激光谐振腔设计软件的算法研究与计算机实现

为使激光工作者可以方便地进行谐振腔诸如热透镜、容差等参量的优化分析与设计,研究了激光谐振腔设计软件的算法并在计算机上得到实现.使用ABCD矩阵方法分析激光光束的传输与变换.为使分析和设计更具有一般性和通用性便于计算机编程,考虑矩阵元素均为复数的情况,同时将光束质量因子M2和介质中的光束传输考虑在激光谐振腔模的传输变换当中,这样当矩阵元素虚部都为零,而M2=1和介质折射率为1时,就可以过渡到通常的基模高斯光束在空气中经实元件矩阵传输变换.并以此为基础使用VB在国内成功开发出具有稳定驻波腔、稳定行波腔、非稳驻波腔、非稳行波腔、相位共轭腔、光束传输变换等多种功能的可视化谐振腔软件.     

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.     

Kerr lens effects in a folded-cavity four-mirror linear resonator

The Kerr-lens model locking of a folded-cavity four-mirror linear Ti: sapphire laser is simulated by applying the ABCD ray-tracing technique for a Gaussian beam. The intensity dependent Kerr-lens ABCD matrix of the Brewster-plate shaped active medium is derived. A split-step parabolic refractive index model is used. the astigmatism compensation condition is derived from the ABCD ray-tracing. Simulations are carried out for a symmetric resonator and an asymmetric resonator design. Hard-aperture loss mode locking and soft-aperture gain mode locking are discussed. The optimum design parameters (slit position for hard-aperture loss mode locking, pump beam focusing for soft-aperture gain mode locking, gain cavity spacing, gain medium position) for Kerr-lens mode locking are determined.     

An explicitly solvable case of the construction of the fundamental cavity mode in the form of a Gaussian beam with a complex astigmatism

An analysis is carried out of the ring cavities whose fundamental modes represent Gaussian beams with complex astigmatism. The analysis is made for the case where the block B or C in the cavity ray matrix ABCD of dimension 4×4 is a symmetric nondegenerate matrix. Explicit formulas are obtained, which permits the expression of beam characteristics directly in terms of the cavity ray matrix without the laborious process of finding its eigenvectors. The results obtained in the study can be used for controlling astigmatism in lasers and laser systems, the calculation of polarization of three-dimensional active media in linear and ring optical cavities of complex configuration, etc.     

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.     

Beam propagation in a linear or nonlinear lens-like medium usingABCD ray matrices: the method of moments

We derive exact expressions for the evolution of the second order moment of the intensity distribution of an arbitrary beam propagating in a nonlinear Kerr medium with a quadratic index profile. The results can be recast in terms of theABCD matrix formalism after introducing a generalized complex radius of curvature,Q(z). Various definitions of the beam quality factor are introduced. Numerical simulations reveal the interest of this approach.An Invited Paper     

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.     

Tailored TEMp0 beams for large size 3-D laser prototyping

The Laser-Lithography technique allows the fabrication of complex objects having microsizes by selectively solidifying polymeric materials layer by layer upon exposure to a focused Gaussian laser beam having a beam propagation factor M²=1. We can expect that extension of this technique to large sizes 3-D prototyping comes up against a large increase in the design time. A possible solution is the increase in the focused spot size, but unfortunately at the price of a great reduction in the longitudinal resolution due to the resulting increase in the depth of focus. To overcome these difficulties, we propose the use of a rectified TEM_p0 beam allowing the obtaining of a Gaussian beam intensity profile in the focus plane of a lens. The reshaped TEM_p0 beam has a beam propagation factor M²≈(2p+1), and this yields to a relative improvement of the longitudinal resolution although the spot size is increased for reducing the processing time.     

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.     

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.     

