利用時域擬譜法分析光學相位共軛現象

Abstract

利用時域擬譜法 (PSTD)，我們開發了一套模擬工具，能夠對光學相位共軛現象 (OPC) 進行模擬。 由於時域擬譜法對於空間微分能精準估計，並節省記憶體。 因此，利用時域擬譜法，我們可以模擬一個大尺度的問題。 然而，利用時域擬譜法所進行的模擬，有一些需克服的問題，包括建構光源及光學相位共軛鏡。 為了避免硬波源 (hard source) 所造成的非自然反射，故我們使用軟波源 (soft source) 來實作光源。 另一方面，吉布斯現象 (Gibbs’ phenomenon) 會使得波源的邊緣不連續處產生高頻場值震盪誤差。我們藉由將光源加寬，降低訊號的空間頻率，以去除此誤差。於是，我們便能利用時域擬譜法來建立一個精確的光學相位共軛模擬。 另外，我們建立的光學相位共軛鏡模擬了實驗中的兩個階段，傳播 (forward) 及回聚 (playback): 在傳播階段，我們利用傅立葉轉換來記錄經過紊亂介質散射的光之相量 (phasor)；而在回聚階段，我們藉由改變記錄光的波印亭向量 (Poynting vector) 的方向並重新入射，此共軛光將會如時光倒流般，循原路往回穿透紊亂介質。 如果我們增大模擬尺度，我們便得以進行將光學相位共軛鏡應用在生物組織上的模擬。由於大尺度的模擬運算量極大，故運用平行化運算來提高此模擬的運算速度是有其必要的。我們將模擬中的運算工作及資料平均分配給不同的CPU及記憶體，因而降低了大尺度光學相位共軛模擬的總運算時間。 在本論文中，我們建立利用時域擬譜法建立了一個精確的數值模型來模擬光學相位共軛現象。利用模擬，我們在光學相位共軛鏡中記錄了紊亂介質散射光的相量，並依此相量入射一相位共軛光至原紊亂介質上，則此共軛光將會穿透此紊亂介質，並聚焦在原光源處。至於未來的應用方面，我們希望經由模擬，能將光導引至紊亂介質(如生物組織)中的任意位置。隨著光學斷層掃描技術的進步，生物組織折射率的分布測量會更加精確。因此，利用光學相位共軛現象來進行非侵入式治療是值得期待的。

In the thesis, we show the development of a simulation tool for optical phase conjugation (OPC) phenomenon. We use the pseudospectral time-domain (PSTD) algorithm to implement our OPC simulation. The PSTD simulation is computationally efficient and memory-economic, enabling accurate modeling of the OPC phenomenon of light penetration through large-scale turbid media. In PSTD algorithm, however, we have a few problems to cope with, including the construction of a light source and an OPC mirror. To avoid the hard-source artificial reflection, a light source is implemented by soft sources. Also, the Gibbs’ phenomenon causes overshoots on the boundary of a soft source. Therefore, we broaden the width of the soft source to reduce the spatial frequency of the input signal. The overshoot noises are eliminated. With these problems solved, the PSTD simulation of OPC phenomenon is robust and error-controllable. The PSTD simulation of OPC phenomenon is divided into two parts as the OPC experiment: the forward and playback scenarios. In the forward scenario, we record the phasor of light scattered by turbid media; in the playback scenario, we emit the recorded scattered light with its phase conjugated and Poynting vectors inverted. The phase-conjugated light penetrates through the turbid media and focus at the location of the original source. By increasing the simulation scale, we can apply the OPC phenomenon to a macroscopic, biological tissue. To speed up the macroscopic simulation, we develop an PSTD simulation of OPC phenomenon with parallel computation, distributing the computation work and data to different CPUs and computer memories, respectively. The time consumption of the OPC simulation reduces as the number of CPUs increases. We develop an efficient simulation technique to model the OPC phenomenon using the PSTD analysis. In the simulation, the phasors of light scattered by turbid media are recorded by the OPC mirror. With these phasors, the OPC mirror emits phase-conjugated light. The light penetrates through the turbid media and focuses at where it originated. As for future applications, our goal is to deliver light to arbitrary location within the turbid media by the OPC simulation. With the progressive tomography of a biological tissue, the development of a non-invasive OPC treatment is promising.