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arXiv 2008.10243physics.optics
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LG33二次谐波产生的数值分析与LG00情况的比较

Numerical analysis of LG33 second harmonic generation in comparison to the LG00 case

Joscha Heinze, Henning Vahlbruch, Benno Willke

摘要:

为了在未来的引力波探测器中降低涂层布朗热噪声,建议使用螺旋拉盖尔-高斯LG 33模式的光来代替目前使用的LG 00模式。然而,量子噪声的同时减少则需要在LG 33模式中有效地产生压缩真空态。当前的压缩光产生技术采用连续波二次谐波产生(SHG)。在这里,我们模拟的SHG两种模式的数值推导出第一个洞察标准的压缩光产生技术的LG 33模式的可转移性。因此,在本文的第一部分中,我们从理论上讨论了在单个未耗尽泵浦模式的情况下的二次谐波,在一般情况下,激发谐波模式的叠加。基于谐波场的微分方程,我们推导出各个相位匹配条件,从而激发谐波模式的转换效率。在第二部分中,我们分析了LG 00和LG 33在单通、双通和腔增强结构下,在聚焦、不同的泵浦光强分布和单独的相位匹配条件的影响下的数值模拟。我们的研究结果预测,LG 33模式需要约14倍的泵浦功率的LG 00模式,以实现相同的倍频转换效率在一个理想的,现实的腔设计,主要产生谐波LG 66模式。

英文摘要:

For coating Brownian thermal noise reduction in future gravitational wave detectors, it is proposed to use light in the helical Laguerre-Gaussian LG33 mode instead of the currently used LG00 mode. However, the simultaneous reduction of quantum noise would then require the efficient generation of squeezed vacuum states in the LG33 mode. Current squeezed light generation techniques employ continuous-wave second harmonic generation (SHG). Here, we simulate the SHG for both modes numerically to derive first insights into the transferability of standard squeezed light generation techniques to the LG33 mode. In the first part of this paper, we therefore theoretically discuss SHG in the case of a single undepleted pump mode, which, in general, excites a superposition of harmonic modes. Based on the differential equation for the harmonic field, we derive individual phase matching conditions and hence conversion efficiencies for the excited harmonic modes. In the second part, we analyse the numerical simulations of the LG00 and LG33 SHG in a single-pass, double-pass and cavity-enhanced configuration under the influence of the focusing, the different pump intensity distributions and the individual phase matching conditions. Our results predict that the LG33 mode requires about 14 times the pump power of the LG00 mode to achieve the same SHG conversion efficiency in an ideal, realistic cavity design and mainly generates the harmonic LG66 mode.

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