Near-diffraction-limited segmented broad area diode laser based on off-axis spectral beam combining

The beam quality of a 500-μm-wide broad area diode laser with five active segments has been improved beyond the beam quality of the individual segments. The principle of this new laser system is based on off-axis feedback in combination with spectral beam combining. By using a double-feedback scheme we are able to improve the beam quality of the laser by a factor of 23 from M²=55 for the free-running diode laser to M²=2.4 for the laser with feedback at a drive current of 2.2 A. The improved M² value is a factor of 3.4 below M²=8.2 for a single free-running segment. This is the first time that the beam quality of a segmented broad area diode laser has been improved beyond the beam quality of the individual segments. PACS 42.55.Px; 42.60.Da; 42.60.Jf     

Effects of the deformation of reflection volume Bragg gratings on the M-factor of super-Gaussian laser beams

When high-power laser beams pass through a volume Bragg grating (VBG), the surface of VBG occurs distortion because of thermal effects, and it results in the decline of the grating’s performance. Considering distortion of the surface induces differences of the index and period, the scalar wave equations for super-Gaussian (SG) laser beams propagating in the reflection VBG have been solved by using finite-different and sparse matrix methods. The changes of the total power reflection coefficient, the beam width, the far-field beam angle and the M²-factor for the laser beams through the reflection VBG with deformation have been analyzed quantitatively. It can be shown that the deformation of the VBG affects evidently on the intensity and phase distributions, the total power reflection coefficient, the beam width, the far-field divergence angle and the M²-factor. The beam width, the far-field divergence angle, and the M²-factor of the output beams increase significantly with the distortions of the grating. The influence of the distortions of the VBG on the power reflection coefficient, the far-field divergence angle and the M²-factor of the output beams are smaller for higher beam orders.     

Theoretical calculation of beam quality factor of large-mode-area fiber amplifiers

In order to evaluate a fiber amplifier’s output beam quality, we have explored the beam quality factor calculation. A theoretical beam quality factor calculation method is presented in this paper. The method bases on modal power decomposition, laser rate equations and Fourier diffraction theory. Through the rate equations, each modal power weight factor at the fiber output facet is obtained. By the modal power decomposition, the optical field at the fiber output facet is established. Finally, running Fourier transformation, the beam diverging state in free space and corresponding M ² parameter are obtained. The calculation process is verified with applying it to working out the beam M ² parameters of large-mode-area (LMA) fiber amplifier system under different conditions. The numerical results help us well know and predict the out beam property. Some obtained results are also accord with other reporting outcomes.     

Investigation of CO2 laser beam modulation by rotating polygon

A beam-modulating system based on the rotating polygon has been proposed in a previous experimental work [14]. The aim was to improve the quality and efficiency of CO₂ laser surface texturing. Based on the generalized ABCD law, the focusing characteristics of a real beam through the modulating system are investigated in this paper. By introducing a precise defocusing, the velocity synchronization between the focal spot and the workpiece can be realized. Micro-dimples of nearly circular shape can be achieved on the surface. Surface texturing of mill roll has been performed. The experimental and theoretical results are in good agreement.     

An alternative approach to determine the spot-size of a multi-mode laser beam and its application to diode laser beams

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.     

Propagation of flat-topped beams

The propagation of flat-topped beams passing through paraxial ABCD optical system is investigated based on the propagation formulas of Gaussian beam. The focal shift of focused coherent flat-topped beam is also studied in detail. Analytical expressions of the M² factor and the far-field intensity distribution for flat-topped beams are derived on the basis of second-order moments.     

High-power Nd:YVO4/BaWO4 intracavity Raman laser emitting at 1,103?nm

A compact BaWO₄ Raman laser is realized with a diode-end-pumped acousto-optically Q-switched YVO₄/Nd:YVO₄ laser. Based on the Raman shift at 332?cm^?1 of BaWO₄, first-Stokes generation at 1,103?nm is generated. At a pump power of 11.3?W and a repetition rate of 45?kHz, an average power of 1.59?W is obtained. The pulse width is measured to be 36.8?ns and the beam quality factor (M ²) in the horizontal and vertical directions is determined to be 1.56?±?0.1 and 1.41?±?0.1, respectively. The thermal focal lengths of the laser medium and Raman medium are calculated theoretically.     

Matrix formulation of the beam quality of the Hermite-Gaussian beam

Based on the M ²-parameter of Hermite-Gaussian beam, we deduced the matrix formulation of the beam quality for nonsymmetric two-dimensional Hermite-Gaussian beam, which at an arbitrary azimyth angle α. And coupled beam radius square, coupled M ²-parameter also have been introduced. The beam radius versus azimuth angle α at different positions has been presented by numerical simulation; and the track of M ²-parameter versus azimuth angle α has been given. The M ²-parameter matrix is universal and available both in the theoretical analysis and the practical measurement of the beam quality for a arbitrary two-dimensional nonsymmetric higher-order Gaussian beam.     

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.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.