High-speed modal decomposition of mode instabilities in high-power fiber lasers

Novel Bidirectional Output Ytterbium-Doped High Power Fiber Lasers: From Continuous to Quasi-Continuous

Traditional ytterbium-doped high-power fiber lasers generally use a unidirectional output structure. To reduce the cost and improve the efficiency of the fiber laser, we propose a bidirectional output fiber laser (BOFL). The BOFL has many advantages over that of the traditional unidirectional output fiber laser (UOFL) and has a wide application in the industrial field. In theory, the model of the BOFL is established, and a comparison of the nonlinear effect in the traditional UOFL and the BOFL is studied. Experimentally, high-power continuous wave (CW) and quasi-continuous wave (QCW) BOFLs are demonstrated. In the continuous laser, we first combine the BOFL with the oscillating amplifying integrated structure, and a near-single-mode bidirectional 2 × 4 kW output with a total power of above 8 kW is demonstrated. Then, with the simple BOFL, a CW bidirectional 2 × 5 kW output with a total power of above 10 kW is demonstrated. By means of pump source modulation, a QCW BOFL is developed, and the output of a near-single mode QCW laser with a peak output of 2 × 4.5 kW with a total peak power of more than 9 kW is realized. Both CW and QCW output BOFL are the highest powers reported at present.

Polarization-resolved mode evolution in TMI-limited Yb-doped fiber amplifiers using a novel high-speed Stokes polarimeter

In this work we have developed a high-speed Stokes polarimeter method based on simultaneous 4-channel imaging with a high-speed camera. Thus, current speed limitations of imaging polarimeters for wavelengths around 1 µm can be overcome, allowing a sub-ms polarization-resolved characterization of transverse mode instability (TMI). Additionally, the Stokes parameters of each individual mode are calculated by a simultaneous 4-beam mode reconstruction algorithm during post-processing and can be analyzed with unprecedented temporal resolution. We demonstrate the measurement capabilities of this polarimeter setup by characterizing TMI of a large-mode-area Yb-doped polarization maintaining (PM) fiber amplifier with 30 kHz video frame rate. Upon thorough characterization, we have found for the first time that at the onset of TMI in a PM fiber, the modal polarization states begin to oscillate on circular and elliptical trajectories at the same frequencies as the modal energy transfer occurs. The ability to measure the modal polarization states with sub-ms temporal resolution is key to developing a fundamental understanding and subsequently possible mitigation strategies of TMI in PM-fiber lasers.

Theoretical study of graded-index fiber for beam quality improvement and SRS suppression

A confined-doped graded-index fiber model was established with reference to Nufern's 42C ytterbium-doped fiber. The core NA of the fiber is ∼0.06; the doping/core/cladding diameter is 30/42/250 µm; and the gain ion doping distribution is double parabolic. Based on a forward tandem-pumped amplifier structure, the numerical simulation was carried out on the physics characters of the fiber model. The fourth-order Runge-Kutta method was used to solve the boundary value problem during the numerical simulation. The differences between the graded-index fiber (GIF) and the step-index fiber (SIF) were studied theoretically, and the results illuminated that the beam quality of the GIF was better than the SIF. The stimulated Raman scattering (SRS) power in the GIF was lower than that in the SIF. These results show that the GIF has great potential for increasing the laser output power while maintaining good beam quality and can provide theoretical guidance and reference to experimental research of the high-power fiber laser.

Mitigation of transverse mode instability by heat-load modulation

We present the first experimental realization of a new mitigation strategy for TMI based on controlling the phase shift between the modal intensity pattern and the thermally induced refractive index grating. If specific modulation parameters are applied while pulsing the seed and/or pump radiation, the direction of energy transfer is forced from the higher-order modes into the fundamental mode. In this way, the fiber amplifier can operate at an average output power significantly higher than the TMI threshold with a diffraction-limited beam profile. A stable beam profile is observed at an average output power that is 83% higher than the TMI threshold of the free-running system, with an intra-burst average power that is 4.15 times higher than the TMI threshold.

