On the Solution of Photorefractive Dynamic Equations by using the Combination of the Finite Element Method and the Finite Difference Method

• Main Authors: Shiang-Yeh Chiang, 江尚曄
• Other Authors: Shon-Fu (Shong-Hu) Chen (Donn)
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/gcu89s

碩士 === 中原大學 === 應用物理研究所 === 91 === Photorefractive material may be used for information storage as well as control or processing elements in optical information processing systems. Understanding photorefractive mechanisms can be very useful in facilitating further material development. The first and the simplest theory for explaining photorefractive mechanisms was proposed by Kukhtarev in 1977 using the single carrier-single energy level model. To date, this set of equations can only be solved analytically under the assumption of a small light modulation. Several authors have done numerical simulations and most of the results followed the line of prediction of the small light modulation model, i.e., Kukhtarev’s model. According to Kukhtarev’s model for the photorefractive effect and the Coupled Wave Theory, the amplitude of such an index grating, Dn, grows exponentially until it reaches its saturation amplitude Dn0. However, this result was obtained under the small light modulation assumption. Experimental results show that Kukhtarev’s model is also valid under large light modulation. This thesis uses a combination of the finite element method for the spatial domain and the finite difference method for the time domain to calculate the grating growth speed t and the saturation amplitude Dn0. We confirm that the Kukhtarev’s equation has a linear solution for large light modulations, which is consistent with the result of finite element calculation of Kukhtarev’s equation at steady state. The algorithms employed for both the steady and dynamic calculation are different from each other yet their results conform. We also confirm the proper assumption for obtaining a linear solution of Kukhtarev’s equation is that the free electron modulation must be smaller than the light modulation. Also the grating period employed in the calculation, L, must be smaller than a maximum grating period in order to obtain a proper linear solution as the one predicted at steady state. This condition is in fact the same as the condition that the free electron modulation must be smaller than the light modulation. We thus have solved n0 numerically as a function of L and found that the n0 for coincide with the prediction of Kukhtarev’s model.