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.
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。
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。
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.
The authors have nothing to disclose.
This work was funded by the Science and Technology Facilities Council (STFC).
The experimental apparatus discussed in this paper requires the following types of instruments: | |||
Instrument | |||
Solid state Laser source, Nd:YAG 1064 nm CW laser | Quantity: 1 | ||
Faraday Isolator | Quantity: 1 | ||
Electro-Optic Modulator (EOM) | Quantity: 1 | ||
CCDcamera beam profiler | Quantity: 1 | ||
Lenses | Quantity: depending on apparatus design | ||
Steering Mirrors | Quantity: depending on apparatus design | ||
Aperture | Quantity: 1 | ||
High reflectivity mirrors (for normal incidence) | Quantity: 2 | ||
Piezoelectric ring | Quantity: 1 | ||
Cavity spacer | Quantity: 1 | ||
Photodiodes and related control electronics | Quantity: 1 or more, depending on apparatus design | ||
Spatial light modulator | Quantity: 1 Holoeye LCR-2500 |
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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’s discretion. | |||
For the interest of the experimenter interested in reproducing the protocol, we recommend the following tools used in our experiment: | |||
Tools | |||
Innolight OEM 300NE, 1064 nm, 300 mW | Laser Source: | ||
SIMTOOLs | Software for data analysis, available at www.gwoptics.org/simtools/ | ||
FINESSE | Software for optical simulations, www.gwoptics.org/finesse/ | ||
Finally, the phase plate employed in the present experiment was manufactured by Jenoptik GmbH, based on a custom design provided by the Authors. |