Beam stabilization is critical in an adaptive optics beam clean-up system to improve the power concentration in the desired area during a period of time. In these systems, the average wavefront slope from a Shack-Hartmann wavefront sensor is widely employed as the feedback of beam stabilization. However, when the adaptive optics system is applied to improve the beam quality of a high-power solid-state slab laser, the “M” shaped aberration at the edge of the slab and the fluctuating intensity distribution of the beam would induce some errors when using the average slope to measure the direction of the beam. In this paper, we present the numerical analysis of beam direction detection errors in solid-state slab laser beam clean-up systems using the average slop. At first, we calculated the direction detection errors with the aberations composed of the first 64 Legendre polynomials using the average slope. Then we measured the wavefront of a solid-state slab laser with a Shack-Hartmann wavefront sensor, and evaluated the influence of the “M” shaped aberration and fluctuating intensity distributions both in the time and frequency domains. It is clear that these factors bring in significant detection errors. Finally, we proposed a method by removing some edge sub-apertures when calculating the average slope.
Shack-Hartmann wavefront sensors calculate the position of focal spot in each sub-aperture from intensity distributions, the noises of the detector itself would have a certain impact on the detecting accuracy and would lead to inaccurate wavefront detections using conventional centroiding method. It has been demonstrated that the correlation algorithms with template matching is able to improve the accuracy. In this paper, several correlation algorithms such as absolute difference function, absolute difference function-squared, square difference function, cross-correlation function and normalized cross-correlation are compared at different signal-to-noise ratios. To further improve the accuracy, interpolation algorithms including equiangular line fitting, parabola interpolation, gauss interpolation and least square method are brought in, which turns out that least square method could minimize the detecting error. Besides, simulations within single aperture and full aperture both illustrate that cross-correlation function is most robust but needs more calculations, so is least square method. Moreover, although absolute difference function would be inaccurate at low signal-to-noise ratios, it still can obtain high detecting accuracy at high signal-to-noise ratios and it minimizes the calculations.
The slab laser is a promising architecture to achieve high beam quality and high power. By propagating the laser beams in zigzag geometries, the temperature gradient in the gain medium can be well averaged, and the beam quality in this direction can be excellent. However, the temperature gradient in the non-zigzag direction is not compensated, resulting in aberrations in this direction which lead to poorer beam quality. Among the overall aberrations, the main contributors are two low-order aberrations: astigmatism and defocus. These aberrations will magnify beam divergence angle and degrade beam quality. If the beam divergence angles in both directions are almost zero, the astigmatism and defocus are well corrected. Besides, the output beams of slab lasers are generally in a rectangular aperture with high aspect ratio (normally 1:10), which need to be reshaped into square in many applications. In this paper, a new method is proposed to correct low-order aberrations and reshape the beams of slab lasers. Three lenses are adapted, one is a spherical lens and the others are cylindrical lenses. These lenses work as a beam shaping system, which converts the beam from rectangular into square and the low-order aberrations are compensated simultaneously. Two wavefront sensors are used to detect input and output beam parameters. The initial size of the beam is 4mm×20mm, and peak to valley (PV) value of the wavefront is several tens of microns. Simulation results show that after correction, the dimension becomes 40mm×40mm, and peak to valley (PV) value of the wavefront is less than 1microns.
Slab geometry is a promising architecture for power scaling of solid-state lasers. By propagating the laser beams along zigzag path in the gain medium, the thermal effects can be well compensated. However, in the non-zigzag direction, the thermal effects are not compensated. Among the overall aberrations in the slab lasers, the major contributors are two low-order aberrations: astigmatism and defocus, which can range up to over 100 microns (peak to valley), leading to detracted beam quality. Another problem with slab lasers is that the output beams are generally in a rectangular aperture with high aspect ratio (normally 1:10), where square beams are favorable for many applications. In order to solve these problems, we propose an automatic low-order aberration compensation system. This system is composed of three lenses fixed on a motorized rail, one is a spherical lens and the others are cylindrical lenses. Astigmatism and defocus can be compensated by merely adjusting the distances between the lenses. Two wave-front sensors are employed in this compensation system, one is used for detecting the initial parameters of the beams, and the other one is used for detecting the remaining aberrations after correction. The adjustments of the three lenses are directly calculated based on beam parameters using ray tracing method. The initial size of the beam is 3.2mm by 26mm, and peak to valley(PV) value of the wave-front is 33.07λ(λ=1064nm). After correction, the dimension becomes 40mm by 40mm, and peak to valley (PV) value of the wave-front is less than 2 microns.
Phase retrieval is a simple and concise way of reconstructing wavefront, especially the method based on single far field formed by just a lens. However, for the symmetry of Zernike polynomial aberrations, light with different wavefront could form the same far-field intensity distribution. The distribution of reconstructed wavefront is likely to be quite different from the real one. In other words, it suffers in the multi-solution problem. A kind of wavefront reconstruction method based on quadrant binary phase plate is proposed. Incident light is modulated by a first-order Modified-Walshfunction pattern quadrant binary phase mask, which violates the special symmetries. Simulation experiments show that this method can retrieval random wavefront distributions accurately. It provides a practical technical solution for precise wavefront sensing with single far field image.
