光折變晶體之自聚焦透鏡及在富氏平面多重分光器之應用

Abstract

本論文研究光折變晶體中的自聚焦現像，使用能帶遷移模型及一維漸變折射率透鏡理論來說明其聚焦性能；然後使用氦氖雷射照射矽酸鉍晶體的聚焦性能來驗證此理論，從實驗得到透鏡的焦距為25m。為了把入射光束為高斯強度分布的條件推廣，本論文提出使用繞射光去感應出自反聚焦透鏡，此繞射光是由均勻的光束照射狹縫產生，從推導出的自聚焦理論及繞射光的輪廓變化找出最佳的光束照射位置，就是在Rayleigh距離時得到最強聚焦力的自感應的微透鏡，用富氏轉換的方式就可觀察到矽酸鉍晶體中所感應出的微透鏡。為了說明此種微透鏡的應用價值，提出應用此微透鏡在一個富氏平面多重分光器中，此分光器的輸入元件通常是液晶顯示器，因此先探討液晶顯示器為輸入元件的富氏平面多重分光器的原理，然後將此分光器應用在具有複合濾波器的光學相關器中，來改善不變性之辨認。為提高此複合濾波器的性能，在原來的富氏平面多重分光器中加入自聚焦材料，就成為自感應透鏡陣列，能夠直接增加分割率，而方法只是在空間光調制器附近，畫素繞射光的Rayleigh距離置入光折變晶體，最後用單一微透鏡間接驗證其可行性。

The self-focusing effect in a photorefractive crystal is studied in this thesis. The focusing property is described by the one-dimensional theory of the gradient index (GRIN) lens and the band transport model, and is experimentally demonstrated with a He-Ne laser illuminating a BSO crystal. A self-focusing focal length(25m) is obtained by the experiment. To generalize the condition of the Gaussian intensity distribution of the illuminating beam, the thesis proposes to use a diffraction beam to induce a self-defocusing lens. The diffraction beam is generated by illuminating a slit with uniform beam. The optimum position along the beam for illuminating the crystal is obtained from the evolution of the diffraction beam and the derived self-focusing theory. Evidently, the position at the Rayleigh distance can generate a microlens with highest focusing power. Once again, the microlens in the BSO crystal is demonstrated by the experiments with the Fourier tranform. The potential application of the self-focusing microlens in a Fourier plane multiple beam splitter (FPMBS) is proposed. The FPMBS usually uses a liquid crystal display (LCD) as an input device. For this reason, the principle of the FPMBS using a LCD as an input device is studied. This FPMBS can then be applied into an optical correlator with a composite filter for improving the invariant recognition. For the purpose of enhancing the performance of the composite filter, the self-focusing material which works as a self-induced microlens array is applied into the original FPMBS. The splitting ratio can be increased. The result is obtained by directly inserting a photorefractive crystal at the Rayleigh distance of the diffraction beam from each pixel nearby the spatial light modulator.