Coherent beam combining of two all-PM thulium-doped fiber chirped pulse amplifiers.

In this paper, we report a coherent beam combining (CBC) system that involves two thulium-doped all-polarization maintaining (PM) fiber chirped pulse amplifiers. Through phase-locking the two channels via a fiber stretcher by using the stochastic parallel gradient descent (SPGD) algorithm, a maximum average power of 265 W is obtained, with a CBC efficiency of 81% and a residual phase error of λ/17. After de-chirping by a pair of diffraction gratings, the duration of the combined laser pulse is compressed to 690 fs. Taking into account the compression efficiency of 90% and the main peak energy proportion of 91%, the corresponding peak power is calculated to be 4 MW. The laser noise characteristics before and after CBC are examined, and the results indicate that the CBC would degrade the low frequency relative intensity noise (RIN), of which the integration is 1.74% in [100 Hz, 2 MHz] at the maximum combined output power. In addition, the effects of the nonlinear spectrum broadening during chirped pulse amplification on the CBC efficiency are also investigated, showing that a higher extent of pulse stretching is effective in alleviating the spectrum broadening and realizing a higher output power with decent combining efficiency.

Numerical simulation of the internal active phase-locking coherent beam combining system.

As a promising way to realize high output power while maintaining high beam quality, coherent beam combining (CBC) of fiber lasers has drawn much interest. Phase control is one of the main technologies to fulfill CBC, which is employed to keep the phases of different fiber lasers consistent. Traditional phase control techniques employ beam splitters after the emitting array to obtain phase mismatch information. Different from the traditional phase-locking technique, the internal phase control technique can obtain phase mismatch information before the laser array output to free space, and the technique is compact and easy to expand to a lager array. In this paper, a CBC system based on an internal phase-locking technique is designed, and relative numerical simulations are studied. By using the cascaded technique, the phase control bandwidth can be greatly increased. The simulation results show that hundreds of laser beams can be effectively combined based on the technique. The results of the numerical simulations can provide significant reference for the compact CBC system design and phase control.

Generating the 1.5†kW mode-tunable fractional vortex beam by a coherent beam combining system.

As an essential component of the vortex beam, the fractional vortex beam has significantly advanced various applications, such as optical imaging, optical communication, and particle manipulation. However, practical applications face a significant challenge as generating high average power fractional vortex beams remains difficult. Here, we proposed and experimentally demonstrated a high average power mode-tunable fractional vortex beam generator based on an internally sensed coherent beam combining (CBC) system. We presented the first, to the best of our knowledge, successful generation of a 1.5 kW continuous wave fractional vortex beam. Moreover, real-time tuning of the topological charge (TC) from -2/3 to +2/3 was easily achieved using the programmable liquid crystals (LCs). More importantly, the fractional vortex beam copier was presented as well, and the generated fractional vortex beam could be easily transformed into a fractional vortex beam array by changing the fill factor of the laser array. This work can pave the path for the practical implementation of high average power structured light beams.

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.

Internal phase control of coherent fiber laser array without ambiguous phase based on double wavelength detection.

High-power fiber lasers have been widely utilized in manufacturing, medical care, and many other fields. Due to mode instability, nonlinear effects, and so on, the output power of a monolithic fiber laser is limited. Coherent beam combining (CBC) of fiber lasers is a promising way to obtain higher output power. An all-fiber CBC structure with internal phase detection has a compact construction and potential for a larger fiber laser array. For the existing internal active phase control of an all-fiber structure, π phase ambiguity always occurs because of double passing the fiber path. Additional compensation is needed under this condition, and the compactness of the system will decrease. In this paper, internal phase control of an all-fiber structure based on double wavelength detection without π-ambiguity is proposed. By adding a beacon laser with a different wavelength, phase locking of a coherent fiber laser array can be achieved internally without π-ambiguity. A corresponding math model is established, and a phase matched condition is derived. The spectral width of the beacon laser is analyzed, and the result shows that it can reach tens of nanometers with a proper optical path difference. Simulations of seven, 19, and 37 beams are carried out, and the results show that the structure proposed in this paper has the ability to achieve phase control with good robustness. The control bandwidth in the simulation is better than 1 kHz. By properly designing elements, the structure is expected to achieve high-power CBC of an all-fiber structure experimentally.

Distributed active phase-locking of an all-fiber structured laser array by a stochastic parallel gradient descent (SPGD) algorithm.

