RU2783630C1 - Method for adaptive intracavity phase correction of laser emission - Google Patents

Abstract

FIELD: lasers.

SUBSTANCE: invention relates to the field of laser technology and can be used for an effective procedure of intracavity phase correction of multimode laser emission. Method for intracavity phase correction of laser emission is based on changing the surface shape of a flexible adaptive mirror (AM) located in place of a fully reflective mirror of the laser resonator by emitting control signals on the actuators of the AM. The control signals are calculated using a stochastic parallel gradient (SPG) algorithm.

EFFECT: implementation of intracavity phase correction of multimode laser emission, consisting in narrowing the directivity pattern of the multimode emission and raising the speed of the adaptive optical system by applying an advanced algorithm for stochastic parallel gradient descent — the SPG algorithm.

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Description

The invention relates to the field of laser technology and can be used for intracavity phase correction of multimode laser radiation.

At present, an adaptive optical system (AOS) is an integral part of pulsed and cw laser systems. The purpose of using AOS is to compensate for static and (or) dynamic distortions of the laser beam wavefront that occurs when it propagates through optical inhomogeneities of the active laser medium and optical path. The main components of a traditional AOS are a wavefront sensor (WFS), a flexible adaptive mirror (AM), a special calculator (for example, a personal computer (PC)), a digital-to-analog converter (DAC) and a high-voltage amplifier. The local gradients of the beam phase surface are measured using the WFS. Restoration of the phase surface and calculation of the required voltages applied to the actuators of the AZ is carried out in a special calculator. The calculated voltages are converted by the DAC into an analog signal, amplified by a high-voltage amplifier and fed to the actuators of the core, resulting in the required deformation of the core surface.

In practice, situations are possible when the beam incident on the WFS is spatially incoherent, that is, it simultaneously contains many independent wave fronts. In this case, the WFS will measure a certain average wave front of the radiation, and the correction of such a beam using AOS with a WFS will be inefficient. For example, this situation is realized in a plane-parallel laser resonator. Several independent laser modes simultaneously propagate inside the resonator, with each mode having its own wavefront. Under the conditions of a nonstationary optically inhomogeneous active laser medium, the structure of wave fronts changes continuously, and the problem of phase correction of multimode radiation becomes more complicated.

At present, intracavity correction of laser radiation using the A3 has already been carried out. Various iterative algorithms are used to control the AZ: sequential “hill climbing”, two-stage “hill climbing”, simulation of “annealing, random search, adaptive random search [M.A. Vorontsov, A.V. Koryabin. IN AND. Polezhaev, V.I. Schmalhausen, "Adaptive intracavity control of the mode composition of solid-state laser radiation", Quantum Electronics, 18, no. 8, (1991), 904-905. 1], [Waiter Lubeigt, Gareth Valentine, John Girkin, Erwin Bente, David Bums, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror", Optics Express, Vol. 10, no. 13. (2002), 550-553. 2], [Walter Lubeigt, Gareth Valentine and David Bums, "Enhancement of laser performance using an intracavity deformable membrane mirror", Optics Express, Vol. 16, no. 15, (2008), 10943-10955. 3], [P. Yang, Y. Liu, W. Yang et al., "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror", Optics Communications, 278, (2007), 377-381. 4], [Ping Yang, MingWu Ao, Yuan Liu, Bing Xu, WenHan Jiang, "Intracavity transverse modes controlled by a genetic algorithm based on Zemike mode coefficients". Optics Express, Vol. 15, no. 25, (2007) 17051-17062. 5]. As the closest analogue that implements the inventive method of intracavity phase correction of laser radiation, the method [P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, B. Xu "Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror", Appl. Phys. B (2010) 100, 591-595. 6]. In this method, a variant of intracavity phase correction of single-mode laser radiation by mode control based on a certain algorithm is considered.

