This work was funded by the Science and Technology Facilities Council (STFC).

序言:在本协议部分中，我们假设，一个纯粹的，噪音低，功率稳定的基模高斯光束，例如含图3中所示的标准设置，通过商业的Nd:YAG激光器产生连续波在1064纳米的波长的光;法拉第隔离器（FI），以避免对激光源的背面反射的光的一个电光调制器（EOM）的红外光的光的相位调制。由此产生的光束被注入到一个三角形的光学谐振腔，其中通过有效的控制回路27的激光频率的光功率稳定，而谐振腔提供不必要的波束形状的空间滤波。 上面描述的设置， 如图3所示，是一个传统的实验安排，科学装置中使用的精度要求低噪声激光稳定测量1-8。协议部分说明这个基本模式高斯光束可以有效地转换成高阶拉盖尔 - 高斯光束相媲美的表演，如果不相同，在纯度，噪声和稳定。这是通过所示的装置在图4中 ，其设计，建设，和操作在下面的章节描述的装置。在这项工作中提出了在这个例子中，所生成的模式将是一个所有33。然而，值得强调的是​​，该技术具有普遍的有效性和描述的协议，适用于任何所需的高阶LG模式。 1。光学模式转换为基本模式激光束的优化转换高阶LG梁的设计和原型一个基本模式束转换成高阶LG光束的相位调制档案中的要求是复制的相位CROβ-边的所需的LG模式，该模式将被印上的波阵面的入射光束26通过成比例的相移。两种类型的模式转换器以这种方式工作:空间光调制器（SLM） - 计算机控制的液晶显示器，其可以控制到压印相的像素上的入射光转变 - 衍射相位板 - 蚀刻玻璃基板所需在传输中产生的相移由故意不同厚度的玻璃元件。 SLM的是灵活的，但缺乏稳定性和效率，而相位板是稳定的，有效的，但缺乏灵活性。因此，我们建议使用最初的研究和原型设计和使用的相位板的长期操作的SLM。 最佳的转换依赖于精确的选择参数（腰围的大小和位置）的形状的光束。因此，注入到模式转换器之前，最初的基本模式时，必须将其特征在于，和它的参数重新塑造，以提供最佳的转换的匹配 - 该操作被称为"模式匹配的"。 <ol><li>拿起束从图3中描述的基本模式设置。 </li><li>使用光束分析仪配备了实时图像分析软件，可以衡量光束半径沿光路。一旦已获得足够一套半径（一般至少10个数据点都需要一个良好的质量结果），适合测量半径和提取束腰的规模和它的位置。 </li><li>建立所需的光束半径转换点。使用大束数毫米大小的顺序才能使用相位转换区域的充分程度。 </li><li>选择一组沿光路的透镜和它们的位置，将重新塑造成所需的入射光束参数（腰围的大小和位置）。对于对齐的目的，可以很方便地放置的模式转换器吨的入射光束的腰身。 </li><li>重复步骤1.2和1.4，通过连续的透镜位置调整，直到已获得所期望的光束模式转换参数。 </li><li> SLM模式转换沿入射光束路径，并注入到SLM束。反射型SLM，我们建议使用一个小的入射角度，5度或以下的订单。在生成的光束入射角大，会造成散光，打破了LG模式圆柱对称。 </li><li>应用相位分布到SLM的液晶显示装置 - ，相位将其转换为所需的高阶LG电子束的横截面。 33的LG模式，这是目前的研究在未来的毛重检测器16的应用程序，在图5中所示的例子中的相位调制模式。 </li><li>选择适当的相位图案的大小（对应的光束的相位图案的大小）的大小的基础上的注入TED束表1到9的顺序，使用数值模拟28导出最佳的光束大小比为LG模式的列表。或者，找到最佳的光束是通过改变施加到空间光调制器的相位图案的大小和分析所得到的光束的图像的图像尺寸比实验。 </li><li>观察反射光束从SLM使用的CCD照相机，在距离中的一个或多个瑞利范围相差从SLM。仔细对准，以优化在CCD上的光束的对称图像的SLM。 </li></ol>一些注入光的相位调制装置的交互期间，仍然未调制的相位调制电平由于量化。此未转化的光转换后的光束沿同一轴线上，损坏所需的相位调制效应。为了规避这个问题，可以对LG模式转换相位图像覆盖闪耀光栅轮廓。调制后的升搭载LG模式相位轮廓的洞察力将闪耀光栅偏转，而未灯光，不与基材互动的，将继续不受干扰。这将导致在两种类型之间的光束的空间分离。 <ol start="10"><li>熊熊结构重叠先前SLM产生的相位分布。 LG模与方位指数升&gt; 0的相位图案将有一个叉形光栅的特点，如在图6的例子中看到。 </li><li>优化燃烧的角度，使得入一阶的衍射角的光束的发散角大于。继续进行，直到较高的衍射级之间的一个合理的分离结果（使用作为外圈本身的直径一样大的连续梁的外圈之间的分离）。 </li><li>一旦实现最佳的转换模式，进行相板的制造。这些是商业上阿瓦伊标签和制造，以满足广泛的定制要求。使用与SLM在优化过程中所获得的结果，确定最佳的相位变换的图案被蚀刻到的相位板。可选步骤:应用中的至少一个的相位板的表面上的防反射涂层，以尽量减少散射的光反射回的光功率向所述激光源和分散。 </li></ol> 2。相板，模式转换和纯度增强操作<ol><li>更换空间光调制器的相位板。至于在SLM，它是方便的，以将其定位在注入的基本模式要转换的光束的腰身。 </li><li>小心地将相位板等的初始光束的相位板是垂直于梁，相对于光束的中心的相结构。 </li><li>传播的光束透过的相位板，直到较高的差异分离raction订单发生。梁与梁卡可以很容易地可视。 </li><li>当达到一个足够的"好"的分离（在步骤1.12中所述），遮掩较高的衍射级次光束的孔为中心的主衍射阶。 </li></ol>所讨论的相位板设计，不能调节幅度以及相位意味着他们将不能转换成所需的模式所有传入的根本束。其结果是一个组合梁的显性其他高阶模式轻微的强度，如在图7中示出的背景下进行所需的LG光束。为了在空间上过滤掉不想要的LG模式和增强模式的纯度，可以将转换后的光束的光学谐振腔的注入。这样的空腔，也可作为一个"模式选择"只允许特定的光学模式的传输，相对于光的波长的谐振腔长度根据。 <ol start="5"><li>设计莫清洁腔。如果在其实施简单，使用由两个反光镜的线性腔结构， 如图4所示，在这种反射镜是平的（通常是输入镜）和其他的反射镜（输出）是凹的。这提供了实施的光稳定性和简单。甲行之有效的具体设计是一个的输出反射镜的曲率半径为1米，而反射镜的反射表面之间的距离是21厘米29。在这种情况下，最佳的输入光束半径大约是365微米在腰部，位于平面镜的反射表面。 </li><li>选择腔镜的反射率来确定的腔技巧。使用低为了几百技巧，有良好的抑制不必要的模式订单，而不会引入大的扭曲，由于耦合退化模式（见第4步）。最好是使用具有相同反射率的反射镜，以最大限度地提高模腔通过。 </li><li>使用RIGID间隔为两腔的支持反映机械振动增强免疫力。胶的反射镜在隔板上，并插入一个压电环元件之间的两个反射镜的一个，与间隔件的纵向长度的控制和稳定的目的，以允许谐振腔长度的微观调整。 </li><li>模式匹配的光束所产生的相位板模式清洁器腔体本征模式。的LG光束的束仿形可以不被执行使用相同的工具用于根本模式束，因此，记录的强度分布的光束与一个放置在不同的位置沿光束路径的CCD相机和分析采用量身定制合身的记录，图像脚本，它可以识别主导的LG模式和光束半径估计在给定的位置30。该光束的强度分布拟合程序的一个例子示于图8。 </li><li>一旦有足够的光束直径已成为连接测量（通常，至少10个数据点所需要的良好的质量的结果），适合测得的半径和外推的束腰直径和它的位置。一个很好的光束轮廓看起来像一个如图9所示。在1.2和1.4，选择透镜，并重复该过程，直到最优波束的大小和位置被发现，2.7，2.8和2.9中描述。一旦实现模式匹配，注入所产生的光束进入模式吸尘器腔，确保输入（平坦）的反射面的反射镜是否正确放置在腰部注入光束。 </li><li>到空腔优化注入的光束的对准，同时，通过移动反射镜与压电扫描腔长，监视发送波束。 </li><li>使用由模式清洁器腔作为调查对LG光束所产生的相位板的模式内容的谐振腔长度（也称为空腔扫描）的函数的透射光的测量，前夕ntually评估的相位板本身的转换效率。 </li><li>通过检查的CCD图像识别有关的寄生模式。评估这种模式下的功率通过在光电二极管的信号其振幅和计算准确的整体光束的模式的内容。的测量结果和确切形式的内容可以进行复制，数值模拟21。的分析结果在图10中给出一个很好的例子，模式含量结果示于表2。 </li></ol>一旦成束的最佳取向模式清洁器腔被实现，分析已注入的光束模式的内容，可以最终实现方式清洁和增强的复合LG束纯度。一斤德雷弗霍尔锁定方案27可用于稳定腔长到所需的谐振模式。光传输模式吸尘器CAVITY可以读取由一个光电二极管，它可以提供错误的信号所​​必需的控制回路，控制腔长。 <ol start="13"><li>腔长锁定到发送的诊断所产生的光束，并限定其纯度与CCD摄像机的空腔产生的光束的档案的主共振和记录图像。 </li></ol> 3。生成的LG光束诊断和表征在这个实验中，两个主要的属性定义一个&#39;好&#39;光束质量的高精度干涉测量的成功实施:束功率和光束的纯度。使用上实现的基本模式的光束中，如上所述的相同的控制技术，可以保存其他相关的属性如频率或功率稳定。 <ol><li> LG电子束功率测量，通过激光功率计。注意梁剪切:LG光束具有较大EXTEN锡永相比，传统的高斯光束，它可能会超过大多数商业工具的敏感面积的尺寸。最高权力明显。 </li><li>通过比较与理论光束​​剖面评估生成的LG电子束的纯度。要做到这一点，通过CCD相机探查和拍摄照片的光束强度估计它的光束半径，推导出理论束振幅剖面比较测量。通过评估的纯度平方内积<img alt="公式1" fo:src="/files/ftp_upload/50564/50564eq1highres.jpg" src="/files/ftp_upload/50564/50564eq1.jpg" />理论和测量振幅分布。高纯度的建议。 </li></ol>两个重要的品质因数是有用的的整个模式转换过程中的质量评价:相板的转换效率和整体设置。 <ol start="3"><li>为了评估CONVERS离子相板效率，遵循腔扫描程序步骤2.11和2.12。 </li><li>评估的生成所需的LG光束的功率与注入基模高斯光束的功率之间的比率设置为整体的转换效率。高转换效率显然是可取的。 </li></ol> 4。注入大干涉模拟研究这个协议的应用之一是调查他们的引力波探测器使用LG光束。这些长基线高精度干涉。基线需要比较大的反射镜和光束大小。然而，这提高了不完善的光学元件的影响，特别是当使用高次模。本节介绍了一种基于模拟的方法进行调查的行为高阶LG模式在现实探测器。 <ol><li>选择光场建模仿真工具，在interferomet的呃为了测试高阶LG模式。仿真软件应该能够在设置不完善的影响（错位，模式不匹配，镜子数字错误等 ）建模的模式内容的光束。一个例子是仿真工具FINESSE 28。 </li><li>建立一个模型，一个真正的探测器使用选定的模拟工具。在高级LIGO的情况下，这是一个双循环迈克耳孙干涉仪臂腔的Fabry-Perot。这些初始模拟的目的是验证了模型的可靠性，假设完美的光学系统。 </li><li>测试模型与完善的基本模式横梁。为了验证该模型的可靠性，这应该允许再生的列表，在实际的检测器进行的实验程序，如:对臂腔，腔的扫描循环中的电源，如预期的数字误差信号，并检查，并角度和长度的干涉仪，其子系统的控制S通过传感和控制方案。进一步的模拟应包括干涉仪引力波信号的响应。一旦模拟按预期执行，该模型可以适于高阶LG模。 </li><li>测试模型与完美的LG33梁:适应干涉仪的设计，使用LG模式。这就需要减少上的空腔，其中可以实现通过改变的反射镜的曲率半径的反射镜的光束的大小。一旦模型已被改编为LG模式，应重复进行的测试4.3的新的输入束。如果在完美的光学系统的情况下，结果应该是非常相似，使用HG 00（见实例19）。 </li></ol>使用更高阶的光束引入了简并性的光学腔，因为有几个不同的光束形状，争取主导地位。高斯模式的光学谐振腔的谐振该命令适用于所有模式。一个HG00 0阶模式是唯一的模式，因此所有其他模式抑制。例如，LG 33模式10模式9阶的一个，所有这些都将在干涉仪得到加强。镜面扭曲，总是存在于真实的干涉夫妇到其他的事件模式。如果这些新的模式是相同的顺序，作为入射光束在臂腔增强，导致高度扭曲的循环光束。这最终会恶化仪器的灵敏度。 <ol start="5"><li>设置一个现实的干涉模型:将腔反射镜的表面数字的真实数据。此数据的属性几何高度或反射率的反射镜的表面，如一个"地图"的形式，在图11中的高级LIGO镜子看到一个例子。包括这些影响后，高阶模的性能，应进行调查，特别是在在检测器的输出和误差信号中的多个过零点的可能性的对比度缺陷。在这些领域中，高阶模式预计将表现逊于HG 00。 </li><li>模拟子系统:为了更好地了解模型中存在的退化效果，模拟子系统简，例如高级LI​​GO的法布里 - 珀罗臂腔。这些子系统模拟产生腔内扫描和错误信号，以识别任何的频率分裂和流通领域的检测，可以分析其模式内容。 </li><li>镜面要求:获得更严格的要求的情况下镜面的平整度4.6步的结果显示这将使执行高阶LG光束不可能在其他模式下的频率分裂或电源不可接受的程度。对于这一点，分析耦合等造成的直接跨阶其中可以实现数字或使用的解析近似19的表面。使用这种方法来识别任何特定的镜子的形状，是造成大量相同的顺序输入光束和模式之间的耦合。通过比较这些结果与模拟，估算为这些形状的镜像要求，对于一个特定的循环束纯度。最后模拟满量程的干涉仪模型修改为新规格的镜像地图，示出了改进对比度的缺陷和频率分裂。 </li></ol>

