光學相位共軛模擬：如何控制光在散射介質裡聚焦

Abstract

在近幾年的生醫光學研究裡，如何使光聚焦在散射介質裡面，一直是個熱門的研究目標。在本論文裡，我們介紹了一種方法可以使光成功聚焦，這種方法叫做光學相位共軛（optical phase conjugation）。為了要觀察這種聚焦的現象，我們採用了一種數值的模擬方法，叫做擬譜時域分析法（pseudospectral time-domain）去模擬光聚焦。擬譜時域分析法是源自於馬克斯威方程式（Maxwell equation）的數值解，這套方法有助於我們去模擬電磁波大範圍空間的問題，也降低了模擬時的電腦記憶體。在本論文裡，我們詳細的推導了擬譜時域分析法的公式以及操作，最後我們成功模擬了光學相位共軛聚焦現象。在光學相位共軛的理論裡，我們會紀錄光通過的振幅以及相位，之後用這振幅和相位去產生一個相位反轉的波，這波會沿著原本的路徑傳播進入散射介質裡，並且聚焦在裡面。之後我們介紹了光學相位共軛的一種應用，這種應用叫做時間反轉超聲波編碼（time-reversed ultrasonically encoded），是一種使用光和超聲波的交互作用，使光能聚焦在散射介質裡面的技術。在我們的模擬結果中，我們改變了相位共軛鏡（phase conjugate mirror）的角度範圍，這是一種鏡子用來產生相位共軛波，我們去研究不同的角度範圍，去觀察哪個角度可使它的聚焦最佳化。此外我們還去分析了不同解析度對聚焦的影響。這個模擬使我們了解光的特性在散射介質裡聚焦成像。

Focusing light through the scattering medium is the optical application due to penetration of biomedical optics. In this thesis, we introduce the novel method of optical phase conjugation (OPC) to focus light inside the scattering medium. In order to observe this phenomenon, we provide the numerical method of pseudospectral time-domain (PSTD) technique to simulate the OPC focusing. PSTD simulation technique is employed to obtain numerical solutions of Maxwell’s equations. PSTD technique is good for simulating large space problems and reducing the computer storage. In this thesis, we demonstrate the derivative of PSTD algorithm and the simulation of OPC focusing. In the OPC theory, amplitude and phase of the outgoing light is recorded and later used to generate phase-conjugated light which back-propagates through the scattering medium, and focuses inside. Then, we introduce the application of OPC theory which called time-reversed ultrasonically encoded (TRUE). TURE is the novel technique which use the light and ultrasound to focus inside the scattering medium. In our results, by changing the angular span of phase conjugate mirror (PCM) which generates the phase-conjugated light, we can analyze back-propagation of light for different angular spans. The simulation results may help determine the optimal angular span for practical back-propagation of light. In addition, we also analyze the influence of the resolution to the focusing phenomenon. In this simulation, we understand property of light focusing through the scattering medium.