laser has been found to be the most efficient, and in this configuration a maximum cw output power of 10.75W in single transverse mode with an optical-to-optical conversion efficiency of 62.5% has been achieved. The laser output spectrum was peaked at 1093nm with full-width at half-maximum (FWHM) line-width of about 9nm. In the low-finesse resonator configuration, it has been found that experimental observations differ from theoretical simulation results. In this case, output power from both ends ceases to increase linearly beyond 1.8W, and starts fluctuating due to the onset of strong random self-pulsing phenomenon. Our investigation shows that a non-uniform steady-state gain along the fiber length facilitates the self-pulsing process.

Self-phase modulation in slow-wave structures: A comparative numerical analysis

Self-phase modulation effects in 1D optical slow-wave structures made of Fabry–Perot cavities coupled by Distributed Bragg Reflectors (DBRs) are discussed. The nonlinear response of the structure is investigated by a comparative analysis of several numerical methods operating either in time or frequency-domain. Time-domain methods include two Finite-Difference Time-Domain approaches, respectively, optimized to compensate for numerical dispersion and to model nonlinearity at any order. In the frequency-domain an efficient method based on a numerical integration of Maxwell’s equations and an iterative nonlinear extension of the Eigenmode Expansion method are discussed. A Nonlinear Equivalent Circuit of DBRs is also presented as a useful model to reduce computational efforts. Numerical results show that bistable effects and self-pulsing phenomena can occur when either the optical power or the number of coupled cavities of the structure are sufficiently increased.

Direct evidence for laser reabsorption as initial cause for self-pulsing in three-level fibre lasers

The temporal characteristics of a standing wave Tm3+-doped silica fibre laser are presented. For uni-directional pumping, the output displays the well-known self-pulsation phenomenon, but with bi-directional pumping, a significant increase in the laser stability is observed. A longitudinally uniform population inversion is shown to be of paramount importance to the stability of three-level lasers.