InnoSlab混合腔输出光束质量的理论研究

对InnoSlab Laser用混合腔的输出光束质量问题从热透镜效应和腔镜的不对准两个方面的影响进行理论分析,并从远场光强分布、远场发散角、光腰半径、光束质量因子M²值和桶中功率曲线等几个角度进行了讨论,特别是离轴非稳腔方向上腔镜倾斜对光束质量的影响,利用M²值和PIB曲线两个参数共同评价非稳腔的光束质量,对目前并无统一标准的非稳腔光束质量评价问题提供了有意义的参考. 关键词： InnoSlab 混合腔 光束质量 桶中功率     

Degradation of beam quality and depolarization of the laser beam in a step-index multimode optical fiber

The characteristics of a laser beam are altered during propagating through large-core multimode optical fibers. The distribution of modes excited by the input laser beam is modified by means of mode coupling on transmission through the fiber, leading to the degradation of beam quality and the depolarization of the delivered beam. The relationship between the beam quality factor (M²) of output beam from a large-core multimode fiber and the fiber length, as well as the relationship between the degree of polarization (V) of output beam from such a fiber and the fiber length, are introduced in this paper. When a laser beam was well launched into a large-core step-index multimode fiber, M² of the output beam was a compound tanh function of the fiber length. A linear polarization beam that well launched into such fiber suffered depolarization. The V of the output beam was an exponent function of fiber length. And the misalignment between beam axis and fiber axis made the beam quality degrade faster but made no difference of the utmost M² in the aligned and misaligned conditions. Also, the misalignment condition made the polarization of output beam degrade faster.     

Performance of a 80 W copper vapor laser with “alignment free” unstable CAT-EYE resonator and other configurations using intra-cavity apertures

Performance of a kinetically enhanced copper vapor laser (KE-CVL) with various stable/unstable “alignment free” CAT-EYE resonator configurations are presented here in this paper. The laser used in the experiment was a 45 mm bore (∼2 l discharge volume) kinetically enhanced copper vapor laser developed in our laboratory and capable of generating maximum power of ∼80 W (at ∼9.8 kHz). The efficiency of the laser was ∼1.4% and beam divergence of ∼3.5 mrad in a plane-plane standard multimode cavity. For the first time performance of unstable CAT-EYE resonator is demonstrated with a CVL/KE-CVL. On using unstable CAT-EYE resonator the divergence of the laser beam reduced to ∼0.22 mrad (∼20-fold reduction as compared to conventional plane-plane cavity), ∼40 W output power and with excellent misalignment tolerance. The laser output power was found to be within ∼5% drift/decline with misalignment angle of about 4 mrad between the mirrors. This is a significant improvement in comparison to standard conventional unstable resonator (M ∼ 50) CVL where ∼0.5 mrad divergence is achieved with power drift/decline of about 45% at ∼4 mrad misalignment angle.Off-axis unstable CAT-EYE unstable resonator was also demonstrated for the first time with further reduction in beam divergence to ∼0.13 mrad and with output power of ∼28 W. The misalignment tolerance was found to be highest in case of off-axis unstable CAT-EYE resonator with decline/drift in laser power of only ∼10% for misalignment angle as high as ∼8 mrad. Performance with intra-cavity apertures in plane-plane type CAT-EYE resonator for transverse mode control is also presented for the first time in CVLs. It is observed that the laser beam divergence reduces significantly to 1.25 mrad (a factor of 2) on using an aperture of ∼3.5 mm at the CAT-EYE reflector as compared to its normal (R = F = d) configuration without aperture. In case of stable CAT-EYE resonator the average beam divergence reduces from 8 mrad to 4 mrad (factor of 2) on using intra-cavity aperture of about 3 mm. It was also observed that high misalignment tolerance was retained on using intra-cavity apertures in almost all the CAT-EYE resonators. Use of intra-cavity mesh was also demonstrated for the first time with stable CAT-EYE resonator for improving the beam focus-ability. Average beam divergence was reduced by a factor of 2.5 (from 8 mrad to 3 mrad) on using intra-cavity mesh. These new configurations in CAT-EYE resonators in KE-CVLs are found to be effective in improving and controlling the laser beam divergence significantly with additional characteristic of high misalignment tolerance.     

Beam parameters,mode structure and diffraction losses of slab lasers with unstable resonators

The properties of unstable resonators in on-axis and off-axis geometry were investigated both theoretically and experimentally. Diffraction loss, mode structure, beam quality and misalignment sensitivity were measured in single-shot operation with a gas-cooled Nd: YAG slab laser (4×12×100 mm³) and compared with theoretical results obtained by solving the Fresnel integral equation numerically. The excellent agreement allowed detailed resonator optimization. Furthermore, the resonator performance in high-power operation was investigated with two water-cooled Nd: YAG slab lasers (6×25×163 mm³ and 7×26×191 mm³) capable of 670 W of output power. Beam quality near the diffraction limit and a maximum output power of 475 W was achieved with an on-axis unstable resonator with variable-reflectivity mirror.     

