Coherent beam combination with single frequency dithering technique

Coherent beam combination of two thulium-doped fiber laser beams with the multi-ditheringtechnique

A novel coherent beam combination system based on double piezoelectric ceramics transducer (PZT) phase modulators is presented and demonstrated for the first time. In this system, two different PZT phase modulators are used for high frequency phase modulation and low frequency phase control, respectively, while in previous demonstrated system, LiNbO3 phase modulators are often employed. The inherent low insert loss and high laser-induced damage threshold of the PZT phase modulator makes the new proposed system more compact and stable. By the way, the experiment of coherent beam combination of two 5-W fiber laser beams based on double PZT phase modulators is done. In the experiment, the PZT phase modulator with 500-kHz frequency response point made in home is used for high frequency phase modulating and another one with 0∼30-kHz linear frequency response range for phase controlling. When the phase control system is in the closed loop, the fringe contrast of far-field intensity pattern is improved to be more than 90 % from 5 % in open loop.

<sec>Ultrafast fiber laser sources with mJ-level pulse energy and kilo-watt average power are of particular importance for various science fields such as attosecond lasers. Currently, several large-scale facilities for attosecond lasers, including ELI-ALPS in Europe, SECUF in China, NeXUS in America and ALFA in Japan are under construction. High-performance femtosecond driven lasers are crucial for attosecond lasers and various ultrafast laser facilities. Fiber lasers have a large surface-to-volume ratio, which enables efficient cooling and is suitable for high average power amplification. However, due to small mode area of optical fibers, detrimental nonlinear optical effects such as self-phase modulation, four-wave mixing, and stimulated Raman scattering limit the peak power of pulse to hundreds of MW, corresponding to pulse energy of hundreds of μJ for femtosecond pulses in large mode area rod-type fibers. In addition, the average power of fiber lasers is limited by transverse mode instability, which reduces the stability and quality of beams above a certain threshold. In rod-type fibers, the threshold is about 250 W. Neither average power nor pulse energy emitted by single fiber meets the requirement for attosecond laser generation.</sec><sec>The average power and pulse energy can be further scaled by coherent beam combination, which involves splitting pulses caused by an frontend laser and recombining them after amplification. It is essential for coherent beam combination to maintain the coherence of pulse replicas, which usually involves high speed photodiode detectors, piezo-driven mirrors, and other electronics forming a feedback system to actively control the phase of all replicas. We present a high-energy high-power ultrafast fiber laser system by using filled-aperture coherent combination of four ytterbium-doped rod-type fiber amplifiers. The phase control is achieved by using stochastic parallel gradient descent method. The frontend includes a passively mode-locked Yb-fiber oscillator, a stretcher, a pulse picker, and three fiber pre-amplifiers, which delivers 1 MHz stretched pulses centered at 1032 nm with 700 ps duration and 20 W average power. The pulse is split into four replicas by polarization beam-splitter and half-wave plate pairs, and the replicas pass through delay lines formed by piezo-driven mirrors before amplification. The pulse replicas are equally split and amplified to ensure the same accumulated nonlinear phase, and are combined by thin film polarizer and half-wave plate pairs. A small portion of the combined pulse is split and collected by a photodiode detector after being filtered spectrally and spatially, serving as a signal for controlling phase. The combined pulse is compressed by a compressor using a double-pass diffraction grating pair consisting of two 1739 l/mm gratings.</sec><sec>At a repetition rate of 1 MHz, our four-channel Yb-fiber coherent beam combination system generates a combined average power value of 753 W and a combination efficiency of 87%. By utilizing an adjustable pulse stretcher and compressor, a 0.67 mJ, 242 fs near transform-limited pulse can be generated with a compressing efficiency of 89%. The compressed pulse is centered at 1032 nm, and the spectrum width is 8.8-nm. In the 30 min measurement, the root-mean-square of average power is less than 1% , while the residual phase error is less than <i>λ</i>/23, indicating excellent stability on different time scales. The beam quality factor of the 0.67 mJ compressed pulses is 1.17×1.11. At 500 kHz, we obtain pulses of 1.07 mJ and 247 fs with average power of 534 W, exhibiting similar efficiency, long-term stability, and beam quality. The residual phase error decreases below <i>λ</i>/29, indicating better short-term stability. Further scaling power and energy can be achieved by increasing the number of channels. By adding the delay stabilization system and pointing stabilization system, which are currently under development, an eight-channel CBC system can be used to generate 1 kW, 2 mJ pulses.</sec><sec>In this work, we implement a four-channel coherent beam combining system based on the SPGD method, and obtain compressed pulses of 673 W, 673 µJ, and 242 fs at 1 MHz and 534 W, 1.07 mJ, and 247 fs at 500 kHz. Both power and energy can be further improved by increasing the channel number, and adding the delay stabilization system and pointing stabilization system which are under construction. By adding coherent pulse stacking amplification technology, the coherent beam combining system ought to generate pulse energy as high as 100 mJ, which constitutes the energy source for applications such as laser wake-field acceleration.</sec>