The method of adaptive intracavity phase correction (prototype method), implemented in [6], consists in the fact that they provide intracavity control of the laser radiation mode generated in the active medium of the laser cavity, and the phase correction of single-mode laser radiation is carried out using the AZ installed inside the laser cavity. resonator in place of a fully reflecting (deaf) resonator mirror. Inside the resonator, between the core and the active laser medium, there is a telescope that expands the laser beam in such a way as to involve the largest number of actuators in the core. The output laser radiation generated in the resonator is taken out of the resonator and directed to the plate, which divides the total radiation flux into two parts. One part of the radiation is diverted for use by the consumer. The other part of the radiation is focused on a photographic recorder, where the integral value of the intensity is measured in a region of a given size in the laser spot. The meaning of focus is as follows. The focal spot size characterizes the beam divergence. And the greater the paraxial intensity, the smaller the size of the focal spot and the smaller the divergence. The value of the paraxial intensity, which characterizes the quality of laser radiation, is taken as the value of the objective function of the AZ control algorithm.

Based on the measurements of the value of the objective function with the help of a PC, the values of the control voltages that need to be applied to the actuators of the AZ are calculated. The calculation of control voltages for AZ is based on the algorithm of stochastic parallel gradient descent (SPGS) [M.A. Vorontsov, V.P. Sivokon. "Stochastic parallel-gradient-descent technique for hight-resolution wave-front phase-distortion correction", J. Opt. soc. amer. A, V. 15, No. 10, (1998), 2745-2758, 7]. The calculated voltage values from the PC are transferred to the DAC and then amplified by a high-voltage amplifier. Next, voltages are applied to the actuators of the core, as a result of which the surface of the core is deformed, which in turn leads to a phase correction of the laser radiation generated inside the resonator. The AZ is controlled in an iterative mode in three stages. The result of the intracavity phase correction is the narrowing of the directivity pattern of the output laser radiation, which characterizes the beam divergence. The achievement of the required correction quality is judged by the value of the objective function of the iterative stochastic (SPGS) algorithm.

The disadvantages of the aforementioned analogs and the prototype method (in the case of single-mode laser radiation) include the use of AZ control algorithms with suboptimal speed. So, in the prototype [6] and analogue [5], under the control of the AD genetic algorithm, individual laser modes are converted into the fundamental mode for a sufficiently long time. This circumstance makes it unsuitable to use AOS controlled by a genetic algorithm for radiation correction in resonators with rapidly changing (within a few seconds or a fraction of a second) parameters of an inhomogeneous active medium, where a high speed of AOS is required. In the prototype method [6], under the control of the AZ SPGS algorithm, individual laser modes are converted to the fundamental mode within about ten seconds. In [Huizhen Yang, Xinyang Li, "Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor", Optics & Laser Technology, 43, (2011), 630-635. 8], [R. Yazdani, M. Hajimahmoodzadeh, and H.R. Fallah, "Adaptive phase aberration correction based on imperialist competitive algorithm", Applied Optics, Vol. 53, no. 1, (2014), 132-140. 9] shows that under identical conditions, the stochastic parallel gradient descent (SPGS) algorithm is 10–15 times faster than the genetic algorithm. In addition, in the aforementioned analogs and the prototype method, the conversion of one high-order laser mode into a mode close to the main Gaussian mode was considered.

For the case with multimode laser radiation, the problem is the lack of information about the possibility of its intracavity phase correction.

At the same time, formally, they did not work with a multimode beam in the prototype, and it is not clear what the use of SPGS (in the prototype) will give in this case.

That is, for the case with multimode laser radiation, the technical problem lies in the need to obtain information about the possibility of its intracavity phase correction, provided that the speed of the procedure is higher than that of the analogue.

The technical result of the invention in comparison with the prototype [6], which reflects the method of intracavity phase correction of single-mode laser radiation, is to enable intracavity phase correction in the multimode laser generation mode, when many modes are simultaneously present in the laser cavity, subject to the speed of the AZ, with to increase the power of the narrowly focused component of the output laser radiation.