Bend-resistant stress-type segmented cladding large-mode-area single-mode fibers

We propose a novel bend-resistant stress-type large-mode-area fiber with segmented cladding, to the best of our knowledge, in which a high refractive index stress rod is introduced at the core, to improve the loss ratio between the least high-order mode (HOM) and fundamental mode loss, and to reduce the fundamental mode loss effectively. The mode loss and effective mode field area with or without heat load, and mode field evolution between the straight and bending transition are investigated, by utilizing the finite element method and the coupled-mode theory. The results show that the effective mode field area and the loss of the fundamental mode can reach up to 1050.1 µm² and 0.0055d B⋅m ^-1, respectively, and the loss ratio between the least loss HOM and fundamental mode loss is greater than 210. The coupling efficient of the fundamental mode in the straight-bending transition reaches 0.85 at a wavelength of 1.064 µm and a bending radius of 24 cm. In addition, the fiber is insensitive to the bending direction and has excellent single-mode performance in any bending direction; the fiber maintains single-mode operation under heat load from 0 to 8 W/m. This fiber has potential application in compact fiber lasers and amplifiers.

Characterization of transverse mode instability with a 4-quadrant photodiode

Transverse mode instability (TMI) represents the main limitation for the power scaling of fiber laser systems with a diffraction-limited beam quality. In this context, it has become increasingly important to find a cheap and reliable way to monitor and characterize TMI and distinguish this effect from other dynamic perturbations. In this work, with the help of a position-sensitive detector, a novel method is developed to characterize the TMI dynamics even in the presence of power fluctuations. The position information of the fluctuating beam is recorded in the X- and Y-axis of the detector, which are used to track the temporal evolution of the center of gravity of the beam. The trajectories described by the beam within a specific time window contain rich information about TMI, which can be used to gain further insight into this phenomenon.

Seeing the strong suppression of higher order modes in single trench fiber using the S2 technique

The single trench fiber (STF) is a promising fiber design for mode area scaling and higher order mode (HOM) suppression. In this Letter, we experimentally demonstrate the strong HOM-suppression in a homemade STF using the spatially and spectrally resolved imaging (S²) technique. This STF has a 20-µm core and its performance is compared to a conventional step-index fiber with almost the same parameter. Results show that the bending loss of the HOM in STF is 8-times larger than conventional fiber at a bend radius of 7 cm. In addition, when severe coupling mismatch is introduced at the input end of the fiber, the STF can keep the fundamental-mode output while the conventional fiber cannot. To the best of our knowledge, this is the first time to experimentally analyze the HOM content in an STF and compare its performance with that of a conventional fiber. Our results indicate the great potential of the STF for filtering the HOM in fiber laser applications.

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

Threshold of transverse mode instability considering four-wave mixing

In this work, the influence of four-wave mixing (FWM) effects on the transverse mode instability (TMI) is incorporated into the TMI model based on stimulated thermal Rayleigh scattering. The model is capable of analyzing the gain characteristics of different high-power fiber amplifiers, based on which the physical mechanism and functioning boundary of FWM are theoretically investigated. Consequently, a new TMI threshold formula is defined to resolve the inconsistencies in the previous TMI models. It is revealed that it is extremely necessary to consider the influence of FWM on TMI in ultra-large mode field laser systems.

Low-numerical aperture confined-doped long-tapered Yb-doped silica fiber for a single-mode high-power fiber amplifier

A low-numerical aperture (NA) confined-doped long-tapered (LCT) Yb-doped fiber is proposed and fabricated by modified chemical vapor deposition combined with solution doping technique. The LCT fiber owns the core NA of ∼0.05 and the gain dopant doping diameter ratio of ∼77%, with a core/cladding diameter of 25/400 µm at both ends and 37.5/600 µm in the middle. The laser performance is demonstrated by a bidirectional pumping all-fiber amplifier, of which a 4.18-kW single-mode (M² factor ∼1.3) laser output is achieved with a slope efficiency of ∼82.8%. Compared with the conventional fiber, the co-pumped and counter-pumped transverse mode instability thresholds and beam quality of the LCT fiber are remarkably enhanced. Throughout the continuous operation, the LCT fiber amplifier presents high power stability with fluctuation of < 1%. These results indicate that LCT fiber has great potential in power scaling remaining excellent beam quality.

