High-power solid-state lasers with unstable resonators

The thermal lensing properties of stable and unstable resonators are compared and rules are given for the design of optimized unstable resonators containing a focusing rod. Experimental verification with a high-power Nd: YAG system proved that for unstable resonators the restricting relationship between beam quality and output power no longer holds. Careful resonator design enables high output power to be extracted with unstable resonators without destroying the output couplers.     

Recent developments in laser resonator design

The problems related to resonators suitable for generation of diffraction-limited beams of high power or energy, and a few of the most significant recent solutions, are reviewed. In particular, this paper is addressed to two promising resonator configurations developed mainly for Nd:YAG (yttrium aluminium garnet) lasers: dynamically stable resonators of minimum misalignment sensitivity for lasers with a strong thermal lensing in the active rod and unstable resonators with variable reflectivity output mirrors of super-Gaussian profile. For both cases experimental data and simple design guidelines are discussed.     

Numerical characterizations of unstable optical resonators and evaluation of the geometry effects

Unstable resonators have been widely used in high-power gas lasers as well as solid-state lasers. The phase and the spatial distribution of intensity of these lasers are very important in some applications such as material processing. In this paper, unstable resonators with three different geometries have been characterized numerically and the results have been compared and evaluated. Based on the Fresnel-Kirchhoff integral, the two-dimensional phase and intensity have been calculated for three different positive branch unstable resonators. The results show that the resonators with rectangular geometry have the best performance for near-field as well as far-field intensity, which is more suitable for material processing. The calculations also show that the maximum output power can be extracted from the rectangular resonator with spherical surface, while the circular resonator with spherical surface has minimum output power. The results also show that the laser has a higher divergence for the cylindrical resonator in compare with those for the circular and rectangular resonators.     

高光学质量,高平均功率非稳腔Nd：YAG激光器

在分析含热透镜的非稳腔固体激光器普遍特性的基础上，分别定义了几何放大率和输出曲率半径的热敏感度，结合腔镜失调敏感度而成为设计该类谐振腔的重要依据，据此，进一步改善和发展的新型的棒成像非稳腔。     

具有均匀相位耦合输出镜非稳腔的模场分析

 利用Prony[1]方法计算均匀相位输出耦合镜非稳腔的输出模场分布及远场方向性,分析了模式分辨率和光束远场发散角与系统各参数之间的关系, 理论计算得到的结果表明,可以在小放大倍率（M=1.3）情况下得到质量达到衍射极限的输出光束,与传统非稳腔比较,这种新型的谐振腔在改善氧碘化学激光器光束质量方面有一定的应用前景。     

Investigation of beam characteristics in toric unstable optical resonator

In this paper the characteristics of the output beam of a toric unstable resonator are investigated. Based on the Fresnel–Kirchhof integral and using numerical methods, the performance of toric unstable resonators is simulated and its output beam characteristics are also evaluated. Geometrical resonator parameters, i.e. Fresnel number and magnification as well as the output coupler diameter, are considered in this investigation. The radial and azimuthal modes of the resonator are calculated and the modal behavior of the resonator is described according to geometrical parameters. The power extraction for each specific laser mode has also been inspected by calculating the finesse factor. Using an iteration mode convergence diagram, the mode discrimination of the resonator is investigated.     

Nonlinear dynamics of planar gyrotrons with transverse diffraction coupling of radiation

We propose that the planar geometry of the interaction space and transverse (relative to the direction of translatory motion of electrons) power extraction be used for increasing the integrated radiation power of short-wavelength gyrotrons. The advantage of such a scheme over the traditional cylindrical geometry of gyrotrons is the possibility to ensure coherence of radiation for a large superdimensionality factor due to diffraction mechanism of mode selection in the open transverse coordinate and locking of radiation from various fractions of the ribbon-shaped polyhelical electron beam by transverse energy fluxes. Simulation of the non-linear dynamics of a planar gyrotron demonstrates the possibility of attaining the output power of hundreds of kilowatts at frequencies of up to 1 THz. A further increase in the output power to the megawatt level can be attained by using resonators with a nonuniform profile, for which the gap between the plates increases from the center to the periphery. Such a configuration is analogous to unstable optical resonators used in some powerful lasers.     

The application of an unstable resonator to a high-pressure CW CO2 laser

Unstable resonators provide high quality beams of high output power needed for material processing. We have developed a CO₂ laser of over 5 kW for material processing with an unstable resonator of positive confocal configuration under high-pressure, sealed condition. High quality beams with high extraction efficiency of the power were obtained and deep pentration was attained in welding tests.     

Multichannel laser resonators — an experimental study

The output characteristics of several large-area multichannel unstable resonators are presented. The conventional unstable resonator and a novel toric unstable resonator, in both confocal and nonconfocal configurations, have been studied. Output beam profiles, optical energy extraction, beam focusability, resonator alignment properties and polarization states of the various resonators have been analysed in depth.     

