Linear quadratic regulator for laser beam shaping

The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.     

Wavelength tunable laser beam shaping

Laser beam shaping by phase-only transformations, often referred to as field mapping, has for a long time been considered wavelength dependent. In this Letter we outline a simple mathematical argument that shows how the problem may be formulated in a wavelength tunable manner, requiring only a minor adjustment in the observation plane. We verify the theoretical prediction by experiment using the example of a Gaussian-to-flattop-beam transformation, and we show that the shaping is valid across a wide range of wavelengths for a single diffractive optical element.     

Control of femtosecond laser written waveguides in silica glass

Writing conditions for the fabrication of optical waveguides in bulk fused silica glass by use of 1 kHz focused femtosecond laser pulses at 800 nm were systematically determined for different focusing geometries. The results demonstrate that waveguides can be formed based on optical breakdown, filamentation (single or multiple), or a combination of both processes, when using pulse energies lower than the threshold of structural damage. The mechanisms of laser-induced index change are also discussed. PACS 42.65.Jx; 42.70.Ce; 42.79.Gn     

Hyperboloid cylinder-plane lens for shaping laser diode array beam

A high coupling efficiency, simple structure refractive lens was designed; a hyperboloid cylinder-plane lens was proposed to reduce the divergence angle of the laser diode array beam in the fast axis direction. Based on the ray-tracing method, the shape of the input refractive surface of the designed lens is determined by numerical analysis, and designed as aspherical profile in one direction. When the beam from source point reaches the input surface of the lens, it is refracted and becomes a parallel output beam in the fast axis direction. The expressions for describing the irradiance behind the lens are also derived.     

线激光束均匀化整形方法研究

为解决核物理工程、表面热处理、激光加工、激光通信中传输激光束的均匀性问题,提出采用三角楔柱透镜改善线激光均匀性的新方法,并在ZEMAX开发环境下建立了整形光路系统的理论模型。利用所建立的模型,分析了整形柱透镜在不同半径、斜面夹角、透镜介质折射率等参数下光束的均匀性。研究表明：在远场条件下,通过改变整形柱透镜的参数,能够得到能量分布均匀的线激光。在实际应用中,可以采用1个半圆柱和2个相同三角楔胶合成型的简单工艺。进一步模拟发现,两种整形系统所得到的均匀度和线宽一致。     

Interference microscopy of femtosecond laser written waveguides in phosphate glass

By focusing fs-laser radiation in the volume of a transparent material the refractive index can be changed locally, leading to 3-dimensional waveguiding structures. Waveguides are written in phosphate glass (IOG from Schott) at a depth of 100 μm below the surface. The pulse energy and the scan velocity are varied. For the first time the optical path difference caused by the waveguides and therefore the refractive index distribution of the waveguides and their cross sections are determined using interference microscopy. The optical path difference measured in the written structures and their cross sections is analyzed by a phase-shift algorithm. Thus, the refractive index distribution both along a line perpendicular to the waveguide and in the plane of a cross section is determined. The results are visualized as 2-dimensional graphics. Several regions of opposite sign of the refractive index change are observed in the cross sections of waveguides generated by femtosecond laser pulses. The number and the size of these regions are increasing with increasing pulse energy and decreasing scan velocity.     

Optical loss measurements in femtosecond laser written waveguides in glass

The optical loss is an important parameter for waveguides used in integrated optics. We measured the optical loss in waveguides written in silicate glass slides with high repetition-rate (MHz) femtosecond laser pulses. The average transmission loss of straight waveguides is about 0.3 dB/mm at a wavelength of 633 nm and 0.05 dB/mm at a wavelength of 1.55 μm. The loss is not polarization dependent and the waveguides allow a minimum bending radius of 36 mm without additional loss. The average numerical aperture of the waveguides is 0.065 at a wavelength of 633 nm and 0.045 at a wavelength of 1.55 μm. In straight waveguides more than 90% of the transmission loss is due to scattering.     