Spatial tomography of light resolved in time, spectrum, and polarisation

Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques apply in limited contexts. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.

The work harnesses principles of spatial state tomography to fully characterise an optical beam in space, time, spectrum, and polarisation. Analysis of the output of a vertical-cavity surface-emitting laser illustrates the technique’s capabilities.

M2 factor estimation in few-mode fibers based on a shallow neural network

A high-accuracy, high-speed, and low-cost M² factor estimation method for few-mode fibers based on a shallow neural network is presented in this work. Benefiting from the dimensionality reduction technique, which transforms the two-dimension near-field image into a one-dimension vector, a neural network with only two hidden layers can estimate the M² factor directly. In the simulation, the mean estimation error is smaller than 3% even when the mode number increases to 10. The estimation time of 10000 simulation test samples is around 0.16s, which indicates a high potential for real-time applications. The experiment results of 50 samples from the 3-mode fiber have a mean estimation error of 0.86%. The strategies involved in this method can be easily extended to other applications related to laser characterization.

Modal decomposition of an incoherent combined laser beam based on the combination of residual networks and a stochastic parallel gradient descent algorithm

With the increase of the superimposed eigenmodes number, the traditional numerical modal decomposition (MD) technique will inevitably suffer from ambiguity and local minima problems and thus is typically unsuitable for conducting modal decomposition of an incoherent combined laser beam. In this paper, we propose a novel, to the best of our knowledge, MD algorithm, named ResNet-SPGD, which combines the advantages of residual networks (ResNet) and stochastic parallel gradient descent (SPGD) algorithm. Via setting the modal mode coefficients obtained from the CNN model as the initial value of the SPGD algorithm, such algorithm shows an attractive solution to mitigate the problem of modal ambiguity. The proposed algorithm is preliminarily applied to the modal decomposition of an incoherent combined laser beam, and the feasibility is demonstrated via numerical simulations. Complete MD is performed with high accuracy, and the only cost is the sacrifice of some real-time capacity.

Control and stabilization of the modal content of fiber amplifiers using traveling waves

In this work we present a novel way to manipulate the effect of transverse mode instability by inducing traveling waves in a high-power fiber system. What sets this technique apart is the fact that it allows controlling the direction of the modal energy flow, for the first time to the best of our knowledge. Thus, using the method proposed in this work it will be possible to transfer energy from the higher-order mode into the fundamental mode of the fiber, which mitigates the effect of transverse mode instability, but also to transfer energy from the fundamental mode into the higher-order mode. Our simulations indicate that this approach will work both below and above the threshold of transverse mode instability. In fact, our model reveals that it can be used to force a nearly pure fundamental mode output in the fiber laser system almost independently of the input coupling conditions. In this context, this technique represents the first attempt to exploit the physics behind the effect of transverse mode instability to increase the performance of fiber laser systems.

Experimental analysis of Raman-induced transverse mode instability in a core-pumped Raman fiber amplifier

The effect of transverse mode instability is a limitation for the power scaling of fiber laser systems, that can originate due to heat caused by stimulated Raman scattering. In this contribution, we experimentally investigate the threshold of transverse mode instability caused by stimulated Raman scattering in a passive fiber. Both, the Stokes seed power and the fiber length of a core-pumped Raman fiber amplifier are varied to systematically study this effect. Mode resolved measurements reveal that the threshold occurs at approximately the same Stokes output power for all tested configurations, independent of the total Raman conversion efficiency. These results increase the understanding of this type of mode instability and show which parameters are important for a further power scaling of high-power Raman fiber amplifiers.