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Quantum Grav. 30, 035004 (2013).</li><li>Carbone, L., Bogan, C., Fulda, P., Freise, A., Willke, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Generation+of+High-Purity+Higher-Order+Laguerre-Gauss+Beams+at+High+Laser+Power.">Generation of High-Purity Higher-Order Laguerre-Gauss Beams at High Laser Power.</a> Physical Review Letters. 110, 251101 (2013).</li><li>Fulda, P., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phaseplate+design+for+Laguerre-Gauss+mode+conversion.">Phaseplate design for Laguerre-Gauss mode conversion.</a> , (2013).</li><li>Willke, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Stabilized+lasers+for+advanced+gravitational+wave+detectors.">Stabilized lasers for advanced gravitational wave detectors.</a> Laser &amp; Photonics Rev. , 1-15 (2010).</li><li>Granata, M., Buy, C., Ward, R., Barsuglia, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Higher-Order+Laguerre-Gauss+Mode+Generation+and+Interferometry+for+Gravitational+Wave+Detectors.">Higher-Order Laguerre-Gauss Mode Generation and Interferometry for Gravitational Wave Detectors.</a> Physical Review Letters. 105, 231102 (2010).</li><li>Matsumoto, N., Ando, T., Inoue, T., Ohtake, Y., Fukuchi, N., Hara, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Generation+of+high-quality+higher-order+Laguerre+Gaussian+beams+using+liquid-crystal-on-silicon+spatial+light+modulators.">Generation of high-quality higher-order Laguerre Gaussian beams using liquid-crystal-on-silicon spatial light modulators.</a> J. Opt. Soc. Am. 25, 1642-1651 (2008).</li><li>Kennedy, S. A., Szabo, M. J., Teslow, H., Porterfield, J. Z., Abraham, E. R. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Creation+of+Laguerre-Gaussian+laser+modes+using+diffractive+optics.">Creation of Laguerre-Gaussian laser modes using diffractive optics.</a> Physical Review A. 66, 043801 (2002).</li><li>Black, E. 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Authors have nothing to disclose.