Coherent beam combining (CBC) of fiber laser array is a promising way to achieve high output power. Phase control is one key point to implement CBC. Appropriate feedback structures should be established to achieve phase control. Most feedback structures of CBC are established after the lasers emit to free space and consist of a set of lenses or mirrors. Those optical elements in free space may hinder array size and integration. In this paper, we demonstrated an all-fiber structured CBC method with distributed phase-locking. By adding an all-fiber measurement loop beside the main laser chain, the phase of main laser chain is appended to the measuring loop. Phases of each main laser chain are locked indirectly though the measurement loops by using stochastic parallel gradient descent (SPGD) algorithm. The principle of distributed phase-locking is also illustrated. Corresponding simulations are carried out and two-channel fiber lasers are coherently combined by this method. The experimental results show that the structure can achieve phase-locking effectively. Stable and distinct interference fringe is observed. Additionally, the structure proposed in this paper is straightforwardly building and expanding.

System design for coherent combined massive fiber laser array based on cascaded internal phase control.

Coherent beam combining (CBC) of a fiber laser can scale the output power while maintaining high beam quality. However, phase detection and control remain a challenge for a high-power CBC system with a massive laser array. This paper provides a novel, to the best of our knowledge, cascaded phase-control technique based on internal phase detection and control, called the cascaded internal phase-control technique. The principle of the technique was introduced in detail, and the numerical simulations were carried out based on the stochastic parallel gradient descent (SPGD) algorithm. The results indicated that the cascaded internal phase-control technique was compatible with the massive laser array. Compared with the traditional CBC based on the SPGD algorithm, the control bandwidth could be improved effectively about seven times (120 steps) than the traditional SPGD algorithm (830 steps). Furthermore, the average root mean square of residual phase error was decreased to 0.03 rad (∼λ/209) with a laser array of 259 channels (7∗37), which was 0.36 rad (∼λ/17) in the traditional SPGD algorithm. In addition, the element expanding capacity was analyzed. Since there is no large-aperture optical device in the phase-detection system, this technique has the advantage of freely designing the caliber of the laser emitting system. This paper could offer a reference for the high-power massive laser array system design and phase control.

Iteration-free, simultaneous correction of piston and tilt distortions in large-scale coherent beam combination systems.

Coherent beam combination (CBC) holds promise for scaling the output power of the laser system while maintaining good beam quality. Owing to the thermal effect and mechanics instability, piston and tilt distortions always exist and affect the performance of the combined beam. To ensure the constructive interference in the far-field, dynamic correction of the distortions is highly required. Here, we propose an approach for the simultaneous correction of piston and tilt distortions in CBC systems. Based on the position and interval information of the near-field interference fringes, the theoretical expressions for the relative piston phase and tilt errors of each array element are derived, indicating that dynamic distortions in CBC systems can be directly calculated and then corrected by employing phase control servos. To demonstrate the feasibility of the proposed approach, Monte-Carlo Simulations have been carried out for different perturbative environments. Our results indicate that both piston phase and tilt errors can be calculated and compensated accurately (λ/25 and 0.11µrad) by the proposed approach even in 169 beamlets, which also has high tolerance for defocus errors. This work could provide valuable reference on the practical implementation of high-power, phase-locked fiber laser array systems.

Switching the orbital angular momentum state of light with mode sorting assisted coherent laser array system.

Light beams carrying orbital angular momentum (OAM) have important implications for future classical and quantum systems. In many applications, controlled switching of the OAM state at high speed is crucial, while accelerating the switching rate presents a long-standing challenge. Here we present a method for flexibly switching the OAM state of light based on a coherent laser array system. In the system, the output structured light beam is tailored by the coherent combination of array elements. By employing an OAM mode sorting assisted phase control subsystem, which continuously performs the optimization algorithm, the dynamic wavefront distortion of the combined OAM beam could be compensated. Meanwhile, our approach allows one to achieve fast states switching of the combined OAM beam via programming the cost function of the algorithm. The results of Monte-Carlo simulations demonstrate the feasibility of the proposed method, and the mode purity and power scaling potential of the controllably generated OAM beam are discussed. This theoretical work could be beneficial to the future implementation of rapidly switchable OAM beams at practical output power.

Tight focusing properties and focal field tailoring of cylindrical vector beams generated from a linearly polarized coherent beam array.

We investigate the focusing properties of cylindrical vector beams (CVBs) generated from the combination of an array of beams, each with sub-apertures and controllable polarization. The analytical expression of the tight focusing field of the combined CVBs has been derived based on the Richard-Wolf vector diffraction integral. To obtain a desired focal spot size which includes efficient sidelobe suppression, the required parameters, such as the exit sub-aperture, numerical aperture and truncation parameter, have been studied in detail. The result shows that the combined CVB distribution has a good match with the theoretical ideal CVB distribution. However, compared with the ideal CVBs, the focal spot width produced by the combined radially polarized beams is smaller. With the increase of initial polarization rotation of sub-aperture, the focal spot width increases, and the focal shape shifts from Gaussian-like to a flat-topped distribution and then to an annular distribution. Furthermore, flexible focal field tailoring can also be realized by adjusting the initial polarization rotation of each sub-aperture. These results might provide a valuable reference for material processing, microlithography and multi-particle manipulation.