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

General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser

The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.

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.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

All-fiber orthogonal-polarized white-noise-modulated laser for short-coherence dynamic interferometry

An all-fiber orthogonal-polarized white-noise-modulated laser (AOWL) for short-coherence dynamic interferometry is proposed. Short-coherence laser is achieved by current modulating of a laser diode with the band-limited white noise. A pair of orthogonal-polarized lights with adjustable delay for short-coherence dynamic interferometry are output by the all-fiber structure. In the non-common-path interferometry, the AOWL can significantly suppress the interference signal clutter with 73% side lobe suppression ratio, that improves the positioning accuracy of zero optical path difference. The wavefront aberrations of a parallel plate are measured with the AOWL in the common-path dynamic interferometers, avoiding the fringe crosstalk.

Analysis of an image noise sensitivity mechanism for matrix-operation-mode-decomposition and a strong anti-noise method

Mode decomposition (MD) based on the matrix operation (MDMO) is one of the fastest mode decomposition methods in fiber laser which has great potential for optical communications, nonlinear optics and spatial characterization applications. However, we found that the image noise sensitivity is the main limit to the accuracy of the original MDMO method, but improving the decomposition accuracy by using conventional image filtering methods is almost ineffective. By using the norm theory of matrices, the analysis result shows that both the image noise and the coefficient matrix condition number determine the total upper-bound error of the original MDMO method. Besides, the greater the condition number, the more sensitive of MDMO method is to noise. In addition, it is found that the local error of each mode information solution in the original MDMO method is different, which depends on the L2-norm of each row vector of the inverse coefficient matrix. Moreover, a more noise-insensitive MD method is achieved by screening out the information corresponding to large L2-norm. In particular, selecting the higher accuracy among the original MDMO method and such noise-insensitive method as the result in a single MD process, a strong anti-noise MD method was proposed in this paper, which displays high MD accuracy in strong noise for both near-filed and far-filed MD cases.

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.

Complete modal decomposition of a few-mode fiber based on ptychography technology

An exact modal decomposition method plays an important role in revealing the modal characteristics of a few-mode fiber, and it is widely used in various applications ranging from imaging to telecommunications. Here, ptychography technology is successfully used to achieve modal decomposition of a few-mode fiber. In our method, the complex amplitude information of the test fiber can be recovered by ptychography, and then the amplitude weight of each eigenmode and the relative phase between different eigenmodes can be easily calculated by modal orthogonal projection operations. In addition, we also propose a simple and effective method to realize coordinate alignment. Numerical simulations and optical experiments validate the reliability and feasibility of the approach.

High-performance mode decomposition using physics- and data-driven deep learning

A novel physics- and data-driven deep-learning (PDDL) method is proposed to execute complete mode decomposition (MD) for few-mode fibers (FMFs). The PDDL scheme underlies using the embedded beam propagation model of FMF to guide the neural network (NN) to learn the essential physical features and eliminate unexpected features that conflict with the physical laws. It can greatly enhance the NN's robustness, adaptability, and generalization ability in MD. In the case of obtaining the real modal weights (ρ2) and relative phases (θ), the PDDL method is investigated both in theory and experiment. Numerical results show that the PDDL scheme eliminates the generalization defect of traditional DL-based MD and the error fluctuation is alleviated. Compared with the DL-based MD, in the 8-mode case, the errors of ρ2 and θ can be reduced by 12 times and 100 times for beam patterns that differ greatly from the training dataset. Moreover, the PDDL maintains high accuracy even in the 8-mode MD case with a practical maximum noise factor of 0.12. In terms of adaptation, with a large variation of the core radius and NA of the FMF, the error keeps lower than 0.43% and 2.08% for ρ2 and θ, respectively without regenerating new dataset and retraining NN. The experimental configuration is set up and verifies the accuracy of the PDDL-based MD. Results show that the correlation factor of the real and reconstructed beam patterns is higher than 98%. The proposed MD-scheme shows much potential in the application of practical modal coupling characterization and laser beam quality analysis.

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.