The XCAN project, which is a three years project and began in 2015, carried out by Thales and the Ecole Polytechnique aims at developing a laser system based on the coherent combination of laser beams produced through a network of amplifying optical fibers. This technique provides an attractive mean of reaching simultaneously the high peak and high average powers required for various industrial, scientific and defense applications. The architecture has to be compatible with very large number of fibers (1000-10000). The goal of XCAN is to overcome all the key scientific and technological barriers to the design and development of an experimental laser demonstrator. The coherent addition of multiple individual phased beams is aimed to provide tens of Gigawatt peak power at 50 kHz repetition rate. Coherent beam combining (CBC) of fiber amplifiers involves a master oscillator which is split into N fiber channels and then amplified through series of polarization maintaining fiber pre-amplifiers and amplifiers. In the so-called tiled aperture configuration, the N fibers are arranged in an array and collimated in the near field of the laser output. The N beamlets then interfere constructively in the far field, and give a bright central lobe. CBC techniques with active phase locking involve phase mismatch detection, calculation of the correction and phase compensation of each amplifier by means of phase modulators. Interferometric phase measurement has proven to be particularly well suited to phase-lock a very large number of fibers in continuous regime. A small fraction of the N beamlets is imaged onto a camera. The beamlets interfere separately with a reference beam. The phase mismatch of each beam is then calculated from the interferences' position. In this presentation, we demonstrate the phase locking of 19 fibers in femtosecond pulse regime with this technique. In our first experiment, a master oscillator generates pulses of 300 fs (chirped at 200 ps). The beam is split into 19 passive channels. Prior to phase locking, the optical path differences are adjusted down to 10 μm with optical delay lines. Interferograms of the 19 fibers are recorded at 1 kHz with a camera. A dedicated algorithm is developed to measure both the phase and the delay between the fibers on a measurement path. The delay and phase shift are thus calculated collectively from a single image and piezo-electric fiber stretchers are controlled in order to ensure compensation of time-varying phase and delay variations. The residual phase shift error is below λ/60 rms. The coherent beam combining is obtained after propagation and compression. The combined pulse width is measured at 315fs. A second experiment was done to coherently combine two amplified channels of the XCAN demonstrator. A residual phase shift error of λ/30 rms was measured in this case.