The technical result is achievable due to the fact that, unlike the known method of adaptive intracavity phase correction of laser radiation, which consists in providing intracavity control of the mode of laser radiation generated in the active medium of the laser cavity, using an adaptive mirror (AM) installed in it, for whereby part of the laser radiation power is removed after the laser resonator from the total radiation flux and focused on the photo recorder, the value of the laser radiation intensity in the central region of a given size in the laser spot on the photo recorder is measured, based on the data obtained, the values of the control voltages that need to be applied to the actuators of the AZ are calculated , and when calculating the control voltages, an iterative stochastic algorithm is used to find the extremum of a given objective function that characterizes the quality of laser radiation, the AZ is controlled in an iterative mode, in which the laser radiation mode is controlled by applying control voltages to the actuators of the core, the resulting deformation of the core surface leads to a phase correction of the laser radiation inside the laser cavity, the result of the intracavity phase correction is a narrowing of the radiation pattern of the output laser radiation, and the achievement of the required correction quality judged by the value of the objective function of the iterative stochastic algorithm, in the proposed method, intracavity control of the multimode composition of the generated laser radiation is provided, to ensure control of the actuators of the AZ when calculating the control voltages applied to the actuators of the AZ, a stochastic parallel gradient (SPG) algorithm is used, the AZ is controlled in iterative mode in two stages, in which the objective function of the SPG algorithm is measured when calculating the values of the control parameters The results of photographic recording before applying test low voltages to the actuators of the AZ, at the first stage of the SPG algorithm, small test voltages with a random sign “+” or “-” are applied to the actuators of the AZ. after the voltages on the AZ are established, the objective function of the SPG algorithm is measured again and the change in the objective function relative to its value is calculated before the trial low voltages are applied to the AZ actuators, in accordance with the SPG algorithm, corrections to the control voltages applied to the AZ actuators are calculated and the voltages are corrected applied to the actuators of the AZ, at the second stage of the LNG algorithm, corrected voltages are applied to the actuators of the AZ, and the corrective corrections to the voltages are proportional to the parameter that controls the rate of convergence of the LNG algorithm, the change in the objective function after the first stage, and the small test voltages applied to the actuators of the AZ at the first stage, and are inversely proportional to the value of the objective function before applying trial low voltages and to the square of the trial voltage amplitude.

The authors made a theoretical assumption about the possibility of using a numerical model based on the SPG algorithm to provide adaptive intracavity phase correction of multimode radiation, taking into account the speed of the process when using the SPG algorithm, and this assumption was technically confirmed when implementing the proposed method.

The peculiarity and advantages of the proposed solution in comparison with the solution adopted in the prototype are that:

- it is possible to control the multimode composition of laser radiation in the mode of laser generation;

- AZ control by applying control voltages to it, the values of which are calculated within the declared sequence of actions, is organized using an iterative SPG algorithm [Garanin S.G., Manachinsky A.N., Starikov F.A., Khokhlov S.V. "Phase Correction of Laser Radiation Using Adaptive Optical Systems at RFNC-VNIIEF", Avtometry, Vol. 48, No. 2, (2012), pp. 30-37. 10], which is based on the three-stage SPGS method [7];

- in the LNG algorithm, the number of stages within one iteration has been reduced from three to two, and a parameter has been introduced that controls the rate of convergence of the LNG algorithm to a given value of the objective function. That is, an increase in the speed of the AOS operation is ensured due to the application of the AZ control algorithm, which has an advantage in the speed of convergence compared to the SPGS algorithm. The fact that the phase correction has occurred is judged by the narrowing of the radiation pattern, and the quality of the correction is judged by the value of the objective function of the LNG algorithm.

Thus, using the above advantages, the method of intracavity phase correction of multimode laser radiation based on the SPG algorithm will allow, in comparison with the prototype, to compensate for static and (or) dynamic distortions of the laser beam wavefront that occur when it propagates through optical inhomogeneities of the active laser beam in the multimode laser generation mode. medium and optical path, and provide a faster procedure for improving the quality of the laser beam at the output of the resonator.

In FIG. 1 shows the phase distributions (in λ) for six different "modes" (#1-#6 mode numbers).

In FIG. Figure 2 shows the transverse intensity distributions (in rel. units) of the laser beam in the far zone before and after the SPG correction.

In FIG. Figure 3 shows the characteristic behavior of the objective function (δР/Р and normalized to the maximum value of the axial intensity of laser radiation (the Strehl number St) in the iterative process.