2D least-squares mode decomposition for mode division multiplexing

We investigate a fast and accurate technique for mode decomposition in multimode optical fibers. Initial decomposition task of near-field beam patterns is reformulated in terms of a system of linear equations, requires neither machine learning nor iterative routines. We apply the method to step and graded-index fibers and compare the decomposition performance. We determine corresponding application boundaries, propose an efficient algorithm for phase retrieval and carry out a specific preselective procedure that increases the number of decomposable modes and makes it possible to handle up to fifteen modes in presence of realistic noise levels.

Benchmarking analysis of computer generated holograms for complex wavefront shaping using pixelated phase modulators

Wavefront shaping with spatial light modulators (SLMs) enables aberration correction, especially for light control through complex media, like biological tissues and multimode fibres. High-fidelity light field shaping is associated with the calculation of computer generated holograms (CGHs), of which there are a variety of algorithms. The achievable performance of CGH algorithms depends on various parameters. In this paper, four different algorithms for CGHs are presented and compared for complex light field generation. Two iterative, double constraint Gerchberg-Saxton and direct search, and the two analytical, superpixel and phase encoding, algorithms are investigated. For each algorithm, a parameter study is performed varying the modulator's pixel number and phase resolution. The analysis refers to mode field generation in multimode fibre endoscopes and communication. This enables generality by generating specific mode combinations according to certain spatial frequency power spectra. Thus, the algorithms are compared varying spatial frequencies applied to different implementation scenarios. Our results demonstrate that the choice of algorithms has a significant impact on the achievable performance. This comprehensive study provides the required guide for CGH algorithm selection, improving holographic systems towards multimode fibre endoscopy and communications.

Intensity-only-measurement mode decomposition in few-mode fibers

Recovery of optical phases using direct intensity detection methods is an ill-posed problem and some prior information is required to regularize it. In the case of multi-mode fibers, the known structure of eigenmodes is used to recover optical field and find mode decomposition by measuring intensity distribution. Here we demonstrate numerically and experimentally a mode decomposition technique that outperforms the fastest previously published method in terms of the number of modes while showing the same decomposition speed. This technique improves signal-to-noise ratio by 10 dB for a 3-mode fiber and by 7.5 dB for a 5-mode fiber.

Sub-sampled modal decomposition in few-mode fibers

Retrieving modal contents from a multimode beam profile can provide the most detailed information of a beam. Numerical modal decomposition is a method of retrieving modal contents, and it has gained significant attention owing to its simplicity. It only requires a measured beam profile and an algorithm. Therefore, a complicated setup is not necessary. In this study, we conceived that the modal decomposition can be notably improved by data-efficiently sub-sampling the beam image instead of using full pixels of a beam profiler. By investigating the window size, the number of pixels, and algorithm for sub-sampling, the calculation time for the algorithm was faster by approximately 100 times than the case of full pixel modal decomposition. Experiments with 3-mode and 6-mode beams, which originally span 201×201 and 251×251 pixels, respectively, confirmed the remarkable improvement of calculation speed while maintaining the error function at a level of ∼10^-3. This first demonstration of sub-sampling for modal decomposition is based on the modified stochastic parallel gradient descent algorithm. However, it can be applied to other numerical or artificial intelligence algorithms and can enhance real-time analysis or active control of beam characteristics.

CNN-based few-mode fiber modal decomposition method using digital holography

Modal decomposition (MD) has become an indispensable analysis approach for revealing the modal characteristics of optical fibers. A new MD approach based on the convolutional neural network (CNN) is presented to retrieve the exact superposition of eigenmodes of few-mode fibers. Using the near-field beam intensity and phase patterns obtained from digital holography, not only the amplitude of each eigenmode but also the exact phase difference between the higher-order modes and the fundamental mode can be predicted. Numerical simulations validate the reliability and feasibility of the approach. When ten modes in the few-mode fiber are considered, the similarities of the intensity and phase pattern between the reconstructed fields and the given fields can achieve to 97.0% and 85.6%, respectively.