COIL简化模型计算

 采用简化动力学、增益模型，分析了常规虚共焦非稳腔和含屋脊镜折叠非稳腔这两种腔型在COIL中的应用，计算表明，折叠腔在改善COIL近场光强分布均匀性和提高近场输出功率方面明显优于常规腔。     

高功率激光器腔镜热变形对输出光束质量的影响

利用有限元分析法结合Fox-Li迭代法,考虑腔内本征模式与腔镜热形变的相互耦合作用,计算模拟了正支共焦非稳腔的本征模式分布,定量分析了高功率激光器腔镜热变形对输出光束质量的影响,重点讨论了腔镜热变形所引起的腔内本征模式相位特性的变化,并从波前功率谱密度、Zernike像差系数及光束质量值等角度对腔镜发生热形变前后的激光器输出光束的光束特性进行比较分析。研究结果表明:高功率激光器腔镜热形变对输出光束的光束质量会产生一定的影响,且随着激光输出功率的增大,镜面热形变引起的输出光束波前相位高频比例及Zernike高阶像差均会有所增大,波前畸变程度也明显变大,光束质量逐渐变差。     

腔内像散扰动对正支共焦腔模式影响的数值分析

 针对激光器出光过程中腔内像差扰动带来的输出光束质量和光束能量下降问题,分析了腔内像差扰动对非稳腔模式的影响,并采用数值迭代法计算了理想情形和腔内像散扰动对无源正支共焦腔输出模式强度和相位分布的影响,进一步采用Zernike模式法对光束相位进行了像差拟合,得到了前35阶Zernike像差系数、点扩散函数(PSF)分布和环围能量曲线,计算了腔内像散扰动量与远场Strehl比的关系。结果表明：对小菲涅耳数正支共焦腔,腔内像散扰动对输出光束强度和相位分布均有明显影响,相位分布中一些高阶Zernike像差也有所增大。因此在进行腔内像差校正时,应优先考虑此类像差的校正。     

High-power terahertz-range planar gyrotrons with transverse energy extraction

To increase the output power of terahertz gyrotrons to several hundred kilowatts, we suggest using a planar geometry of interaction space with a sheet electron beam and transverse energy extraction. An advantage of this scheme in comparison with conventional cylindrical geometry is the possibility to ensure effective mode selection over the open transverse coordinate in combination with radiation outcoupling that leads to a substantial reduction of Ohmic losses. Similar to unstable resonators in optics for further growth of the radiation power it is beneficial to introduce waveguide tapering.     

变反射率镜非稳腔的研究进展

回顾了变反射率镜非稳腔的研究历史,总结了实现变反射率的方法,分析了它们的优缺点,最后列表总结了典型使用VRM作为非稳腔输出耦合器的实验参数和结果.为大能量固体激光器的设计提供了理论和实验参考.     

激光输出功率随耦合率及放大率的变化规律

建立了涵盖稳定腔和非稳腔的激光有源理论模型和激光开式谐振腔的边界条件。根据定态薛定谔方程与亥姆霍兹方程的等价性,采用量子力学方法求解谐振腔的亥姆霍兹波动方程,得到满足方程、边界条件、矩阵光学、稳定条件的本征解和本征方程。根据本征方程推导出横模数目随耦合率变化的规律,进而推导出激光输出功率随耦合率变化公式,以及激光输出功率随放大率的变化规律。该理论模型能够从稳定腔自然过渡到非稳腔,在小耦合率情况下退化到与传统公式基本一致的形式,又能在大耦合率情形下与实验结果符合得很好。     

孔径光阑输出对太赫兹激光器模式特性的影响

孔径光阑耦合技术是大功率光泵气体太赫兹激光器的一种常用谐振腔设计方法。在不考虑波导对腔内模式形成的影响下,采用传输矩阵的特征向量法,针对孔径光阑耦合太赫兹谐振腔的腔内本征模式以及输出光束特性进行了数值模拟,得到了该种谐振腔在不同g参数下损耗最低的几种本征模式及其相应的衍射损耗;采用衍射积分与矩阵光学结合的方法计算了孔径光阑输出太赫兹激光的光束特性,得到不同本征模式的远场衍射光斑及发散角。研究工作为孔径光阑耦合的气体太赫兹激光器设计提供了理论参考。     

Output Beam Quality of Edge Pumped Planar Waveguide Lasers with Confocal Unstable Resonators

Output beam quality of edge pumped planar waveguide lasers with confocal unstable resonators is investigated by diffraction methods, taking into account gain saturation, asymmetric pumping, and beam interaction. The influences of pumping uniformity, doping concentration, cavity length and effective Fresnel number are analyzed with respect to output beam quality and pumping efficiency. It is found that good beam quality and high efficiency can be obtained with asymmetric pumping and optimized negative branch confocal unstable resonators.     

Injection locked single mode operation of a tea CO2 laser with high energy extraction

Generation of reproducible smooth pulses from longitudinal mode control of a TEA CO₂ laser by signal injection from a cw CO₂ laser is reported and the operating conditions investigated for several new geometries. Applied to unstable resonators, the efficient and spectrally pure, high power output obtains has important application in the area of optical pumping.     

Unstable resonator and output-coupling design study for diffraction radiation generator near-mm sources

Configurations of unstable resonators that could be used for diffraction radiation generators (DRG's) are presented. The output coupling of a negative branch unstable resonator exhibits an extreme sensitivity to mirror radius and appears to be unsuited to DRG use. The positive branch resonator does not exhibit this sensitivity to mirror radius, and the mirror radii that are needed to give output couplings of a few percent appear practical.Work conducted at the Harry Diamond Laboratories.     

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.