Transverse mode instability and thermal effects in thulium-doped fiber amplifiers under high thermal loads

We experimentally analyze the average-power-scaling capabilities of ultrafast, thulium-doped fiber amplifiers. It has been theoretically predicted that thulium-doped fiber laser systems, with an emission wavelength around 2 µm, should be able to withstand much higher heat-loads than their Yb-doped counterparts before the onset of transverse mode instability (TMI) is observed. In this work we experimentally verify this theoretical prediction by operating thulium doped fibers at very high heat-load. In separate experiments we analyze the performance of two different large-core, thulium-doped fiber amplifiers. The first experiment aims at operating a short, very-large core, thulium-doped fiber amplifier at extreme heat-load levels of more than 300 W/m. Even at this extreme heat-load level, the onset of TMI is not observed. The second experiment maximizes the extractable average-output power from a large-core, thulium-doped, fiber amplifier. We have achieved a pump-limited average output power of 1.15 kW without the onset of TMI. However, during a longer period of operation at this power level the amplifier performance steadily degraded and TMI could be observed for average powers in excess of 847 W thereafter. This is the first time, to the best of our knowledge, that TMI has been reported in a thulium-doped fiber amplifier.

Modal analysis of structured light with spatial light modulators: a practical tutorial

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections-a modal analysis of light-for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Experimental investigations of seeding mechanisms of TMI in rod fiber amplifier using spatially and temporally resolved imaging

In this work we investigate transverse mode instability (TMI) in the presence of pump intensity noise and a controlled perturbation of the input coupling for a rod-type fiber amplifier using spatially and temporally resolved imaging (ST). We show that inherent pump intensity noise from the power supply can define significant peaks in the resulting TMI spectrum. ST measurements show that the TMI in the transition region consists of different orientations of LP₁₁. This finding indicates that the simple picture of TMI being seeded by the combination of a static initial fraction of LP₁₁ and pump or signal intensity noise is not valid for our measurements. Furthermore we present seeding of TMI by perturbing the input coupling dynamically. ST measurements of the resulting TMI as a function of perturbation frequency provides quantitative information regarding the frequency response of the non-linear coupling coefficient. Finally, ST measurements of the resulting TMI as a function of signal power shows that the TMI experiences an exponential gain long before visible beam fluctuations appear.

Transverse mode instability in a passive fiber induced by stimulated Raman scattering

Transverse mode instabilities are a major limitation for power scaling of fiber lasers but have so far only been observed in laser-active fibers. In this contribution we present experimental observations of transverse mode instabilities in a passive fiber. In this fiber, stimulated Raman scattering acted as heat source. To demonstrate the effect, a kW-level ytterbium-doped fiber laser was used as pump for a Raman amplifier. Transverse mode instabilities were only observed in the case with high Raman amplification. Frequency resolved stability measurements at various fiber positions as well as spectral and mode resolved measurements pin their origin to the passive fiber. This observation might help to gain further understanding of transverse mode instabilities and shows limitations of high-power Raman amplifiers.

Instability transverse mode phase transition of fiber oscillator for extreme power lasers

High-power fiber lasers have been widely explored in engineering and science, and improving the beam quality restricted by transverse mode instability (TMI) is waiting to be solved for extra high-power applications. Here, we theoretically propose a phase transition model for understanding TMI in a fiber oscillator. A general dynamics model describing TMI is established by modifying the heat equation, and then a special dynamics model of a two-mode fiber (TMF) oscillator is obtained by applying this general dynamics model to TMF oscillator case. Theoretical analysis shows that there is a reversible phase transition point in this TMF oscillator model, which can well explain the sudden and reversible change of TMI. Based on linear stability analysis near the phase transition point, an analytical threshold formula of TMI is given to calculate the TMI threshold in the TMF oscillator. The calculated results are consistent with the reported experimental results. Furthermore, the relationship between the TMI threshold and several parameters was also discussed in detail such as laser wavelength, pump wavelength, core radius, cladding radius, etc. This theoretical model will be useful to understand and suppress the TMI in fiber oscillators.

Experimental study of the influence of mode excitation on mode instability in high power fiber amplifier

Mode instability with different mode excitation has been investigated by off-splicing the fusion point in a 4 kW-level monolithic fiber laser system, which reveals that the fiber systems exciting more high order mode content exhibits lower beam quality but higher mode instability threshold. The static-to-dynamic mode degradation and dynamic-only mode degradation have also been observed in the same high power fiber amplifier by varying the mode excitation, which implicates that the mode excitation plays an important role in mode characteristics in high power fiber lasers. By employing a seed with near fundamental mode beam quality, only dynamic mode degradation-mode instability sets in with negligible static beam quality degradation. Then the fusion point in the seed laser is offset spliced to excite high order mode. As the output power of the main amplifier scales, the beam quality degrades with the beam profile being static, and then the dynamic mode instability sets in, the power threshold of which is higher than that with good beam quality seed. We consider that the static mode degradation is caused by the presence of incoherent supposition of fundamental and high order mode, which leads to that the measured dynamic mode instability threshold is higher.