Modal decomposition of fiber modes based on direct far-field measurements at two different distances with a multi-variable optimization algorithm

We present a novel method for modal decomposition of a composite beam guided by a large-mode-area fiber by means of direct far-field pattern measurements with a multi-variable optimization algorithm. For reconstructing far-field patterns, we use finite-number bases of Hermite Gaussian modes that can be converted from all the guided modes in the given fiber and exploit a stochastic parallel gradient descent (SPGD)-based multi-variable optimization algorithm equipped with the D4σ technique in order for completing the modal decomposition with compensating the centroid mismatch between the measured and reconstructed beams. We measure the beam intensity profiles at two different distances, which justifies the uniqueness of the solution obtained by the SPGD algorithm. We verify the feasibility and effectiveness of the proposed method both numerically and experimentally. We have found that the fractional error tolerance in terms of the beam intensity overlap could be maintained below 1 × 10^-7 and 3.5 × 10^-3 in the numerical and experimental demonstrations, respectively. As the modal decomposition is made uniquely and reliably, such a level of the error tolerance could be maintained even for a beam intensity profile measured at a farther distance.

Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer

Recently, the growing interest in few-mode fibers in telecommunications and high-power lasers has stimulated the demand for fiber mode decomposition (MD). Here we present a fast fiber MD method with a lensless fiber-point-diffraction interferometer. The complex amplitude at the fiber end is achieved by the polarization phase-shifting technique and the lensless imaging technique. Then, the eigenmode coefficients are determined by the mode orthogonal operations of the complex amplitude. In the experiment, the SMF-28e fiber containing 10 linear polarized modes at the wavelength of 632.8 nm is studied for MD. The decomposition of the 50 * 50 pixels interferograms takes only 0.0168 s. The similarity of the intensity patterns of the testing light is larger than 97% before and after the MD. This new, to the best of our knowledge, method can achieve fast and accurate 10-mode MD without using any imaging systems.

Fast mode decomposition in few-mode fibers

Retrieval of the optical phase information from measurement of intensity is of a high interest because this would facilitate simple and cost-efficient techniques and devices. In scientific and industrial applications that exploit multi-mode fibers, a prior knowledge of spatial mode structure of the fiber, in principle, makes it possible to recover phases using measured intensity distribution. However, current mode decomposition algorithms based on the analysis of the intensity distribution at the output of a few-mode fiber, such as optimization methods or neural networks, still have high computational costs and high latency that is a serious impediment for applications, such as telecommunications. Speed of signal processing is one of the key challenges in this approach. We present a high-performance mode decomposition algorithm with a processing time of tens of microseconds. The proposed mathematical algorithm that does not use any machine learning techniques, is several orders of magnitude faster than the state-of-the-art deep-learning-based methods. We anticipate that our results can stimulate further research on algorithms beyond popular machine learning methods and they can lead to the development of low-cost phase retrieval receivers for various applications of few-mode fibers ranging from imaging to telecommunications.

Characterizing the modes at the output of a multimode fiber is time consuming due to computational cost. Here the authors present an algorithm for few-mode-fiber mode decomposition with a fast processing time and using only intensity measurements.

Focal field analysis of highly multi-mode fiber beams based on modal decomposition

In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured intensity profiles along the laser beam caustic with consideration of intermodal degrees of coherence derived from spectral analysis. To enhance the accuracy of the model, different approaches and strategies are applied and discussed. The presented decomposition into a set of linearly polarized modes enables both the wave-optical simulation of radiation transport by highly multi-mode fibers and, additionally, the analysis of free-space propagation with arbitrarily modified complex amplitude distributions.

Fast modal analysis for Hermite-Gaussian beams via deep learning

The eigenmodes of Hermite-Gaussian (HG) beams emitting from solid-state lasers make up a complete and orthonormal basis, and they have gained increasing interest in recent years. Here, we demonstrate a deep learning-based mode decomposition (MD) scheme of HG beams for the first time, to the best of our knowledge. We utilize large amounts of simulated samples to train a convolutional neural network (CNN) and then use this trained CNN to perform MD. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error of 0.013 when six eigenmodes are involved. The scheme takes only about 23 ms to perform MD for one beam pattern, indicating promising real-time MD ability. When larger numbers of eigenmodes are involved, the method can also succeed with slightly larger prediction error. The robustness of the scheme is also investigated by adding noise to the input beam patterns, and the prediction error is smaller than 0.037 for heavily noisy patterns. This method offers a fast, economic, and robust way to acquire both the mode amplitude and phase information through a single-shot intensity image of HG beams, which will be beneficial to the beam shaping, beam quality evaluation, studies of resonator perturbations, and adaptive optics for resonators of solid-state lasers.