In this paper, we present an experimental comparison of coherent beam combining (CBC) effect with different truncation factors based on a triangle fiber laser array for the first time to our best knowledge. First, we fabricate a triangle fiber laser array based on adaptive fiber optics collimators with the fixed focusing length of 0.18m and clear aperture of 50mm. Two output fiber arrays (6/125 fiber array and 20/400 fiber array) with different numerical apertures (0.12 and 0.065, respectively) are used to generate different truncation factors. The direct measurement method is used to measure the intensity distribution of the two collimated beams with different sizes. Results show that the beam diameters are 14.5mm and 27.6mm for 20/400 output fiber and 6/125 output fiber, separately. This means that two fiber laser arrays with truncation factors of 0.29 and 0.55 are achieved. Then we numerically calculate the CBC efficiencies of two situations with different truncation factors. The analytical results show that the CBC efficiency improves from 0.144 with truncation factor of 0.29 to 0.413 with truncation factor of 0.55. At last, a CBC experiment platform is set up. Throughout the whole experiment, single frequency dithering algorithm and SPGD algorithm are separately used to perform the phase-locking control and the tilt control. Two CBC experiments of triangle fiber laser arrays are achieved successfully both with residual phase errors about λ/15. By analysis the experimental results, we get the CBC efficiencies are 0.099 (69% of 0.144) and 0.264 (64% of 0.413) for the two fiber arrays. The experimental results identify the importance of truncation factor on CBC efficiency and provide an important reference on the selection of fiber array parameters in order to achieve the largest energy proportion in the central lobe.

Coherent beam combination laser system using SBS-PCM for high repetition rate solid-state lasers

We demonstrate the coherent beam combination of a hexagonal distributed high power fiber amplifier array. Six polarization-maintained fiber amplifiers are tiled into a hexagonal array by use of a novel beam combiner. The phase control signal for fiber amplifiers is generated by running a stochastic parallel gradient descent algorithm on a digital signal processor. The coherent beam combination with a total output power of 73.5 W is demonstrated. The contrast of the coherent combined beam profile is as high as 81% when the system is closed-loop controlled.

We report on what is, to our knowledge, one of the first realizations of a CBC (coherent beam combining)-based laser emitter carrying a 10.66 Gb/s telecom signal in free-space optics, within the laboratory environment. Two telecom modulations have been tested: NRZ (non-return-to-zero, in amplitude) and DPSK (differential phase-shift keying, in phase). The modulated signal is split and amplified in three fiber amplifiers, delivering up to 3 W each. CBC of data amplified signals is achieved with residual phase errors well below < λ/60 RMS, using a phase-tagging technique (LOCSET). A first analysis of the influence of various parameters (such as phase-tagging modulation depth, optical path difference, number of channels, amplifier power) on the locking and data transmission quality is investigated. The study shows that the phase-tagging modulation depth and optical path difference are the main critical issues when carrying data on a CBC signal.

For phase retrieval in a coherent beam combining of 7 fiber amplifiers arranged in a tiled aperture experiment, we demonstrate the feasibility of direct implementation of a light-weight deep-learning model trained on simulated data only. Deep-learning-assisted phase control performs efficiently with lower than λ/30 residual phase error. The use of simulation-trained neural networks allows for fast training (<10 min), a priori optimization, without the need for experimental data acquisition, and easier experimental portability.

The application of a conical wavefront in the near field of the tiled aperture coherent beam combination (CBC) produces a segmented, similar to Bessel-Gauss irradiance pattern (BG-CBC), in the far field. The properties of such a structured optical field were numerically investigated. In contrast to that for the classical CBC, the power diffracted beyond the 'zero' BG-CBC diffraction order is more smoothly and homogenously distributed, not evidencing sharp maxima and dark regions typical for CBC. The novelty of the BG-CBC with segmented conical wavefront is a simple way of caustics elongation and redistribution of power density for the same CBC architecture.

Coherent beam combination has emerged as a promising strategy for overcoming the power limitations of individual fibre lasers. This approach relies on maintaining precise phase difference between the constituent beamlets, which are typically established using phase retrieval algorithms. However, phase locking is often studied under the assumption that the power levels of the beamlets remain stable, an idealisation that does not hold always in practical applications. Over the operational lifetime of fibre lasers, power degradation inevitably occurs, introducing additional challenges to phase retrieval. To address this, we propose a deep learning algorithm for single-step simultaneous phase and amplitude identification, directly from a single camera observation of the intensity distribution of the combined beam. By leveraging its ability to detect and interpret subtle variations in intensity interference patterns, the deep learning approach can accurately disentangle phase and power contributions, even in the presence of significant power fluctuations. Using a spatial light modulator, we systematically investigate the impact of power-level fluctuations on phase retrieval within a simulated coherent beam combination system. Furthermore, we explore the scalability of this deep learning approach by evaluating its ability to achieve the required phase and amplitude precision as the number of beamlets increases.