The output beams of most lasers used in high-precision measurements are designed to have a shape well described as a fundamental Gaussian mode. This particular beam geometry combines low diffraction with a spherical wave front. While the low diffraction is one of the key advantages of laser light, the spherical wave front is equally important, as it allows the low-loss transformation of the laser beam by standard optical components with spherical surfaces. Different beam shapes can be created as well, and recently Laguerre-Gauss beams have become of interest for their potential application in high-precision interferometry.
In this paper we demonstrated the experimental procedure to create higher-order Laguerre-Gauss modes with 95% purity for high-power, ultra stable laser beams. To achieve this, we have combined standard techniques from different aspects of optical research, namely diffractive phase plates and laser pre-stabilization to mode cleaner cavities. Our experiment provides a simple, modular and very reliable method to create high power beams in user defined higher-order modes. A commercial ultra-stable laser is used as the light source. Its output is injected to a diffractive phase plate, which can convert up to 75% of the light into the desired Laguerre-Gauss mode. This light is then injected to a small optical cavity and an electronic feedback loop is used to stabilize the laser frequency of the laser to the cavity length. The beam transmitted by the cavity is to 95% in the desired mode and, like the fundamental mode beam at the origin of the setup, has very good frequency stability at audio frequencies. All the parts represent standard components in modern optical experiments. We have successfully demonstrated this technique for laser powers up to 80 W pure Laguerre-Gauss 33 mode.
It could be possible to achieve similar results by replacing the phase plate with another mode-converting element (for example, other diffractive elements or astigmatic mode converters). Alternatively a laser could be setup with an optical resonator tuned for the desired Laguerre-Gauss modes, using for example, an amplitude mask. Finally the laser frequency stabilization to the reference optical cavity could be exchanged with a similar scheme that uses an atomic reference. The need for an electronic feedback system is probably the main disadvantage, but this is inevitable for any light source used for precision interferometer.
However, we believe that the method demonstrated in this paper provides a simple and modular scheme which can be scaled to all ranges of required laser frequency, power, or shape and thus presents a powerful and versatile method. Each part, the laser source, the diffractive element, as well as the optical cavity can be changed or optimized individually, which means that also existing laser injection systems can be upgraded to use Laguerre-Gauss modes.

在过去的几十年里，高精度干涉实验推向最终灵敏度制度量子效应开始发挥了决定性的作用。在这些目前和未来的实验，如激光冷却机械振荡器1，光学陷阱一代纠缠测试群众镜2，3，量子非拆迁干涉的4刚性腔5，稳频激光器，引力波探测6 ，7，8，研究人员正面临着许多限制基本面和技术面的噪声源。最严重的问题之一是谐振器反射镜的干涉的设置，这是造成由热激发的原子构成的反射镜基板和反射涂层的反射镜7，8，9的热噪声。这样的效果，也被称为布朗运动 ，将导致一个不确定性的相位反射光的任何测试的群众，所以会表现为根本干涉仪的输出噪声限制。例如，在项目设计先进的引力波天线，如高级，高级LIGO的处女座，和爱因斯坦望远镜的灵敏度是有限的这种类型的噪声最敏感的区域的观测频段10，11，12。 实验物理学家在社区努力做出持续的努力，以尽量减少这些噪声贡献，并提高他们的仪器的灵敏度。在镜子布朗噪声的特定情况下，缓解的一个方法是采用更大范围内的光束点的大小，因为目前使用的标准的基本HG 00束测试质量表面的更有效的表面的随机运动的更大范围内的平均束13，14。已经显示出扩展的反射镜的热噪声的功率谱密度逆高斯光束的大小的反射镜基板和镜子9平方成反比。然而，束斑变大时，较大部分的光功率丢失的反射面的边缘。如果使用比通常使用的HG 00束（见例如图1）的径向光强分布更均匀的光束， 布朗热噪声电平可以减小而不会增加这种类型的损失。在所有的更均匀的光束类型，已经提出了新版本的高精度的干涉，例如梅萨梁或圆锥形模式13，14，最有前途的是高阶LG与目前使用的球形光束由于其潜在的兼容性反射镜表面15。例如，二进制中子星螺旋系统的检出率 - 这被认为是最有前途的天体物理源第一毛重检测-离子约为系数2或更大的16上面的最小量的成本在目前正在建设10，11的第二代干涉仪的设计修改，可以增强。除了 ​​热噪声的好处，更广泛的高阶LG光束的强度分布（见，例如， 图2）已被证明，以减轻热像差的光学干涉仪内的幅度。这将减少热补偿系统在何种程度上依赖在未来的实验，以达到设计的敏感性19。 我们也调查，成功证明了可行性产生LG光束成功运作最好的灵敏度16，18，19，20，21，22 GW干涉所需的纯度和稳定性水平。该方法结合在不同的领域物理和光学齐全的开发技术和专业知识h为新一代的高稳定性，低噪声的单模激光束23，利用空间光调制器，衍射光学元件的操纵空间分布的光束18，22，24，25，26，和使用旨在进一步纯化和稳定的激光的光学谐振腔27的感测，控制和稳定化的先进技术。该方法已成功地证明，在实验室实验中，出口为测试在大型原型干涉仪20，用于产生在高的激光功率的LG模式高达80 W 21。在这篇文章中，我们提出高阶LG光束的方法的细节，并讨论所产生的光束的表征和验证的方法论。另外，在步骤4中概述了数值研究了一种用于与非完美反射镜19的空腔。