用于激光光束整形的连续自由曲面的设计

设计一个有效的连续自由曲面,将给定的准直激光光束映射成任意模式的目标照明,仍然是一个具有挑战性的问题。提出一种基于光线映射来构造连续自由曲面的方法,通过计算光源与目标区域两者辐照度分布之间的光线映射关系,构造出光滑连续的自由曲面。对于准直输入光束,采用最优运输法计算光源与目标之间的光线映射;根据折反射定律和可积条件,推导出用于求解可积映射关系和连续自由曲面的一般条件;证明在小角度近似的情况下,基于最优运输法得到的光线映射关系可以满足可积条件;通过逐线积分法求解出满足一定边界条件的线性平流方程,从而完成连续自由曲面的构造。实验表明,利用逐线积分法求解标准积分方程构造出的连续自由曲面能实现任意模式的目标照明,能量利用率达98.95%。结果表明,基于最优运输法得到的光线映射关系在自由曲面和目标平面之间的距离较大时近似可积,提供了一种有效的构造连续自由曲面的方法。     

Thermal optimization and erasing of Nd:YAG proton beam written waveguides

We report on how the optical and structural properties of Nd:YAG proton beam written waveguides are modified when they experienced annealing treatments from 50 °C to 950 °C. The microstructural changes caused in the vicinity of the nuclear damage region were found to be stable up to 700 °C, so that higher annealing temperatures lead to a complete waveguide erasing. Before this "erasing" temperature, the partial thermal-induced defect recombination reduces the propagation losses, reaching its minimum value (below 1 dB/cm) after a 400 °C thermal annealing.     

Near-diffraction-limited laser beam shaping with diamond-turned aspheric optics

We used a pair of diamond-turned CaF(2) aspheres to convert the pure TEM(00) Gaussian spatial profile output of a diode-pumped Nd:YAG laser oscillator into a super-Gaussian intensity profile with a nearly flat phase front. The resulting super-Gaussian beam was nearly diffraction limited with an M(2) of 1.75; in the near field the 5-mm diameter beam retained a nominally flat-top intensity distribution without significant diffraction peaks for an excellent working distance of more than 50cm. A 10% improvement in amplifier-energy extraction obtained by use of the reshaped beam is demonstrated.     

Silica-taper array for beam shaping of high power laser diode bar

A low-cost, easy producing and novel beam shaping system for concentration and homogenization of a high power laser diode bar (LDB) beam is demonstrated by experiment and simulation. It consists of a silica-taper array (beam shaper) and a silica-taper (beam integrator) which are fabricated by using chemical etching technique. By using this device, the output beam of LDB is reshaped to a small spot with uniform intensity and angular distributions, and could be coupled into a 200 ??m silica fiber.     

Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations

The effect that femtosecond laser filamentation has on the refractive index of Nd:YAG ceramics, and which leads to the formation of waveguide lasers, has been studied by micro-spectroscopy imaging, beam propagation experiments and calculations. From the analysis of the Nd³⁺ luminescence and Raman images, two main types of laser induced modifications have been found to contribute to the refractive-index change: (i) a lattice defect contribution localized along the self-focusing volume of the laser pulses, in which lattice damage causes a refractive-index decrease, and (ii) a lattice strain-field contribution around and inside the filaments, in which the pressure-driven variation of the inter-atomic distances causes refractive-index variations. Scanning near-field optical-transmission and end-coupling experiments, in combination with beam propagation calculations, have been used to quantitatively determine the corresponding contribution of each effect to the refractive-index field of double-filament waveguides. Results indicate that the strain-field induced refractive-index increment is the main mechanism leading to waveguiding, whereas the damage-induced refractive-index reduction at filaments leads to a stronger mode confinement.     