Adaptive phase correction of dynamic multimode beam based on modal decomposition

We propose and demonstrate a method for the adaptive phase correction of dynamic multimode fiber beams. The phase of incident beam is reconstructed in real-time based on the complete modal information, which obtained by using the modal decomposition of correlation filter method. For the proof of principle, both of the modal decomposition and the phase correction are implemented using the same computer-generated hologram, which was encoded into a phase-only spatial light modulator. We demonstrate the phase correction of dynamic multimode beam at a rate of 5 Hz and achieve a 1.73-fold improvement on the average power-in-the-bucket. The experimental results indicate the feasibility of the real-time phase correction for the large mode area fiber laser by adaptive optics.

Learning to decompose the modes in few-mode fibers with deep convolutional neural network

We introduce a deep-learning technique to perform complete mode decomposition for few-mode optical fibers for the first time. Our goal is to learn a fast and accurate mapping from near-field beam patterns to the complete mode coefficients, including both modal amplitudes and phases. We train the convolutional neural network with simulated beam patterns and evaluate the network on both the simulated beam data and the real beam data. In simulated beam data testing, the correlation between the reconstructed and the ideal beam patterns can achieve 0.9993 and 0.995 for 3-mode case and 5-mode case, respectively. While in the real 3-mode beam data testing, the average correlation is 0.9912 and the mode decomposition can be potentially performed at 33 Hz frequency on a graphic processing unit, indicating real-time processing ability. The quantitative evaluations demonstrate the superiority of our deep learning-based approach.

Study on thermal-lens induced mode coupling in step-index large mode area fiber lasers

In this paper, the thermal-lens induced mode coupling in step-index large mode area fiber laser is systematically investigated. The pertinent mode coupling coefficient is studied firstly, to the best of our knowledge. It is demonstrated that the mode coupling can be induced by the thermal-lens induced waveguide changing along the active fiber. It is found that the mode coupling can be enhanced mainly by the thermally-induced mode distortion and refractive index variation, both of which will become severe with the large thermal load. The impacts of fiber configuration parameters on the mode coupling are discussed. It is found that in the straight fiber, the mode coupling in a larger-core fiber can be weakened when the thermal load is low, but it will become stronger when thermal-lens effect is severe enough. However, in the bent fiber, enlarging core size, reducing core numerical aperture (NA), or decreasing bend radius will all aggravate the mode coupling. Especially when NA is excessively reduced, the mode coupling will be dramatically raised even with a small thermal load. The pertinent study is significant for understanding the mode coupling phenomenon in high-power fiber lasers.

Dynamic characteristics of stimulated Raman scattering in high power fiber amplifiers in the presence of mode instabilities

Impact of mode instability on dynamic characteristics of stimulated Raman scattering in high power fiber amplifiers has been studied for the first time, which reveals another characterization of mode instability from the aspect of optical spectrum. It shows that, after the onset of mode instability, the measured light spectrums, especially the Raman light spectrums, are different from those without mode instability, which become burr-like. As mode instability evolves into different stages, the intensity of stimulated Raman scattering effects as laser power increasing also behaves differently. During the transition region, the stimulated Raman scattering effect becomes stronger as the lasing power increases until the mode instability evolves into chaotic regions, where the stimulated Raman scattering effect weakens. The effect of stimulated Raman scattering on mode instability has also been studied. Due to that the stimulated Raman scattering effect is weak and that the fraction of Raman light is only a few percent, the stimulated-Raman-scattering-induced mode instability has not been observed in the experiment, and the observed mode instability is induced by ytterbium ion gain of signal laser. It also revealed that the stimulated Raman scattering has negligible influence on the mode instability induced by ytterbium ion gain.