<table><tbody><tr><td colspan="4">&lt;em&gt;The experimental apparatus discussed in this paper requires the following types of instruments:&lt;/em&gt;</td></tr><tr><td colspan="4">&lt;strong&gt;Instrument&lt;/strong&gt;</td></tr><tr><td>Solid state Laser source, Nd:YAG 1064 nm CW laser</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;1</td></tr><tr><td>Faraday Isolator</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;1</td></tr><tr><td>Electro-Optic Modulator (EOM)</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;1</td></tr><tr><td>CCDcamera beam profiler</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;1</td></tr><tr><td>Lenses</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;depending on apparatus design</td></tr><tr><td>Steering Mirrors</td><td></td><td></td><td>&lt;strong&gt;Quantity: &lt;/strong&gt;depending on apparatus design</td></tr><tr><td>Aperture</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 1</td></tr><tr><td>High reflectivity mirrors (for normal incidence)</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 2</td></tr><tr><td>Piezoelectric ring</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 1</td></tr><tr><td>Cavity spacer</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 1</td></tr><tr><td>Photodiodes and related control electronics</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 1 or more, depending on apparatus design</td></tr><tr><td>Spatial light modulator</td><td></td><td></td><td>&lt;strong&gt;Quantity:&lt;/strong&gt; 1&lt;br/&gt; Holoeye LCR-2500</td></tr><tr><td colspan="4">&lt;em&gt;All the above instruments are commercially available and no particular specification is required. We leave the choice of the most suitable instruments to the experimenter&amp;rsquo;s discretion.&lt;/em&gt;</td></tr><tr><td colspan="4">&lt;em&gt;For the interest of the experimenter interested in reproducing the protocol, we recommend the following tools used in our experiment:&lt;/em&gt;</td></tr><tr><td colspan="4">&lt;strong&gt;Tools&lt;/strong&gt;</td></tr><tr><td>Innolight OEM 300NE, 1064 nm, 300 mW</td><td></td><td></td><td>Laser Source:</td></tr><tr><td>SIMTOOLs</td><td></td><td></td><td>Software for data analysis, available at &lt;a href=&quot;http://www.gwoptics.org/simtools/&quot; target=&quot;_blank&quot;&gt;www.gwoptics.org/simtools/&lt;/a&gt;</td></tr><tr><td>FINESSE</td><td></td><td></td><td>Software for optical simulations, &lt;a href=&quot;http://www.gwoptics.org/finesse/&quot; target=&quot;_blank&quot;&gt; www.gwoptics.org/finesse/&lt;/a&gt;</td></tr><tr><td colspan="4">Finally, the phase plate employed in the present experiment was manufactured by Jenoptik GmbH, based on a custom design provided by the Authors.</td></tr></tbody></table>

the generation of higher-order laguerre-gauss optical beams for high-precision interferometry

在高反射镜的热噪声是几种类型的高精度干涉实验，旨在达到标准量子极限或机械系统冷却到其量子基态的一个主要障碍。这是，例如预计将在最敏感的频段限制的情况下，未来的引力波观测站，其引力波信号的敏感性，通过原子振动镜群众。一所追求的有前途的方法来克服这个限制是采用高阶拉盖尔 - 高斯（LG）光束代替传统使用的基本模式。由于他们的更均匀的光强度分布的光束平均更有效地在热驱动的镜子，这反过来又降低了检测出的激光在反射镜的位置的不确定性的波动。 我们展示了一个有前途的方法来生成高阶LG光束的帮助下，衍射光学元件的一个基本的高斯光束整形。我们表明，与传统的传感和控制技术是已知的用于稳定基波激光束的高阶LG模可以被纯化，并稳定在一个相对较高的水平一样好。了一套诊断工具，使我们能够控制和定制生成的LG光束的属性。这使我们生产的LG电子束报告日期纯度最高。证明高阶LG干涉测量技术与标准和使用标准球面光学模式的兼容性，使得应用在下一代的高精度干涉他们的理想人选。

