圓形及橢圓之微碟共振腔的遠場量測與分析

Abstract

本論文中，我們研究微碟的幾何形狀與遠場的關係，以達成指向性的控制。我們研究的微碟形狀包括：主要作為對照組的圓形微碟、具有不同長短軸比例的橢圓微碟，以及半圓半橢的非對稱形狀。 在頻譜量測時，雖觀察到量子點的發光，但並未從圓形微碟觀察到迴音廊模態，可能是因為量子點材料經長期儲放後已劣化；在長短軸比為1.25的橢圓與1.125之半圓半橢頻譜量測中，當激發光源分別聚焦於長軸或短軸時，訊號會有強弱之分，乃因為長軸相比於短軸，其激發後穿越共振腔的距離較短，訊號衰減程度較少。在長短軸比為2.5的橢圓，因其形狀已不利於全反射的產生，故訊號極微弱；至於長短軸比為1.75的半圓半橢，因具有半圓的結構，使得光仍能一定程度沿週邊運行，故能區分訊號與雜訊。 除了進行不同形狀共振腔的頻譜量測外，我們同時也進行了遠場場型的量測。使用532 nm綠光雷射激發量子點，通過550nm濾波片後，由Si photodetector收光，再經由Lock-in Amplifier放大，最後由Labview程式讀取。因遠場量測時，發光並未經單光儀濾光，且共振腔本身的形狀也不完美，因此圓形微碟的遠場場型並非完美的圓。 橢圓微碟中因曲率大的地方容易以切線的方向漏光，故在傾向垂直長軸的方向有較大的光強度；在半圓半橢中，因曲率最大的地方只有一處，位於橢圓長軸邊上的端點，故只有此點的切線方向光強度明顯較大，其遠場場型具備顯著的指向性。此外，我們刻意改變長短軸比為1.75的半圓半橢的0度位置，證實光強度確實與曲率大小有關連。

In this paper, we studied the relationship between the geometry of microdisks and their far-field properties to achieve directional control. The microdisk shapes we studied include: the circular microdisk, which serves as the primary control group, elliptical microdisks with different aspect ratios, and an asymmetric semi-circle-ellipse shape. During spectral measurements, although the quantum dot luminescence was observed, no whispering-gallery modes were detected in the circular microdisk. This might be due to degradation of the quantum dot after prolonged storage. In the case of elliptical microdisks with an aspect ratio of 1.25 and the semi-circle-ellipse shape with an aspect ratio of 1.125, the signal intensity varied depending on whether the excitation light was focused on the long axis or the short axis. The reason is the excitation light travels a shorter distance through the cavity along the long axis compared to the short axis, leading to less signal attenuation. For the elliptical microdisk with an aspect ratio of 2.5, the shape was unfavorable for total internal reflection, resulting in a very weak signal. On the other hand, there is the semicircular structure in the semi-circle-ellipse shape with an aspect ratio of 1.75 and it allows the light to propagate along the periphery so that we can enable differentiation between signal and noise. In addition to spectral measurements of various cavity shapes, we also performed far-field pattern measurements. Quantum dots were excited with a 532 nm green laser, and the emitted light was filtered through a 550 nm filter before being detected by a Si photodetector. The signal was then amplified by a lock-in amplifier and read by a Labview program. In the far-field measurement, because we didn’t use the monochromator for filtering and the cavity shapes were imperfect, the far-field pattern of the circular microdisk was not a perfect circle. In elliptical microdisks, the light tends to leak out more at regions with larger curvature, leading to higher intensity along directions perpendicular to the long axis. The point with maximum curvature is only one and located at the end of the ellipse’s long axis in the semi-circle-ellipse shape, and thus the light intensity is significantly higher at this point, resulting in the obvious directional far-field pattern. Additionally, we deliberately varied the 0 degree position of the semi-circle-ellipse with an aspect ratio of 1.75 to confirm that the light intensity is indeed related to the curvature size.