Analysis of beam quality for the laser beams after spectral beam combining

The beam quality of the laser beams after spectral beam combining (SBC) has been analyzed in this paper. Based on the propagation model of the spectral beam combining system, the expression for the output field of an individual beam passing through the spectral beam combining system with lens aberration has been given and the intensity distribution of the combined beam has been studied by the principle of incoherent superposition. Consequently, according to the intensity second-order moments method, the M²-factor of the combined beam has been calculated and the effect of lens aberration on the characteristics of the combined beam has been analyzed quantitatively. It can be shown that the SBC system can improve the beam quality of laser array significantly, and the M²-factor of the combined beam passing through the ideal spectral beam combining system is almost the same as that of an individual beam. For the spectral beam combining system with lens aberration, the spherical aberration has greater effect on the off-axis beam than on the on-axis beam, and the beam quality of combined beam degrades with increase in lens aberration.     

Investigation of the beam propagation in a pumped laser rod

A method investigating the beam propagation in a pumped laser rod is proposed. In this method, the pumped laser rod in a resonator is evenly divided into N segments along the laser rod axis, and each segment is considered as a small thermal lens with thermal focus length of f. Accordingly, the beam radius distributions in the laser rod for the symmetric and asymmetric resonators are thus calculated, respectively. The beam radius distribution in the whole resonator is also calculated. Moreover, the calculated beam distribution in the whole resonator and in the rod is also described in detail.     

利用特征向量法分析有源失调腔的2维模场

 利用一种用于光腔模式及光束传输模拟计算的特征向量法计算有源腔的2维失调,通过对谐振腔几何关系的求解,以及对增益进行薄层模型处理,最后利用特征向量法计算有源腔失调后的模式分布,发现失调造成了模式强度分布不均匀,并带来模式阶数的改变。计算了相应的光束质量因子,结果表明:在一定失调范围内,失调可能会带入新的模式竞争;谐振腔在一定范围的失调情况下,各阶模式的光束质量可能变好,也有可能变差,随着模式阶数的增加光束质量整体趋势是越来越差;原来简并的模式可能不再简并。该方法可以为计算失调后谐振腔的模场带来方便。     

Beam propagation factor of partially coherent beams in gain or absorbing media

The definition of second-order intensity moments in the spatial domain and spatial frequency domain has been generalized for the case that the linear gain or absorbing media are included, where the wave number is generally complex. The formula for beam propagation M²-factor of partially coherent beams in linear gain or absorbing media has been given. The partially coherent flat-topped Schell-model beam is taken as an example. The closed-form expression for the beam propagation M²-factor of partially coherent flat-topped beam in gain or absorbing media has been derived. The changes of the M²-factor in media have been discussed with numerical examples. It can be shown that the M²-factor of flat-topped Schell-model beams in gain or absorbing media depends on the coherent parameter β, the coherent length σ₀, the beam order M, the propagation distance B, the imaginary part of the wave number K_i, as well as the real part of the wave number K_r.     

Beam quality factor for coherently combined fiber laser beams

The beam quality factor for a coherently combined beam is studied in detail. A theoretical analysis and a numerical calculation are given to illustrate that the M² factor is not a proper means for evaluating the beam quality of a coherently combined beam. The beam propagation factor is introduced to evaluate the beam quality. The effect of phase error on the beam quality is also studied. Results indicate that the beam quality of a coherently combined beam depends mainly on the fill factor of the laser array and not on the number of lasers. It is also revealed that the allowed phase error does not change with the number of lasers in order to ensure the energy encircled in a certain bucket.     

Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor

In this paper, propagation of a Gaussian laser beam through turbulent atmosphere is evaluated numerically. The beam quality factor for the propagated beam has been estimated for different turbulent conditions that are characterized by parameter C_n. The calculations show that the beam quality can be affected dramatically by atmospheric turbulence and the laser beam size and wavelength have major role in the results. Furthermore, the propagation of laser beam in longer distance results in more spatial perturbation of the beam. The results of these calculations and evaluation of beam quality factor M² can be used for estimating the refractive index structure parameter (or atmosphere turbulent parameter) C_n.     

Beam propagation of a higher-order cosh-Gaussian beam

On the basis of the second-order moment, the beam propagation of a higher-order cosh-Gaussian beam has been investigated. Two analytical expressions of the M² factor have been derived, which corresponds to the parity of the beam order n. The M² factor is determined by the beam order n and the parameter δ. The influences of the beam order n and the parameter δ on the M² factor are illustrated with numerical examples. The analytical kurtosis parameter has also been presented. The analytical formula is further simplified in the source plane and the far field, respectively. With given appropriate values of n and δ, the kurtosis parameter in the far field is smaller than 3. This research is helpful to the practical applications of a higher-order cosh-Gaussian beam.     