All the experimental results so far described in the text and shown in the figures constitute a representative example of a successful execution of the beam conversion protocol. The most representative result is the purity of the generated beam: a successful beam conversion should lead to a beam purity on the order of 95% or above. A good example of successful beam conversion is the measurement of the intensity profile of an 82.8 Watts, 96% pure LG33 beam obtained in 21 and here shown in Figure 12.
Similarly, as discussed in protocol sections, the mode conversion efficiencies of the phase plate and of the overall experimental setup are a good indicator of the successful design of the experimental apparatus, including the phase plate and the mode cleaner cavity. Values of order 50% to 60% and above are generally considered a good value for the mode conversion efficiency. The highest conversion efficiency reported so far with this type of setup is about 70% 21.
The simulation investigation described in Protocol Sec 4 should result in numbers for beam purity with realistic mirrors, suggested mirror specifications and the resulting beam purity when these specifications are adopted. An example of the results you can expect with realistic mirror maps are shown in 19 where an original LG33 purity of 89% is obtained, compared to a purity of &gt;99% for HG00. A purity of &gt;99% for the LG33 mode is achieved using specific mirror requirements with a major reduction of astigmatism in the mirror surface.
<img alt="Figure 1" src="/files/ftp_upload/50564/50564fig1.jpg" /> 
Figure 1. Intensity patterns for Hermite-Gauss (HG) modes up to order 6. The intensity patterns are normalized to have the same peak intensity, for visibility.
<img alt="Figure 2" src="/files/ftp_upload/50564/50564fig2.jpg" /> 
Figure 2. Intensity patterns for helical LG modes up to order 9. The intensity patterns are normalized to have the same peak intensity, for visibility.
<img alt="Figure 3" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig3highres.jpg" src="/files/ftp_upload/50564/50564fig3.jpg" /> 
Figure 3. Sketch of a conventional setup for production and stabilization of HG00 beams.
<img alt="Figure 4" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig4highres.jpg" src="/files/ftp_upload/50564/50564fig4.jpg" /> 
Figure 4. A sketch of the experimental setup discussed in this paper. The HG00 beam is first mode-matched to a desired waist size via a telescope then injected on the phase plate. The main diffracted beam is separated from the higher diffraction orders with an aperture and then sent to the Mode Cleaner cavity. A photodiode is used to extract the error signal for controlling the cavity length. The beam intensity is analyzed by a CCD camera.
<img alt="Figure 5" src="/files/ftp_upload/50564/50564fig5.jpg" /> 
Figure 5. Phase modulation profile to convert a HG00 mode to LG33 mode.
<img alt="Figure 6" src="/files/ftp_upload/50564/50564fig6.jpg" /> 
Figure 6. Example of blazed phase modulation profiles for generating LG33 modes.
<img alt="Figure 7" src="/files/ftp_upload/50564/50564fig7.jpg" /> 
Figure 7. Comparison between the intensity distribution of the composite beam generated by the phase plate (left) and the theoretical intensity distribution for a pure LG33 beam with same parameters.
<img alt="Figure 8" src="/files/ftp_upload/50564/50564fig8.jpg" /> 
Figure 8. Example of beam intensity profile fitting applied to a real LG33 beam transmitted from a phase plate (left) compared to fit results (center) and residuals of fit (right). <a href="https://www.jove.com/files/ftp_upload/50564/50564fig8large.jpg" target="_blank"> Click here to view larger figure</a>.
<img alt="Figure 9" fo:conten-width="4.5in" fo:src="/files/ftp_upload/50564/50564fig9highres.jpg" src="/files/ftp_upload/50564/50564fig9.jpg" /> 
Figure 9. Profile of an LG33 beam with Gaussian fit shown for comparison.
<img alt="Figure 10" fo:conten-width="4.5in" fo:src="/files/ftp_upload/50564/50564fig10highres.jpg" src="/files/ftp_upload/50564/50564fig10.jpg" /> 
Figure 10. Light power transmitted by a linear cavity as a function of the cavity length, when injecting a beam generated by the phase plate. The resonant peaks at 0 and 1 FSR correspond to the desired LG33 mode. A fit to this dominant mode is shown for comparison (blue line). The red curve shows the result of the numerical model, based on the modal content described in Table 2. Pictures of the unwanted beams to be filtered by the cavity are shown in the insets.
<img alt="Figure 11" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig11highres.jpg" src="/files/ftp_upload/50564/50564fig11.jpg" /> 
Figure 11. An example of a mirror surface map for one of the Advanced LIGO optical mirrors 19.
<img alt="Figure 12" src="/files/ftp_upload/50564/50564fig12.jpg" /> 
Figure 12. Intensity profile of a 82.8 W LG33 beam transmitted by a linear cavity (left) compared with fit residuals (right).
<table border="1">
	<tbody>
		<tr>
			<td>p</td>
			<td>l</td>
			<td>0</td>
			<td>1</td>
			<td>2</td>
			<td>3</td>
			<td>4</td>
			<td>5</td>
			<td>6</td>
			<td>7</td>
			<td>8</td>
			<td>9</td>
		</tr>
		<tr>
			<td colspan="2">0</td>
			<td>1.0</td>
			<td>2.8</td>
			<td>1.7</td>
			<td>2.0</td>
			<td>2.2</td>
			<td>2.5</td>
			<td>2.6</td>
			<td>3.1</td>
			<td>3.0</td>
			<td>3.2</td>
		</tr>
		<tr>
			<td colspan="2">1</td>
			<td>1.7</td>
			<td>2.7</td>
			<td>2.2</td>
			<td>2.4</td>
			<td>2.6</td>
			<td>2.8</td>
			<td>2.9</td>
			<td>2.8</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">2</td>
			<td>2.2</td>
			<td>2.4</td>
			<td>2.5</td>
			<td>2.7</td>
			<td>2.9</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">3</td>
			<td>2.5</td>
			<td>2.7</td>
			<td>2.8</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">4</td>
			<td>2.9</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
	</tbody>
</table>
Table 1. Optimum ratio between input HG00 beam size and LGpl phase image beam size for LG modes up to the order 9.
<table border="1">
	<tbody>
		<tr>
			<td>Mode</td>
			<td>LG33</td>
			<td>LG63</td>
			<td>LG43</td>
			<td>LG53</td>
			<td>LG32</td>
			<td>LG62</td>
		</tr>
		<tr>
			<td>Power</td>
			<td>75%</td>
			<td>8%</td>
			<td>4%</td>
			<td>4%</td>
			<td>4%</td>
			<td>1%</td>
		</tr>
	</tbody>
</table>
Table 2. Mode content analysis described by the cavity scan shown in Figure 10.

Watch this Scientific Journal Video about The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry at JoVE.com

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Large laser-interferometers are being constructed to create a new type of astronomy based on gravitational waves. Their sensitivities, as for many other high-precision experiments, are approaching fundamental noise limits such as the atomic vibration of their components. We are pioneering technologies to overcome these limits using novel laser beam shapes.

代高阶拉盖尔 - 高斯光束的高精度干涉

Thermal noise in high-reflectivity mirrors is a major impediment for several  types of high-precision interferometric experiments that aim to reach the  ...

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21.6K 次观看.  University of Birmingham. Large laser-interferometers are being constructed to create a new type of astronomy based on gravitational waves. Their sensitivities, as for many other high-precision experiments, are approaching fundamental noise limits such as the atomic vibration of their components. We are pioneering technologies to overcome these limits using novel laser beam shapes.

视频: The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Construction of a High Resolution Microscope with Conventional and Holographic Optical Trapping Capabilities

High resolution microscope systems with optical traps allow for precise manipulation of various refractive objects, such as dielectric beads 1 or cellular organelles 2,3, as well as for high spatial and temporal resolution readout of their position relative to the center of the trap. The system described herein has one such "traditional" trap operating at 980 nm. It additionally provides a second optical trapping system that uses a commercially available holographic package to simultaneously create and manipulate complex trapping patterns in the field of view of the microscope 4,5 at a wavelength of 1,064 nm. The combination of the two systems allows for the manipulation of multiple refractive objects at the same time while simultaneously conducting high speed and high resolution measurements of motion and force production at nanometer and piconewton scale.

The system described herein employs a traditional optical trap as well as an independent holographic optical trapping line, capable of creating and manipulating multiple traps. This allows for the creation of complex geometric arrangements of refractive particles while also permitting simultaneous high-speed, high-resolution measurements of the activity of biological enzymes.

