串接式布拉格反射鏡用於窄頻寬帶通光學濾波器之研究

Abstract

本論文旨在探討如何藉由布拉格反射鏡的串聯，來實現一個具有窄頻寬的帶通光學濾波器，並討論如何以體積全像光柵來製作光學濾波器所需的布拉格反射鏡，進而分析此種體積全像串接式光學濾波器的穿透響應特性，再以光學實驗來證實我們設計的可行性。因此，論文內容中，我們首先由傳輸矩陣分析法出發，分析傳統的薄膜光學濾波器在不同結構下的穿透響應特性，了解如何設計一個具有理想矩形響應的窄頻寬帶通濾波器。然後再以由體積全像波耦合理論推導出反射式體積光柵的散射矩陣分析法，得以討論體積全像光柵在不同的串接結構下對於穿透響應的影響。在實作上，我們以PQ/PMMA光感高分子材料記錄體積全像反射式光柵，並嘗試以熱蒸鍍MgF2光學薄膜的方式製作光學共振腔，由理論及實驗上的分析可得知，若以體積全像光柵串聯，亦可由調整光柵長度、光柵週期、光學共振腔等串聯結構及條件，來達成我們所想要的窄頻寬光學濾波器，然而不同的是體積全像光柵對於結構、折射率變化、光柵長度的影響更為敏感，必須經由理論分析設計再行實作，才有成功的可能。

In this thesis, we propose a method to achieve a narrow band-pass optical filter using cascaded Distributed-Bragg-Reflectors (DBRs) and optical cavity, which construct a Fabry-Perot-like interferometry. Firstly, we analyze the traditional thin-film coating multi-layer optical filter by the use of transfer matrix method. The results can give us a guide how to design an optical narrow band-pass filter with nearly rectangular transmission spectrum. Secondly, by using the coupled-wave analyses of a volume hologram, we derive the scattering matrix method to analyses the diffraction properties of a reflection-type volume hologram. It provides us an extended matrix method to investigate the transmission characteristics of different cascaded structures of the volume holographic gratings. In experiment, we use PQ/PMMA photopolymer to fabricate volume holographic reflection-type gratings, and then the resonance cavities are fabricated by using thermal coating of MgF2 thin film. The theoretical and experimental results show that it is possible to achieve a narrow band-pass optical filter by using cascaded volume holographic gratings. However, the grating length, cascading structure and optical resonance cavity length must be chosen carefully such that the phase condition of Fabry-Perot-like structure can be matched.