Modal energy transfer by thermally induced refractive index gratings in Yb-doped fibers

Thermally induced refractive index gratings in Yb-doped fibers lead to transverse mode instability (TMI) above an average power threshold, which represents a severe problem for many applications. To obtain a deeper understanding of TMI, the evolution of the strength of the thermally induced refractive index grating with the average output power in a fiber amplifier is experimentally investigated for the first time. This investigation is performed by introducing a phase shift between the refractive index grating and modal interference pattern, which is obtained by applying a pump power variation to the fiber amplifier. It is demonstrated that the refractive index grating is sufficiently strong to enable modal energy coupling at powers that are significantly below the TMI threshold if the induced phase shift is sufficiently large. The experiments indicate that at higher powers, the refractive index grating becomes more sensitive to such phase shifts, which will ultimately trigger TMI. Furthermore, the experimental results demonstrate beam cleaning above the TMI threshold via the introduction of a positive phase shift. This finding paves the way for the development of a new class of mitigation strategies for TMI that are based on controlling the phase shift between the thermally induced refractive index grating and modal interference pattern.

Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold

A new way of stabilizing the output beam of a fiber laser system operating above the mode instability threshold is described and the first proof-of-principle experimental results are presented. This technique, which relies on a modulation of the pump power, works by washing the thermally-induced refractive index grating out, which weakens the coupling efficiency between transverse modes. One of the main advantages of this simple, yet powerful, approach is that it can be easily incorporated in already existing fiber laser systems since it does not require any additional optical elements. Using this beam stabilization strategy, a significant pointing stability and beam quality improvement has been demonstrated up to an average power of ~600W, which is a factor of 2 above the mode instability threshold.

Multimode fiber modal decomposition based on hybrid genetic global optimization algorithm

Numerical modal decomposition (MD) is an effective approach to reveal modal characteristics in high power fiber lasers. The main challenge is to find a suitable multi-dimensional optimization algorithm to reveal exact superposition of eigenmodes, especially for multimode fiber. A novel hybrid genetic global optimization algorithm, named GA-SPGD, which combines the advantages of genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm, is firstly proposed to reduce local minima possibilities caused by sensitivity to initial values. Firstly, GA is applied to search the rough global optimization position based on near- and far-field intensity distribution with high accuracy. Upon those initial values, SPGD algorithm is afterwards used to find the exact optimization values based on near-field intensity distribution with fast convergence speed. Numerical simulations validate the feasibility and reliability.

Fast modal decomposition for optical fibers using digital holography

Eigenmode decomposition of the light field at the output end of optical fibers can provide fundamental insights into the nature of electromagnetic-wave propagation through the fibers. Here we present a fast and complete modal decomposition technique for step-index optical fibers. The proposed technique employs digital holography to measure the light field at the output end of the multimode optical fiber, and utilizes the modal orthonormal property of the basis modes to calculate the modal coefficients of each mode. Optical experiments were carried out to demonstrate the proposed decomposition technique, showing that this approach is fast, accurate and cost-effective.

Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier

The study on mode instability (MI) in the large-mode-area fiber is generating great interest regarding the high-power applications of fiber lasers. To the best of our knowledge, we have investigated for the first time the dynamics of the output beam from a kilowatt-level all-fiber amplifier based on the low-numerical-aperture (<0.04) step-index (SI) fiber before and after the onset of the MI, including the temporal dynamics and mode evolution. The temporal power fluctuations indicate three evolution stages apart from the onset threshold of the MI, defined as stable, transition, and chaotic regions. In addition, the mode decomposition technique is utilized to accurately observe and investigate the mode evolution and relevant modal content corresponding to the transition and chaotic regions in the SI fiber laser for the first time. According to the mode decomposition results, the reduction of the extracted power can be explained by the high bending loss of the high-order mode excited in the MI process. Finally, the difference of MI dynamics between the fiber lasers based on the SI fiber and rod-type photonic crystal fiber is discussed.