高分辨率显微镜与常规和全息光学捕获能力建设

High resolution microscope systems with optical traps allow for precise manipulation of various refractive objects, such as dielectric beads 1 or cellular ...

科研

工程学

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

We present a method for visualizing laser-induced, ultrafast molecular rotational wave packet dynamics. We have developed a new 2-dimensional Coulomb explosion imaging setup in which a hitherto-impractical camera angle is realized. In our imaging technique, diatomic molecules are irradiated with a circularly polarized strong laser pulse. The ejected atomic ions are accelerated perpendicularly to the laser propagation. The ions lying in the laser polarization plane are selected through the use of a mechanical slit and imaged with a high-throughput, 2-dimensional detector installed parallel to the polarization plane. Because a circularly polarized (isotropic) Coulomb exploding pulse is used, the observed angular distribution of the ejected ions directly corresponds to the squared rotational wave function at the time of the pulse irradiation. To create a real-time movie of molecular rotation, the present imaging technique is combined with a femtosecond pump-probe optical setup in which the pump pulses create unidirectionally rotating molecular ensembles. Due to the high image throughput of our detection system, the pump-probe experimental condition can be easily optimized by monitoring a real-time snapshot. As a result, the quality of the observed movie is sufficiently high for visualizing the detailed wave nature of motion. We also note that the present technique can be implemented in existing standard ion imaging setups, offering a new camera angle or viewpoint for the molecular systems without the need for extensive modification.

We present a protocol for creating a real-time movie of a molecular rotational wave packet using a high-resolution Coulomb explosion imaging setup.

激光驱动的超快分子旋转直接成像

We present a method for visualizing laser-induced, ultrafast molecular rotational wave packet dynamics. We have developed a new 2-dimensional Coulomb ...

化学

High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis

Recent years have witnessed a significant increase in the use of spontaneous Brillouin spectrometers for non-contact analysis of soft matter, such as aqueous solutions and biomaterials, with fast acquisition times. Here, we discuss the assembly and operation of a Brillouin spectrometer that uses stimulated Brillouin scattering (SBS) to measure stimulated Brillouin gain (SBG) spectra of water and lipid emulsion-based tissue-like samples in transmission mode with &lt;10 MHz spectral-resolution and &lt;35 MHz Brillouin-shift measurement precision at &lt;100 ms. The spectrometer consists of two nearly counter-propagating continuous-wave (CW) narrow-linewidth lasers at 780 nm whose frequency detuning is scanned through the material Brillouin shift. By using an ultra-narrowband hot rubidium-85 vapor notch filter and a phase-sensitive detector, the signal-to-noise-ratio of the SBG signal is significantly enhanced compared to that obtained with existing CW-SBS spectrometers. This improvement enables measurement of SBG spectra with up to 100-fold faster acquisition times, thereby facilitating high spectral-resolution and high-precision Brillouin analysis of soft materials at high speed.

We describe the construction of a rapid continuous-wave-stimulated-Brillouin-scattering (CW-SBS) spectrometer. The spectrometer employs single-frequency diode-lasers and an atomic vapor notch-filter to acquire transmission spectra of turbid/non-turbid samples with high spectral-resolution at speeds up to 100-fold faster than those of existing CW-SBS spectrometers. This improvement enables high-speed Brillouin material analysis.

用于材料分析的高速连续波受激布里渊散射光谱仪

Recent years have witnessed a significant increase in the use of spontaneous Brillouin spectrometers for non-contact analysis of soft matter, such as ...

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser radiation. The method is based on the coherent sum of two uniform waves, previously encoded into a phase-only spatial light modulator (SLM) by spatial multiplexing of their phases. Here, the interference process is carried out by spatial filtering of light frequencies at the Fourier plane of certain imaging system. The correct implementation of this method allows arbitrary phase and amplitude information to be retrieved at the output of the optical system.
It is an on-axis, rather than off-axis encoding technique, with a direct processing algorithm (not an iterative loop), and free from coherent noise (speckle). The complex field can be exactly retrieved at the output of the optical system, except for some loss of resolution due to the frequency filtering process. The main limitation of the method might come from the inability to operate at frequency rates higher than the refresh rate of the SLM. Applications include, but are not limited to, linear and non-linear microscopy, beam shaping, or laser micro-processing of material surfaces.

We show how to encode the complex field of laser beams by using a single phase element. A common-path interferometer is employed to mix the phase information displayed into a phase-only spatial light modulator to finally retrieve the desired complex field pattern at the output of an optical imaging system.

利用相位空间光调制器建立激光光束的振幅和相位

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser ...

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

We present a high-performance source of unconditional polarization-entangled photons that have a high-emission rate, a broadband distribution, are degenerated and postselection free. The property of the source is based on the multiple quantum interference effect with a round-trip configuration of a Sagnac interferometer. The quantum interference effects make it possible to use the high generation efficiency of the polarization-entangled photons to process parametric down-conversion, and separate degenerated photon pairs into different optical modes without a postselection requirement. The principle of the optical system was described and experimentally used to measure the fidelity and Bell parameters, and also to characterize the generated polarization-entangled photons from a minimum of six combinations of polarization correlated data. The experimentally obtained fidelity and Bell parameters exceeded the classical local correlation limit and are clear evidence of the generation of unconditional polarization-entangled photons.

We describe an optical system for the generation of unconditional polarization-entangled photons based on multiple quantum interference effects with a detection scheme to estimate the experimental fidelity of generated entangled photons.

基于多重量子干扰生成无条件极化纠缠光子的光子系统

We present a high-performance source of unconditional polarization-entangled photons that have a high-emission rate, a broadband distribution, are ...

Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy

A protocol is presented to build a custom low-cost yet high-performance femtosecond (fs) fiber laser. This all-normal-dispersion (ANDi) ytterbium-doped fiber laser is built completely using commercially available parts, including $8,000 in fiber optic and pump laser components, plus $4,800 in standard optical components and extra-cavity accessories. Researchers new to fiber optic device fabrication may also consider investing in basic fiber splicing and laser pulse characterization equipment (~$63,000). Important for optimal laser operation, methods to verify true versus apparent (partial or noise-like) mode-locked performance are presented. This system achieves 70 fs pulse duration with a center wavelength of approximately 1,070 nm and a pulse repetition rate of 31 MHz. This fiber laser exhibits the peak performance that may be obtained for an easily assembled fiber laser system, which makes this design ideal for research laboratories aiming to develop compact and portable fs laser technologies that enable new implementations of clinical multiphoton microscopy and fs surgery.

A method is presented to build a custom low-cost, mode-locked femtosecond fiber laser for potential applications in multiphoton microscopy, endoscopy, and photomedicine. This laser is built using commercially available parts and basic splicing techniques.

用于多光子显微镜的全正常分散飞秒光纤激光器的低成本定制制造和模式锁定操作

A protocol is presented to build a custom low-cost yet high-performance femtosecond (fs) fiber laser. This all-normal-dispersion (ANDi) ytterbium-doped ...

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for moving mechanical parts. This technology is particularly useful for beam steering applications. Here, we focus on OPAs integrated into SiN photonic circuits for a wavelength in the near infrared. A characterization method of such circuits is presented, which allows the output beam of integrated OPAs to be shaped and steered. Furthermore, using a wafer-scale characterization setup, several devices can easily be tested across multiple dies on a wafer. In this way, fabrication variations can be studied, and high-performance devices identified. Typical images of OPA beams are shown, including beams emitted from OPAs with and without a uniform waveguide length, and with varying numbers of channels. In addition, the evolution of output beams during the phase optimization process and beam steering in two dimensions is presented. Finally, a study of the variation in the beam divergence of identical devices is performed with respect to their position on the wafer.

Here, we describe the operation of a SiN integrated photonic circuit containing optical phased arrays. The circuits are used to emit low divergence laser beams in the near infrared and steer them in two dimensions.

晶圆级试验站上SiN集成光学相控阵列的特性

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for ...

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

The transmission of multiple independent optical signals through a multimode fiber is accomplished using wavefront shaping in order to compensate for the light distortion during the propagation within the fiber. Our methodology is based on digital optical phase conjugation employing only a single spatial light modulator, where the optical wavefront is individually modulated at different regions of the modulator, one region per light signal. Digital optical phase conjugation approaches are considered to be faster than other wavefront shaping approaches, where (for example) a complete determination of the wave propagation behavior of the fiber is performed. In contrast, the presented approach is time-efficient since it only requires one calibration per light signal. The proposed method is potentially appropriate for spatial division multiplexing in communications engineering. Further application fields are endoscopic light delivery in biophotonics, especially in optogenetics, where single cells in biological tissue have to be selectively illuminated with high spatial and temporal resolution.

We demonstrate the transmission of multiple independent signals through a multimode fiber using wavefront shaping employing a single spatial light modulator. By modulating the wavefront for each signal individually, spatially separated foci are transmitted. Potential applications are multiplexed data transfer in communications engineering and endoscopic light delivery in biophotonics.

通过光纤使用波前整形多个信号的传输

The transmission of multiple independent optical signals through a multimode fiber is accomplished using wavefront shaping in order to compensate for the ...

生物工程

法布里-珀罗标准具的制备在痕量气体光谱中的应用

Fabrication of a Low-Cost, Fiber-Coupled, and Air-Spaced Fabry-P&#233;rot Etalon

Fabry-P&#233;rot etalons (FPE) have found their way into many applications. In fields such as spectroscopy, telecommunications, and astronomy, FPEs are used for their high sensitivity as well as their exceptional filtering capability. However, air-spaced etalons with high finesse are usually built by specialized facilities. Their production requires a clean room, special glass handling, and coating machinery, meaning commercially available FPEs are sold for a high price. In this article, a new and cost-effective method to fabricate fiber-coupled FPEs with standard photonic laboratory equipment is presented. The protocol should serve as a step-by-step guide for the construction and characterization of these FPEs. We hope this&#160;will enable researchers to conduct fast and cost-effective prototyping of FPEs for various fields of application. The FPE, as presented here, is used for spectroscopic applications. As shown in the representative results section via proof of principle measurements of water vapor in ambient air, this FPE has a finesse of 15, which is sufficient for the photothermal detection of trace concentrations of gases.

作者聚焦：低成本、光纤耦合和空气间隔法布里-佩罗标准具的制造  

This protocol describes the construction of a low-cost, discrete, fiber-coupled, and air-spaced Fabry-Perot etalon with various applications, such as in trace-gas spectroscopy. The fabrication is possible in any facility with standard optical laboratory equipment available.

制造低成本、光纤耦合和空气间隔的法布里-佩罗标准具

Fabry-P&#233;rot etalons (FPE) have found their way into many applications. In fields such as spectroscopy, telecommunications, and astronomy, FPEs are ...

代高阶拉盖尔 - 高斯光束的高精度干涉

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此视频中的章节

高分辨率显微镜与常规和全息光学捕获能力建设

激光驱动的超快分子旋转直接成像

用于材料分析的高速连续波受激布里渊散射光谱仪

利用相位空间光调制器建立激光光束的振幅和相位

基于多重量子干扰生成无条件极化纠缠光子的光子系统

用于多光子显微镜的全正常分散飞秒光纤激光器的低成本定制制造和模式锁定操作

晶圆级试验站上SiN集成光学相控阵列的特性

通过光纤使用波前整形多个信号的传输

制造低成本、光纤耦合和空气间隔的法布里-佩罗标准具

制造低成本、光纤耦合和空气间隔的法布里-佩罗标准具