Mode Instability Threshold Research Articles

Impact of photodarkening on the mode instability threshold.

The threshold-like onset of mode instabilities is currently the main limitation for the scaling of the average output power of fiber laser systems with diffraction limited beam quality. In this contribution, the impact of a wavelength shift of the seed signal on the mode instability threshold has been investigated. Against expectations, it is experimentally shown that the highest mode instabilities threshold is reached around 1030 nm and not for the smallest wavelength separation between pump and signal. This finding implies that the quantum defect is not the only source of thermal heating in the fiber. Systematic experiments and simulations have helped in identifying photodarkening as the most likely second heat source in the fiber. It is shown that even a negligible photodarkening-induced power loss can lead to a decrease of the mode instabilities threshold by a factor of two. Consequently, reduction of photodarkening is a promising way to mitigate mode instabilities.

Optimizing mode instability in low-NA fibers by passive strategies.

Systematic experimental investigations toward the mode instability (MI) threshold in low-NA fibers are performed. By testing several fibers with varying V-parameters drawn from the same preform, a high degree of reproducibility of the experimental conditions could be achieved. This allows for systematic investigations on isolated parameters influencing the complex behavior of MI. A maximum MI threshold of 2 kW could be demonstrated for the tested fibers, which represents a new record output power for narrow linewidth fiber amplifiers. The MI threshold was found to sensitively depend on the V-parameter for large V-parameters (>2), but to be robust for smaller V-parameters. Furthermore, the fiber bending diameter and the seed excitation conditions were identified to sensitively influence the MI threshold.

13 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities

We report on the high power amplification of 1064nm linearly-polarized laser in all-fiber polarization-maintained MOPA, which can operate at output power level of 1.3kW. The main amplifier was pumped with six 915nm laser diodes, and the slope efficiency is 65.3%. The beam quality (M2) was measured to be <1.2 at full power operation. The polarization extinction rate of the fiber amplifier was measured to be above 94% before mode instabilities (MI) sets in, which reduced to about 90% after the onset of MI. Power scaling capability of strategies for suppressing MI is analyzed based on a novel semi-analytical model, the theoretical results of which agree with the experimental results. It shows that mitigating MI by coiling the gain fiber is an effective and practical way in standard double-cladding large mode area fiber, and, by tight coiling of the gain fiber to the radius of 5.5cm, the MI threshold can be increased to 3 times higher than that without coiling or loose coiling. Experimental study has been carried out to verify the idea, which has proved that MI was suppressed successfully in the amplifier by tight coiling.

Long-lasting energetic particle modes in tokamak plasmas with low magnetic shear

A long-lasting (for hundreds of milliseconds) m/n = 1 energetic particle mode driven by trapped fast ions, other than conventional fishbone bursts, is studied theoretically and in comparison with HL-2A experimental results. The mode can be observed in weak shear tokamak plasmas during neutral beam injection with a mostly steady amplitude envelope of long-lasting magnetic perturbation signals. The dispersion relation and radial structure of the mode are calculated with a weak shear q-profile. Both the m/n = 1/1 component and its higher frequency m/n = 2/2 harmonics are found to be unstable, in good agreement with experimental observations on HL-2A. On the other hand, due to the feature of weak magnetic shear, the mode is also significantly different from bursty fishbones, especially the mode structure, temporal behavior, instability threshold and growth rate dependence on the fast ion gradient. The nonlinear evolution of the mode and the comparison with fishbone bursts are also further investigated.

Spatial rogue waves in a photorefractive pattern-forming system.

We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material.

On certain properties of the compact Zakharov equation

AbstractLong-time evolution of a weakly perturbed wavetrain near the modulational instability (MI) threshold is examined within the framework of the compact Zakharov equation for unidirectional deep-water waves (Dyachenko and Zakharov, JETP Lett., vol. 93, 2011, pp. 701–705). Multiple-scale solutions reveal that a perturbation to a slightly unstable uniform wavetrain of steepness $\mu $ slowly evolves according to a nonlinear Schrodinger equation (NLS). In particular, for small carrier wave steepness $\mu &lt;\mu _{1}\approx 0.27$ the perturbation dynamics is of focusing type and the long-time behaviour is characterized by the Fermi–Pasta–Ulam recurrence, the signature of breather interactions. However, the amplitude of breathers and their likelihood of occurrence tend to diminish as $\mu $ increases while the Benjamin–Feir index (BFI) decreases and becomes nil at $\mu _{1}$. This indicates that homoclinic orbits persist only for small values of wave steepness $\mu \ll \mu _{1}$, in agreement with recent experimental and numerical observations of breathers. When the compact Zakharov equation is beyond its nominal range of validity, i.e. for $\mu &gt;\mu _{1}$, predictions seem to foreshadow a dynamical trend to wave breaking. In particular, the perturbation dynamics becomes of defocusing type, and nonlinearities tend to stabilize a linearly unstable wavetrain as the Fermi–Pasta–Ulam recurrence is suppressed. At $\mu =\mu _{c}\approx 0.577$, subharmonic perturbations restabilize and superharmonic instability appears, possibly indicating that wave dynamical behaviour changes at large steepness, in qualitative agreement with the numerical simulations of Longuet-Higgins and Cokelet (Proc. R. Soc. Lond. A, vol. 364, 1978, pp. 1–28) for steep waves. Indeed, for $\mu &gt;\mu _{c}$ a multiple-scale perturbation analysis reveals that a weak narrowband perturbation to a uniform wavetrain evolves in accord with a modified Korteweg–de Vries/Camassa–Holm type equation, again implying a possible mechanism conducive to wave breaking.