Measuring spatiotemporal ultrafast field structures of pulses from multimode optical fibers

Ultrashort pulses emerging from multimode optical fibers are spatiotemporally complex, because inside these fibers the modes have different spatial intensity patterns and experience different propagation velocities and dispersions. To determine the spatiotemporal field from multimode fibers, we applied a technique for the complete measurement of the output pulses called a spatially and temporally resolved intensity and phase evaluation device: full information from a single hologram. It yields the complete electric field over space and time from multiple digital holograms, simultaneously recorded at different frequencies on a single camera frame. Using femtosecond pulses from a Ti:sapphire laser, we measured the first few linearly polarized modes (LP₀₁, LP₁₁, LP₀₂, and LP₂₁) inside several few-mode fibers. We also generate movies displaying the measured spatial, temporal, and spectral field features.

Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities

The average output power of Yb-doped fiber amplifier systems is currently limited by the onset of transverse mode instabilities. Besides, it has been recently shown that the transverse mode instability threshold can be significantly reduced by the presence of photodarkening in the fiber. Therefore, reducing the photodarkening level of the core material composition is the most straightforward way to increase the output average power of fiber amplifier systems but, unfortunately, this is not always easy or possible. In this paper we present guidelines to optimize the output average power of fiber amplifiers affected by transverse mode instabilities and photodarkening. The guidelines derived from the simulations do not involve changes in the composition of the active material (except for its doping concentration), but can still lead to a significant increase of the transverse mode instability threshold. The dependence of this parameter on the active ion concentration and the core conformation, among others, will be studied and discussed.

Adaptive mode control of a few-mode fiber by real-time mode decomposition

A novel approach to adaptively control the beam profile in a few-mode fiber is experimentally demonstrated. We stress the fiber through an electric-controlled polarization controller, whose driven voltage depends on the current and target modal content difference obtained with the real-time mode decomposition. We have achieved selective excitations of LP01 and LP11 modes, as well as significant improvement of the beam quality factor, which may play crucial roles for high-power fiber lasers, fiber based telecommunication systems and other fundamental researches and applications.

Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening

In this paper we present a simple model to predict the behavior of the transversal mode instability threshold when different parameters of a fiber amplifier system are changed. The simulation model includes an estimation of the photodarkening losses which shows the strong influence that this effect has on the mode instability threshold and on its behavior. Comparison of the simulation results with experimental measurements reveal that the mode instability threshold in a fiber amplifier system is reached for a constant average heat load value in good approximation. Based on this model, the expected behavior of the mode instability threshold when changing the seed wavelength, the seed power and/or the fiber length will be presented and discussed. Additionally, guidelines for increasing the average power of fiber amplifier systems will be provided.

Phenomenological model of stochastic, spatiotemporal, intensity dynamics of stimulated Brillouin scattering in a two-mode optical fiber

We present a simple numerical model that is used in conjunction with a systematic algorithm for parameter optimization to understand the three-dimensional stochastic intensity dynamics of stimulated Brillouin scattering in a two-mode optical fiber. The primary factors driving the complex dynamics appear to be thermal density fluctuations, transverse pump fluctuations, and asymmetric transverse mode fractions over the beam cross-section.

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.

Real-time mode decomposition for few-mode fiber based on numerical method

Today a specific attention has been paid to look into the modal characteristics of the high-power laser beam. And the instantaneous monitoring and analyzing on modal content via the mode decomposition technique will provide a novel route. We implement the first-ever experimental investigation on the real-time mode decomposition technique for few-mode laser beam based on stochastic parallel gradient descent algorithm. It will reduce the cost and the complexity of the mode decomposition system. We have succeeded to decompose the mode spectra as well as calculating the beam quality factor at about 9 Hz monitoring rate, while the high agreement between the measured and reconstructed intensity profiles in each frame indicating the high accuracy and stability during the process. By employing a fiber-squeezing-based polarization controller, the modal content under test can be time-varying automatically.

Low-threshold mode instability in Yb3+-doped few-mode fiber amplifiers

Spatio-temporal instability of the fundamental mode in Yb(3+)-doped few-mode PM fiber amplifiers with a core diameter of 8.5 μm was registered at 2-30 Watts pump power. Both experimental and theoretical analysis revealed the nonlinear power transformation of the LP(01) fundamental mode into high-order modes. Numerical simulation revealed self-consistent growth of the higher-order mode and traveling electronic index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb(3+) ions). Experimental results and numerical calculations showed the increase of the instability threshold along with an increase of the signal frequency bandwidth.

