厄米高斯光束的模態分離

Abstract

「貝爾不等式」是一道古典定律遵守，但量子理論卻會違背的限制式。經由實驗貝爾不等式的正確性，可知物質「在測量前」是否就具有確切的物理特性，其特性又是否會受到遙遠事件的影響。一般這樣的實驗都是利用光的偏振方向，也就是光子的「內秉」性質來測試二維的貝爾不等式。然而，我們希望能利用「厄米高斯模態」這樣的「空間」模態來達成更高維度的實驗。為了達成這個目的，在這篇論文中我們將討論如何建構厄米高斯模態的測量裝置。此種裝置可視為是多出口的「模態分離器」，正如同「偏極化分光器」能將不同極化方向的光分離一樣。構成此分離器的關鍵是一種名叫「模態相位延遲器」的元件，它的效果類似於「波片」，能對不同的厄米高斯模態產生對應的相位延遲。將適當的模態相位延遲器裝置在由一群「馬赫任德干涉儀」所組成的二元樹結構中，就能完成我們所要的模態分離器。另外，我們使用電腦全像技術產生已知的複合模態，利用這些光源來測試裝置的分離效果，並搭配電腦模擬來驗證這套構想的可信度。

The experiment of Bell’s inequality (BI) is one designed to test whether the real world obeys the principle of “local realism”, which states that objects have definite properties independent of measurements and other events far away. While this experiment is usually based on the intrinsic property of photons, i.e. polarization, we attempt to accomplish it based on the spatial features of photons, such as Hermite-Gaussian (HG) modes. For this purpose, analyzers which can be used to measure the HG modes of photons are needed. In this thesis, we provide the schemes of these analyzers, which can separate HG modes to different ports just as a polarized beam splitter does. To construct the analyzers, we also introduce another kind of devices called “mode retarders”, which are analogous to wave plates because they introduce phase differences between corresponding HG modes. By coupling these mode retarders with sets of Mach-Zehnder interferometers (MZIs) in the configuration of a binary tree, one can perform measurements on passing light in the HG basis. Several sources are produced by computer-generated holograms (CGHs) to demonstrate these schemes experimentally, while the corresponding simulations are also made to confirm our predictions in the more precise way.