Direct liquid-cooling is a promising way of power scaling and heat management for solid-state lasers. A side-pumped direct liquid-cooled solid-state pulsed zigzag MOPA system is established based on this advanced concept. However, its beam quality is degraded by the thermal distortions in the non-zigzag direction and the flowing coolant. We develop an adaptive optics system to improve its beam quality, which primarily includes a low-order aberration compensator and a 59-actuator deformable mirror. The beam is first corrected by the low-order aberration compensator to remove large defocus and astigmatism, and its size is reshaped simultaneously to fulfill the demands of applications. Then the beam is further corrected by the deformable mirror. With collaborative operation of the low-order aberration compensator and the deformable mirror, we have achieved average beam quality of β=2.8.
In order to maintain sufficient performance of a laser, proper alignment of the resonator is very important. We present online laser resonator alignment based on machine vision. In this method, a camera detects the displacement of the laser beam spot on the rear mirror from a reference location, and the displacement of this spot is used to indicate the misalignment of the cavity mirrors. The resonator could be automatically aligned using the displacement as feedback. We give a detailed analysis of the relation between tilt of resonator mirrors and the beam spot location on the rear mirror by calculating the modes of the resonator. Both a stable symmetric confocal resonator and a positive branch confocal unstable resonator are investigated. Calculation results show that the displacement of the beam spot on the rear mirror continuously grows with tilt of the resonator mirrors, and the direction of the displacement can well reflect the direction of the misalignment, indicating that the displacement can effectively denote resonator misalignment.
Adaptive optics (AO) schemes are often applied to the inertial confinement fusion (ICF) system, such as SG-Ⅲ Prototype which has been set in China. This laser systm mainly includes a pulsed seed laser source, a multi-pass laser amplifier with the configuration of beam rotate-90° and expansion. When AO system is employed in this sytem, the beam bounces twice on the deformable mirror (DM) which works as the cavity mirror (CM) of the multi-pass laser amplifier, moreover, after the first bounce on the DM, the beam rotate 90° and expansion with a ratio. Therefore, the relationship between the DM’s correction stroke and the aberrations within the laser sytem must be known before applying a adaptive correction. This paper demonstrates that any output wave-front aberrations within the DM’s correction stroke range can be well corrected, as well as illuminates that the expansion ratio of beam and the types of output wave-front aberrations both affect the correction stroke range of DM. Furthermore, through building a theoretical calculating model and some simulation. the relationship between the DM’s surface stroke needed and different aberrations within the laser sytem is ascertained clearly. Results show that this configuration is proper for compensting most low order aberrtions besides some special ones. As a result, it will provides a useful guidance for those rotate-90°laser systems adopting adaptive optics technique.
Walsh functions have been modified and utilized as binary-aberration-mode basis which are especially suitable for representing discrete wavefronts. However, when wavefront sensing techniques based on binary-aberration-mode detection trying to reconstruct common wavefronts with continuous forms, the Modified Walsh functions are incompetent. The limited space resolution of Modified Walsh functions will leave substantial residual wavefronts. In order to sidestep the space-resolution problem of binary-aberration modes, it’s necessary to transform the Modified-Walsh-function expansion coefficients of wavefront to Zernike-polynomial coefficients and use Zernike polynomials to represent the wavefront to be reconstructed. For this reason, a transformation method for wavefront expansion coefficients of the two aberration modes is proposed. The principle of the transformation is the linear of wavefront expansion and the method of least squares. The numerical simulation demonstrates that the coefficient transformation with the transformation matrix is reliable and accurate.
The search-based intra-cavity beam cleanup systems are typical feedback loop systems which have been used in both gas
and solid-state laser cavity to enhance laser performance. The studies on search-based intra-cavity beam cleanup systems
mostly rely on experiments. However there are few reports about numerical simulation. In this paper, we attempt to use
numerical method to analysis the search-based intra-cavity beam cleanup system. These systems contain three main
elements: an adaptive laser cavity, a fitness sensor of laser performance and a computer-based search algorithm.
According to the compositions of beam cleanup systems, three modules have been set up in our numerical simulation
framework. We detail the theory, structure and numerical method of these modules in this paper. To demonstrate the
feasibility of the numerical method, we calculated the results based on stochastic parallel gradient descent algorithm.
Based on a 979-actuator adaptive optics system, this paper analyzes the different performance of iterative wavefront
reconstruction algorithms. Under the condition of dynamic wavefront errors, the iteration number, storage space and the
number of multiplication of steepest descent method, conjugate gradient method and G-S iterative method are studied.
The steepest descent method and conjugate gradient method need smaller storage space. Both the G-S iterative method
and the conjugate gradient method converge faster than steepest descent method, while the latter takes the least number
of multiplication. Finally, the optimal iterative algorithm is selected considering storage space, iteration numbers and the
number of multiplication.
In wavefront sensor-less adaptive optics systems, wavefront sensing is often replaced with far-field detection. If the detection is inaccurate, even if the optimal performance metric is achieved, the correction quality may still be poor. In this paper we focus on the effects of improper far-field detection positions. At first we build a simple modal of a wavefront sensor-less adaptive with improper detection position. Then a series of analyses are carried out using this modal and the precision of placing far-field sensor is concluded. Finally simulations with practical systems are presented and the method for analysis are given.
As for master-oscillator-power-amplifier (MOPA) laser systems, Aberrations generated by thermal
effects, the mirrors surface and optical elements play important roles to deteriorate laser beam quality.
To obtain good beam performance, a compact adaptive optics (AO) system for a Nd:YAG zigzag slab
amplifier is built. A rectangular tilt mirror (DM) and a 39-element rectangular piezoelectric deformable
mirror in combination with a stochastic parallel gradient descent (SPGD) algorithm is introduced for
aberrations correction. Experimental results demonstrate that the output beam quality can enhanced
greatly at different power level when the AO system is in operation.
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