2 kW average power from a pulsed Yb-doped rod-type fiber amplifier

This Letter reports on a fiber-laser system that, employing a 1 m long rod-type photonic-crystal fiber as its main-amplifier, emits a record average output power of 2 kW, by amplifying stretched ps-pulses. A further increase of the output power was only limited by the available laser-diode pump power. The energy of the pulses is 100 μJ, corresponding to MW-level peak powers extracted directly from the fiber of the main amplifier. The corresponding M2 at the maximum output power is <3, due to the onset of mode instabilities. The Letter covers the influence of this effect on the evolution of the beam quality with the output power. The numerical results show that the M2 value settles at around 3, even if the output average power is further increased.

High-power beam transport through a hollow-core photonic bandgap fiber

We investigate the use of a seven-cell hollow-core photonic bandgap fiber for transport of CW laser radiation from a single-mode, narrow-linewidth, high-power fiber laser amplifier. Over 90% of the amplifier output was coupled successfully and transmitted through the fiber in a near-Gaussian mode, with negligible backreflection into the source. 100 W of power was successfully transmitted continuously without damage and 160 W of power was transmitted briefly before the onset of thermal lensing in the coupling optics.

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.

Rapid complex mode decomposition of vector beams by common path interferometry

We have used common path interferometry for rapid determination of the electric field and complex modal content of vector beams, which have spatially-varying polarization. We combine a reference beam with a signal beam prior to a polarization beam splitter for stable interferograms that preserve intermodal phase shifts even in noisy environments. Interferometric decomposition into optical modes (IDIOM) provides a direct, sensitive measure of the complete electric field, enabling rapid modal decomposition and is ideally suited to single-frequency laser sources. We apply the technique to beams exiting optical fibers that support up to 10 modes. We also use the technique to characterize the fibers by determining a scattering matrix that transforms an input superposition of modes into an output superposition. Furthermore, because interferograms are linear in the field, this technique is very sensitive and can accurately reconstruct beams with signal-to-noise << 1.

Comparative analysis of numerical methods for the mode analysis of laser beams

We present a comparative study of four numerical methods to detect the mode content of a laser beam from, at most, two intensity images. The techniques are compared regarding temporal effort, stability, and accuracy, using the example of three multimode optical fibers that differ in the number of supported modes.

Frequency resolved transverse mode instability in rod fiber amplifiers

Frequency dynamics of transverse mode instabilities (TMIs) are investigated by testing three 285/100 rod fibers in a single-pass amplifier setup reaching up to ~200W of extracted output power without beam instabilities. The pump power is increased well above the TMI threshold to uncover output dynamics, and allowing a simple method for determining TMI threshold based on standard deviation. The TMI frequency component is seen to appear on top of system noise that may trigger the onset. A decay of TMI threshold with test number is identified, but the threshold is fully recovered between testing to the level of the pristine fiber by thermal annealing the fiber output end to 300°C for 2 h.

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.

Estimating modal instability threshold for photonic crystal rod fiber amplifiers

We present a semi-analytic numerical model to estimate the transverse modal instability (TMI) threshold for photonic crystal rod amplifiers. The model includes thermally induced waveguide perturbations in the fiber cross section modeled with finite element simulations, and the relative intensity noise (RIN) of the seed laser, which seeds mode coupling between the fundamental and higher order mode. The TMI threshold is predicted to ~370 W - 440 W depending on RIN for the distributed modal filtering rod fiber.

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.

Modal characterization of fiber-to-fiber coupling processes

We present a detailed experimental investigation of a fiber-to-fiber coupling process by characterizing the mode content at the output of the system. In our experiment a single-mode fiber is transversally scanned with respect to a multimode fiber, revealing position-dependent higher-order mode excitation. The outlined measurement system can be used for automated optimization of fundamental mode content and beam quality. Additionally, our approach characterizes the modal transmission properties of the multimode waveguide in its present state and is hence of high relevance for the conception of transport fibers and fiber laser systems.