Deep Learning for Computational Mode Decomposition in Optical Fibers

Multimode fibers are regarded as the key technology for the steady increase in data rates in optical communication. However, light propagation in multimode fibers is complex and can lead to distortions in the transmission of information. Therefore, strategies to control the propagation of light should be developed. These strategies include the measurement of the amplitude and phase of the light field after propagation through the fiber. This is usually done with holographic approaches. In this paper, we discuss the use of a deep neural network to determine the amplitude and phase information from simple intensity-only camera images. A new type of training was developed, which is much more robust and precise than conventional training data designs. We show that the performance of the deep neural network is comparable to digital holography, but requires significantly smaller efforts. The fast characterization of multimode fibers is particularly suitable for high-performance applications like cyberphysical systems in the internet of things.

Modal decomposition for the fiber beams with arbitrary degree of coherence based on the Wigner distribution function

Modal decomposition (MD) plays an increasingly important role in characterizing fiber beams. Several promising MD techniques have been proposed in literature, all of which are based on a common hypothesis that the modal field is coherently superposed by transverse modes. However, the partially coherent conditions have to be expected in general. In order to take account of this ordinary case, a novel MD scheme employing the Wigner distribution function (WDF) is introduced, which allows the decomposition of fiber beams without any restrictions regarding their degree of coherence. The four-dimensional (4D) WDF (two spatial and two spatial frequency dimensions) of the 2D fiber beam is reconstructed using the coded aperture technique. Based on the measured WDF and orthogonal property of transverse modes, the modal coefficients as well as the mutual modal degree of coherence will be determined unambiguously. The validity and reliability of the proposed approach are illustrated with numerical examples.

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.

Modal decomposition for few mode fibers using the fractional Fourier system

Modal decomposition (MD) has become an indispensable diagnostic tool for optical fibers. A novel MD method using the fractional Fourier system is developed in this paper. Firstly, the existing phase retrieval (PR) algorithm based on the the fractional Fourier transform (FrFT) power spectra is extended to account for the effect of optical vortex. The extended capability can then be employed to reconstruct the phase of modal field to high fidelity in a non-iterative and non-interferometric manner. Combining the reconstructed phase with the measured near-field (NF) intensity, the modal field could be obtained and based upon which the complete MD (involving modal weights and phases) is performed. The validity and reliability of the method are demonstrated through several numerical examples including the noisy signals with different signal-to-noise ratio (SNR) levels.

Fast measurement of the laser beam quality factor based on phase retrieval with a liquid lens

In this paper, a new method for measuring the beam quality (M²) of lasers based on phase retrieval with a liquid lens is proposed. With intensity profiles obtained under different focal lengths in a certain position, a variable-focus iterative retrieval algorithm is established for the reconstruction of the complex amplitude. Then M² can be calculated with the angular spectrum theory. Feasibility of the proposed method is demonstrated with single- and multimode lasers through both simulations and experiments. Compared with the traditional liquid lens method, the M² of lasers can be measured faster with the proposed method.

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.

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.

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.

Evaluating the beam quality of double-cladding fiber lasers in applications

We put forward a new β_FL factor, which is used exclusively in fiber lasers and is suitable to assess beam quality and choose the LP₀₁ mode as the new suitable ideal beam. We present a new simple measurement method and verify the reasonability of the β_FL factor in experiment in a 20/400 μm fiber laser. Furthermore, we use the β_FL factor to evaluate the beam quality of a 3-kW-level fiber laser. It can be concluded that β_FL is a key factor not only for assessing the performance of the high-power fiber laser that is our main focus, but also for the simple measurement.

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.

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.