Let us show how it is possible to achieve the above technical result. The implementation of the declared sequence of operations is numerically modeled. In numerical simulation, several beams with a uniform intensity distribution and phase in the form of two-dimensional Legendre polynomials were directed simultaneously to a 19-element AZ. These beams were considered as separate modes of the laser cavity. The wavelength of laser radiation λ=1 μm. In FIG. 1 shows the phase distributions (in λ) for six different "modes". The output radiation of a laser on a photodetector is represented by the sum of the intensities of various "modes" in the far zone. The target function of the SPG algorithm in this case is the fraction of radiation power δР/Р in a paraxial diaphragm with an angular size θ _d , where δP is the radiation power in the diaphragm, P is the total radiation power. The transverse intensity distributions (in relative units) of the laser beam in the far zone before and after the SPG correction are shown in Fig. 2. The circle indicates the aperture limit. The calculations show that after the SPG correction, the radiation intensity is redistributed in the far zone: a bright paraxial core and a wing are formed, which can even somewhat go beyond the localization region of the original beam. In FIG. Figure 3 shows the characteristic behavior of the objective function δР/Р and normalized to the maximum value of the axial intensity of laser radiation (the Strehl number St) in the iterative process. It can be seen that the value of the objective function δP/P as a result of correction for N≈100 iterations of the LNG algorithm increases by 2 times from the initial value, the Strehl number increases by 3.3 times from the initial value. At the same time, it is important that the organization of the AZ control mode using the control voltage algorithm calculated on the basis of the SPG is carried out in accordance with the declared sequence of actions. It is obvious that any AP cannot adjust to the correction of different modes at the same time, but, nevertheless, the ability to transform the mode composition in such a way as to increase the power of the narrowly directed component of the radiation of the laser generator is of great importance for practice, including when building systems "master generator and amplifier.

Thus, a technical solution for adaptive intracavity phase correction of laser radiation can be implemented with the achievement of a technical result consisting in narrowing the radiation pattern of multimode laser radiation and applying, to achieve this goal, a faster, compared to SPGS, SPGS algorithm used to control AZ inside the laser cavity.

The invention will find application in the creation of an adaptive optical system for intracavity phase correction of multimode laser radiation, including the creation of continuous laser systems built according to the “master oscillator and amplifier” scheme.

Claims (19)

A method for adaptive intracavity phase correction of laser radiation, which consists in the fact that - provide intracavity control of the mode of laser radiation generated in the active medium of the laser cavity, using an adaptive mirror (AM) installed in it, for which - part of the laser radiation power is removed after the laser resonator from the total radiation flux and focused on the photo recorder, - measure the value of the intensity of laser radiation in the central region of a given size in the laser spot on the photo recorder, - on the basis of the data obtained, the values of the control voltages that need to be applied to the actuators of the AZ are calculated, - moreover, when calculating the control voltages, an iterative stochastic algorithm is used to find the extremum of a given objective function that characterizes the quality of laser radiation, - AZ control is carried out in an iterative mode, in which - control of the laser radiation mode is carried out by applying control voltages to the actuators of the AZ, - the deformation of the surface of the core provided in this case leads to a phase correction of the laser radiation inside the laser resonator, - the result of intracavity phase correction is the narrowing of the radiation pattern of the output laser radiation, and the achievement of the required correction quality is judged by the value of the objective function of the iterative stochastic algorithm, characterized in that - provide intracavity control of the multimode composition of the generated laser radiation, - to ensure the control of the actuators of the AZ when calculating the control voltages applied to the actuators of the AZ, a stochastic parallel gradient (SPG) algorithm is used, - AZ control is carried out in an iterative mode in two stages, in which - measure the objective function of the SPG algorithm when calculating the values of control voltages based on the results of photographic recording before applying trial low voltages to the actuators of the AZ, - at the first stage of the SPG algorithm, small test voltages with a random sign “+” or “-” are applied to the actuators of the AZ, - after the establishment of voltages on the AZ, the objective function of the SPG algorithm is again measured and the change in the objective function relative to its value is calculated before applying trial low voltages to the actuators of the AZ, - in accordance with the SPG algorithm, corrections are calculated to the control voltages supplied to the actuators of the AZ, and the voltages supplied to the actuators of the AZ are corrected, - at the second stage of the SPG algorithm, corrected voltages are applied to the actuators of the AZ, - moreover, the corrective corrections to the stresses are proportional to the parameter that controls the rate of convergence of the LNG algorithm, the change in the objective function after the first stage and the small test voltages applied to the actuators of the AZ at the first stage and are inversely proportional to the value of the objective function before applying the test small voltages and the square of the amplitude of the test voltages .

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