束旋转90°对束变换环孔腔输出性能的影响

 使用积分方法和差分方法结合的快速计算方法，在实际燃烧驱动氟化氢化学激光器增益介质沿径向分布不均匀的情况下，考虑在光束变换环形孔径激光谐振腔的紧束段引入光束旋转90°对其输出性能的影响。计算结果显示：在无腔失调的情况下，在紧束段引入光束旋转对束变换环孔激光谐振腔输出功率及光束质量的改善并不显著；在存在腔失调的情况下，紧束段光束旋转对于输出功率和光束质量的改善有显著效果。     

Generalized beams in ABCDGH systems

For a generalized beam at the source plane passing through co-located aperture and a propagation path consisting of an off-axis x-y asymmetric ABCDGH system, the receiver plane irradiance expression is derived using the Collins integral. A collection of source beam profiles that are obtainable from the generalized beam formulation are illustrated. Plots are given for viewing the progress of selected generalized beam types along the propagation axis, containing a single thin lens, co-centric and misaligned in the x-direction. The received power falling onto a finite aperture surface is calculated for various misalignment situations.     

Generalised ABCD matrix treatment for laser resonators and beam propagation

A generalised ABCD matrix treatment for laser resonators and beam propagation is developed for computer programming. In this treatment, imaginary parts are introduced into the matrixes for all optical elements, and the beam quality factor M² and the index of the medium are also taken into account. When the imaginary parts of the complex matrix are zero and the beam quality factor M² and medium index are unity, the stated method is transformed back into the more classic ABCD matrix format in which the fundamental-mode Gaussian beam transmits through real elements in the vacuum. Based on this method, laser resonator software is realised by the VB programme language. The software can be used to analyse and design stable/unstable standing/travelling cavities, phase-conjugate cavities and beam transformations.     

Beam quality factor of mixed modes emerging from a multimode step-index fiber

The beam quality factors (or M² parameter) of coherent and incoherent superposition of the several lower-order LP modes emerging from a step-index fiber have been calculated by using the second-order moment method. The results indicate that, for an individual LP mode, the M² parameter takes its maximum value when the normalized frequency V of the step-index fiber approaches the cut-off frequency, and it gradually becomes constant as V increases. In the case of incoherent superposition, the larger the fraction intensity carried by the higher-order mode, the larger the beam quality factor M². Under certain circumstances, the value of the M² parameter of the mixed mode that comprises several LP-modes contents may become even smaller and closer to the ideal Gaussian beam than that of the fundamental mode in a step-index fiber. However, in the case of the coherent superposition, the value of the M² parameter of the mixed mode may be greater than that of the higher-order constituent mode. The results reported here could be helpful for the application of the high-power fiber laser systems.     

High beam quality in a HyBrID copper laser operating with an unstable resonator made of a concave mirror and a plano-convex BK7 lens

This paper presents a very simple unstable resonator, made of a concave mirror (total reflector) and a bare plane–convex BK7 lens working as a convex coupling mirror, which is quite efficient for HyBrID copper laser. In addition to a good quality factor (M²=4.9), experimental results showed that it is possible to control the laser output power by introducing a variable aperture iris inside the cavity, close to the coupling lens, without spoiling beam quality. A rough theoretical model helped to explain these results as a combined effect of unstable resonator plus radial gain distribution.     

Thermal lens determination of LD end-pumped solid-state laser with stable resonator by slit scanning method

A simple method to determine the thermal focal length of LD end-pumped solid-state laser with stable resonator is presented. The M² factor describing the quality of the beam can be obtained by scanning a slit through the multi-mode Gaussian beam field. The waist width of the beam and the corresponding TEM₀₀ under the same parameters of laser are then deduced through the law of multi-mode Gaussian beam propagation. Based on the standard matrix theory of stable resonator, the thermal focal length of the gain medium can be easily achieved. To show the application of this approach, the thermal focal length of an LD pumped Nd:YVO₄ laser is measured and the experimental results are in agreement with the theoretical prediction.     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

The LD end-pumped Q-switched solid-state laser design software based on the adaptive method

In the LD end-pumped acousto-optic (A-O) Q-switched solid-state laser, according to the requirements of users on the laser peak power, the pulse width, the repetition rate and the beam quality factor M², if the main parameters of the pumping source and the laser resonator can be pre-designed by a software, will effectively guide experiments, and save cost. A kind of laser design software is introduced in this paper, which is based on the adaptive adjustment method and using MATLAB/C mixed programming. According to the user requirements, a compact LD end-pumped A-O Q-switched Nd:YAG laser which peak power is 100-kW-class can be designed and actual outputs can be calculated based on the design results. Drawing the laser pulse waveform, analyzing of the thermal effect in laser gain medium and drawing the temperature distribution map, exporting and saving the data are the additional functions of this software.     

腔镜失调与面型误差对光束质量影响研究

 在准确测量腔镜面形加工精度的基础上，通过光学模拟软件ZEMAX实现了氧碘化学激光器折叠虚共焦非稳腔的光学建模，利用光腔模型进行了腔镜面形误差对光束质量影响的研究以及腔镜失调对光束波前影响的分析，在空腔的情况下利用调腔He-Ne激光进行了光束质量测量实验。实测结果与建模数据基本符合，验证了该方法的可行性。