Impact of gain saturation on the mode instability threshold in high-power fiber amplifiers.

We present a coupled-mode model of transverse mode instability in high-power fiber amplifiers, which takes the effect of gain saturation into account. The model provides simple semi-analytical formulas for the mode instability threshold, which are valid also for highly saturated amplifiers. The model is compared to recently published detailed numerical simulations of mode instability, and we find reasonably good agreement with our simplified coupled-mode model.

Scaling the mode instability threshold with multicore fibers.

Mode instabilities (MIs) have quickly become the most limiting effect for the average power scaling of nearly diffraction-limited beams from state-of-the-art fiber laser systems. In this work it is shown that, by using an advanced multicore photonic crystal fiber design, the threshold power of MIs can be increased linearly with the number of cores. An average output power of 536 W, corresponding to 4 times the threshold power of a single core, is demonstrated.

On the persistence of breathers at deep water

The long-time behavior of a perturbation to a uniform wavetrain of the compact Zakharov equation is studied near the modulational instability threshold. A multiple-scale analysis reveals that the perturbation evolves in accord with a focusing nonlinear Schrodinger equation for values of wave steepness μ < μ1 ≈ 0.274. The long-time dynamics is characterized by interacting breathers, homoclinic orbits to an unstable wavetrain. The associated Benjamin-Feir index is a decreasing function of μ, and it vanishes at μ1. Above this threshold, the perturbation dynamics is of defocusing type and breathers are suppressed. Thus, homoclinic orbits persist only for small values of wave steepness μ ≪ μ1, in agreement with recent experimental and numerical observations of breathers.

Spontaneous Rayleigh Seed for Stimulated Rayleigh Scattering in High Power Fiber Amplifiers

We estimate the Stokes wave starting power for stimulated thermal Rayleigh scattering (STRS) produced by thermal fluctuations in the fiber core that transiently alter the refractive index profile in the core. A transverse temperature gradient creates a transverse refractive index gradient via the thermooptic effect, and if the fluctuation frequency lies in the STRS gain band, it can couple light from mode LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> to LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> to seed STRS. This spontaneous Rayleigh seed may be stronger than the quantum background and may affect the mode instability thresholds of fiber amplifiers. This new seed estimate can be incorporated in STRS models to improve threshold calculations.

Passive mitigation strategies for mode instabilities in high-power fiber laser systems

Mode instabilities have quickly become the most limiting effect when it comes to scaling the output average power of fiber laser systems. In consequence, there is an urgent need for effective strategies to mitigate it and, thus, to increase the power threshold at which it appears. Passive mitigation strategies can be classified into intrinsic, which are related to the fiber design, and extrinsic, which require a modification of the setup. In order to evaluate the impact of mitigation strategies, a means to calculate its power threshold and predict its behavior is required. In this paper we present a simple semi-analytic formula that is able to predict the changes of the mode instability threshold by analyzing the strength of the thermally-induced waveguide perturbations. Furthermore, we propose two passive mitigation strategies, one intrinsic and one extrinsic, that should lead to a significant increase of the power threshold of mode instabilities.

Controlling mode instabilities by dynamic mode excitation with an acousto-optic deflector

We demonstrate an approach to actively stabilize the beam profile of a fiber amplifier above the mode instability threshold. Both the beam quality and the pointing stability are significantly increased at power levels of up to three times the mode instabilities threshold. The physical working principle is discussed at the light of the recently published theoretical explanations of mode instabilities.

Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations

We present detailed numerical simulations of modal instabilities in high-power Yb-doped fiber amplifiers using a time-dependent temperature solver coupled to the optical fields and population inversion equations. The temperature is computed by solving the heat equation in polar coordinates using a 2D second-order alternating direction implicit method. We show that the higher-order modal content rises dramatically in the vicinity of the threshold and we recover the three power-dependent regions that are characteristic of the transfer of energy. We also investigate the dependence of the threshold on the seed power and the modal content ratio of the seed. The latter has a minimal effect on the threshold while it is shown that for the fiber configuration investigated, the modal instability threshold scales linearly over a wide range with the seed power. In addition, two different gain-tailored core designs are investigated and are shown to have higher thresholds than that of a uniformly doped core. Finally, we show that this full time-dependent model which does not assume a frequency offset between the modes a priori, predicts a reduced threshold when the seed is modulated at the KHz level. This is in agreement with the steady-periodic approach to this phenomenon.

Increasing mode instability thresholds of fiber amplifiers by gain saturation

We show by numerical modeling that saturation of the population inversion reduces the stimulated thermal Rayleigh gain relative to the laser gain in large mode area fiber amplifiers. We show how to exploit this effect to raise mode instability thresholds by a substantial factor. We also demonstrate that when suppression of stimulated Brillouin scattering and the population saturation effect are both taken into account, counter-pumped amplifiers have higher mode instability thresholds than co-pumped amplifiers for fully Yb3+ doped cores, and confined doping can further raise the thresholds.

Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers

Using numerical simulations of thermally induced mode coupling we show how the instability threshold can be substantially reduced if the pump or injected signal is modulated in the kHz range. We also show how the mode coupling gain varies with the frequency offset of the parasitic mode. We model thresholds when the source of detuned light is quantum background, amplitude modulation of the pump power, and amplitude modulation of the signal seed. We suggest several key experimental and modeling tests of our model.

Beam quality degradation of a single-frequency Yb-doped photonic crystal fiber amplifier with low mode instability threshold power

A current limit in power scaling of Yb-doped fiber amplifiers is the sudden onset of mode instabilities. We investigated this effect on a single-frequency Yb-doped photonic crystal fiber amplifier with a low mode instability threshold power. By measuring the overlap of the fiber output beam with the fundamental mode of an external cavity to be about 95%, we could exclude significant modal power transfer below a sharp power threshold. Furthermore, we directly measured the frequency resolved intensity noise spectra. No fluctuations in the overall output power were observed, but for the modal content different oscillation regimes were identified.

Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission

Spontaneous and induced modulation instability (MI) in the presence of rather broadband spectra are shown in the conventional single-mode fiber (SMF) for the first time. The broadband spectra are caused by the amplified spontaneous emission (ASE) of the erbium-doped fiber amplifiers (EDFAs). The two kinds of MI are seeded by noise components and a probe beam which results from two EDFAs amplification, respectively. For the spontaneous MI, the MI threshold is shown to be ∼170 mW, which contains the laser as well as the ASE component. For the induced MI, an idler beam appears and grows with the peak power of input pulses at first, and then multiple spectral peaks emerge.

Modulation instability of bright photovoltaic solitons on a partially incoherent background

We present the observation of incoherent anti-dark photovoltaic solitons in LiNbO3:Fe crystal. This new class of soliton states involves bright photovoltaic solitons on a background beam meeting κ > 1, where κ is the ratio of background illumination photovoltaic constant to that of soliton beam. For κ < 1, dark photovoltaic solitons are generated. Furthermore, this novel type solitons are investigated experimentally by injecting coherent light and partially coherent background of infinite extent. In case of spatial coherence of the background lower than the threshold of incoherent modulation instability, these results indicate that bright photovoltaic solitons can propagate in a stable fashion.

Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers

The temporal behavior of mode instabilities in active large mode area fibers is experimentally investigated in detail. Thus, apart from the onset threshold of mode instabilities, the output beam is characterized using both high-speed camera measurements with 20,000 frames per second and photodiode traces. Based on these measurements, an empiric definition of the power threshold of mode instabilities is introduced. Additionally, it is shown that the temporal dynamics show a transition zone between the stable and the unstable regimes where well-defined periodic temporal fluctuations on ms-timescale can be observed. Finally, it is experimentally shown that the larger the mode-field area, the slower the mode-instability fluctuation is. The observations support the thermal origin of mode instabilities.

Build up and decay of mode instability in a high power fiber amplifier

State-of-the-art high power Yb-doped large mode area fibers have been developed to a performance level able to reach the so-called mode instability threshold. In this contribution we will discuss the experimental results regarding the temporal evolution (build up and decay) of this effect to come closer to a comprehensive understanding of its driving mechanisms. Our investigations prove that the relevant time scale for build up and decay of mode instability is in the millisecond range and thus deliver experimental evidence of underlying thermal effects. To the best of our knowledge these are the first systematic, time resolved investigations on that topic.