In this chapter, several beam combining architectures suitable for DE applications have been reported, and are divided into two distinct categories: incoherent beam combination (IBC) and coherent beam combination (CBC). The purpose of each method is to increase the far field intensity when brightness and power of a single fiber amplifier is limited. In IBC, an array of fiber lasers is superimposed in the far field without control of the relative spectra or phases of the different fibers. No brightness enhancement is obtained from this method, limiting the maximum intensity in the far field. Although such beam combining has been successfully demonstrated by the Navy [5], this approach is limited to propagation ranges on the order of a few kilometers. In spectral beam combining (SBC), a separate class of IBC, incoherent beams of different wavelengths are spatially overlapped to create a single output beam of multiple colors. The brightness of the propagating beam can be increased at the cost of increased spectral bandwidth. Similarly, SBC has the advantage of not requiring active phase control or mutual temporal coherence of the individual beams. Alternatively, coherent beam combining (CBC) schemes require proper phase, frequency, and polarization relationships for efficient beam combination. Overall, due to their brightness enhancements, for longer range and higher power/ intensity DE applications, SBC and CBC are potentially more appealing.

A laser testbed based on active coherent combination (CBC) of seven 1.5 µm fiber amplifiers has been developed for applications requiring high power such as power density deposition on target or free space laser communication. The seven 3W fiber amplifiers are combined using the frequency-tagging LOCSET technique in a Target-in-the-loop (TIL) configuration [1] as shown in fig. 1 . In situ Piston and Tilt (PISTIL) interferometer provides the relative phase of each emitter in the emitter plane [2] . Successful combination has been achieved after a 300m horizontal propagation, 1.5m above the ground, with low wind velocity and an average estimated turbulence strength $C_n^2 = {10^{ - 13}}{m^{ - 2/3}}$ .

In this Letter, a first (to our knowledge) demonstration of phase conjugate self-organized coherent beam combination is reported. A demonstration involving combination of two self-adaptive gain grating holographic laser resonators is presented. Output powers of up to 27 W, with a combination efficiency of 94%, are demonstrated. This technique coherently combines individual phase conjugate laser modules, which do not have predefined spectral or spatial modes. This removes the problem of finding shared resonator modes, which should allow coherent beam combination of much larger laser arrays than standard self-organized coherent beam combination.

Coherent beam combining (CBC) by active phase control could be useful for power scaling fiber-laser-pumped optical frequency converters like optical parametric oscillators (OPOs). However, a phase modulator operating at the frequency-converted wavelength would be needed, which is a non-standard component. Fortunately, nonlinear conversion processes rely on a phase-matching condition, correlating not only the wave-vectors of the coupled waves, but also their phases. It is therefore possible to control the phase indirectly, using more standard phase modulators. Feasibility of this technique was previously demonstrated for second harmonic generators (SHG). Controlling the phase of the fundamental wave, excellent harmonic wave combining efficiency was achieved in both cases of phase matching and quasi phase matching, with lower than &lambda;/30 residual phase error. In this paper, coherent combining of difference frequency generators (DFG) is experimentally tested. Even if DFG is more challenging than SHG as it implies handling three waves instead of two, phase control of the sole 1-&mu;m pump waves is sufficient to combine the 3.4-&mu;m waves generated. The mid-infrared DFG crystals are pumped and signal-seeded with standard all-fiber sources at 1 &mu;m and 1.5 &mu;m respectively. Phase control is performed with an electro-optic phase modulator which is a standard all-fiber component operating at 1 &mu;m. CBC of mid-infrared DFG modules is a first step towards combining continuous wave OPOs.