平面激光诱导荧光实验中激励激光的光束整形

分析了激励激光光强分布对平面激光诱导荧光（PLIF）实验中荧光强度的影响。基于柱面微透镜列阵设计了一套激光片状光束匀滑整形系统,并根据PLIF实验的具体要求,通过光线追迹方法优化了系统参数。建立了片状光束整形实验系统,对染料激光进行了匀滑整形,获得了不均匀性〈4%的均匀片状光束,满足了PLIF实验所需。在此基础上建立了PLIF实验系统,获得了酒精灯火焰和CH4/air预混火焰中OH的二维荧光分布。     

Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit

We describe a low-loss single-mode waveguide in planar light-wave circuit (PLC) glass doped with boron and phosphorus, which is more difficult to write than pure-silica glass. The written waveguide has a rectangular core, a symmetric near-field pattern, and a propagation loss of 0.35 dB/cm. The loss that originates from the mode-field mismatch between the mode-field diameters of the written and the PLC waveguides is less than 0.1 dB/point. In addition, we successfully connected PLC waveguides with a 500-microm-long waveguide written with a laser. The laser-written waveguide can flexibly connect PLC waveguides with a low coupling loss.     

Ring beam shaping optics fabricated with ultra-precision cutting for YAG laser processing

In this study, a method for generating ring intensity distribution at a refraction-type lens with an aspheric element was proposed, and the beam shaping optical element was finished using only ultra-precision cutting. The shape of the optical element and its irradiance pattern were determined from numerical calculation based on its geometrical and physical optics. An ultra-precision lathe was employed to fabricate beam shaping optical elements, and acrylic resin was used as the material. The transmittance of an optical element (a rotationally symmetrical body) with an aspheric surface fabricated using a single-crystal diamond tool was over 98%, and its surface roughness was 9.6 nm Ra. The method enabled the formation of a circular melting zone on a piece of stainless steel with a thickness of 300 μm through pulse YAG laser (λ 1:06 μm) processing such that the average radius was 610 μm and the width was 100–200 μm. Circular processing using a ring beam shaping optical element can be realized by single-pulse beam irradiation without beam scanning.     

Iterative algorithm for the design of diffractive phase elements for laser beam shaping

An improved iterative algorithm for designing diffractive phase elements for laser beam shaping in free space is presented. The algorithm begins with the Gerchberg-Saxton approach to obtain a stable solution. This is followed by several new iterations, in which modified constraining functions are imposed in the Fourier domain while the phase distribution of each iteration remains unchanged. For super-Gaussian beam shaping suitable for inertial confinement fusion applications the mean-square errors of the amplitude and the intensity profile of the entire beam fitted to the corresponding parameters of the 12th-power super-Gaussian beam are approximately 0.035 and 9.75x10(-3), respectively. Approximately 97.4% of the incident energy is converged into the desired region.     

光电偶效应和光束整形对激光稳定气体保护焊接的增益

为了开发和改进激光诱导稳定焊接加工技术,需要通过激光辐射使电弧的导电率达到最大值。光电偶效应是控制该过程的主导因素,该过程的优化将会保证电弧的稳定性。光电偶效应提高了等离子体粒子电离的概率,从而提高了电弧的导电率。激光光子和氩原子之间的电子-原子碰撞相互作用产生了带电粒子。电离率越高,电弧的导电率就越高。为了充分利用光电偶效应,我们还应考虑工件上的光束焦点位置、光束形状和激光波长因素。     

High-damage-threshold static laser beam shaping using optically patterned liquid-crystal devices

Beam shaping of coherent laser beams is demonstrated using liquid crystal (LC) cells with optically patterned pixels. The twist angle of a nematic LC is locally set to either 0 or 90° by an alignment layer prepared via exposure to polarized UV light. The two distinct pixel types induce either no polarization rotation or a 90° polarization rotation, respectively, on a linearly polarized optical field. An LC device placed between polarizers functions as a binary transmission beam shaper with a highly improved damage threshold compared to metal beam shapers. Using a coumarin-based photoalignment layer, various devices have been fabricated and tested, with a measured single-shot nanosecond damage threshold higher than 30?J/cm2.     

Study on the beam shaping of high-power laser diode bars

Based on the Collins form, the intensity distribution of the resulting beam is derived when Gaussian beams of a high-power laser diode bar pass through a paraxial optical system. Then flattop beam profiles are obtained by a concave cylindrical lens, and the propagation properties are discussed in detail, such as the peak-intensity axis inclined at an angle γi. In addition, an expression to calculate beam angular width is presented.