線狀液晶光學圖像形成之研究

Abstract

近十年來，非線性光學系統中光學圖像形成的研究吸引了很多學者投入心思探討。在這些研究中，理論的分析和模擬大致可以分為兩大類的光學系統，一為被動系統，一為光學共振腔系統；本論文將針對被動非線性光學系統中的光學圖像形成加以探討。被動光學系統指的是由外場驅動的光學系統，理想來說是穩定且固定的，並沒有考慮到例如光學共振腔中的居數反轉的現象。由於外場和非線性材料的作用，在系統存在微擾或雜訊時，透過強大的非線性作用，外場原本的狀態會受到雜訊的微擾而變得不穩定，因而造成光學圖像的產生。 在本論文中，我們探討利用外加似靜電場偏壓的線狀液晶在單一光回饋的系統中，其光學圖像形成的特性，雖然在此單一光回饋系統中光學圖像形成的穩定和控制已有很多的研究，但是線狀液晶基本的物理特性對於此光學圖像形成的現象影響尚未有深入的探討。在以往利用線狀液晶做此類研究的文獻中，據我們所知並無考慮電場效應的影響，是故我們針對在外加電壓偏壓下的線狀液晶其本身物理非等向特性，研究此光學圖像形成現象的影響。在理論分面，我們根據線狀液晶連續體理論，藉由系統最低能量的Euler-Lagrange分析步驟過程中推導出液晶分子在外場條件下的橫向分佈之擴散方程，根據此擴散方程，我們可以明顯看出液晶本身的彈性非等向性會造成擴散方程中擴散長度的非等向性； 針對此系統的擴散方程作線性穩定性分析，我們可以得到光學圖像形成所需的臨界入射光強度，分析此臨界光強我們發現擴散長度的非等向性也會造成臨界光強在橫截面分佈的非等向特性。在外加電場偏壓下的線狀液晶樣品，由於其本身的介電非等向性，液晶分子的排列可以利用外加電場加以適當地控制。在理論分析中，我們發現擴散長度和系統的非線性強度會和液晶分子的分佈有關。 所以，考慮液晶的彈性非等向性及液晶分子分佈的可電調特性，我們提出了不外加傅立葉空間濾波器的條件下，利用液晶本身非等向性造成臨界光強度非等向的特性，簡單地控制入射光強，即可得到條狀和六角狀的光學圖像。此外，由於彈性非等向性會造成臨界光強分佈的非等向性，所以我們更針對液晶法蘭克彈性常數的相對值對此光學圖像之形成會有哪些更進一步的影響作更深入的理論分析。另一方面，由於系統的非線性強度會和液晶分子的分佈有很大的關係，所以我們也就外加偏壓對系統非線性強度的影響作了進一步的分析。考慮電壓和臨界光強度非等向分佈的特性，我們更提出了在適當單一入射光強下，藉由電壓控制系統的非線性強度調變臨界光強的分佈曲線，也可以得到條狀和六角狀的光學圖像的證據。 在理論分析中我們所提出的圖像形成特性，不論是利用控制入射光強或是電壓調變臨界光強分佈的方法，皆可以實驗加以印證。我們的實驗結果也可定性的和理論分析相符。

Optical pattern formation in nonlinear optical systems has been widely studied in the last decade. Analysis and simulations of pattern formation in two classes of systems are presented. These are passive systems and the cavity systems. Here, we focus on the pattern formation in passive nonlinear optical systems. Passiveness means that the excitation is driven by an externally field, smoothly and constantly in the ideal case, rather than through population inversion. Optical pattern formation results from the nonlinear interaction between the external field and the nonlinear materials. Once a perturbation exists in this nonlinear system, such as the scattering light or the noise, the initial state of the external field may be perturbed and become unstable through the high nonlinearity of the system. In this dissertation, we investigate the optical pattern formation phenomena by using the quasi-static electric-field-biased liquid crystal (NLC) films in combination with the one-feedback-mirror system proposed by Firth and Pare. Though the controlling and stabilizing methods have been widely studied the basic physical uniqueness of the nematic liquid crystals appeared in these optical pattern formation phenomena has not been explored very clearly. The governing diffusion-like equation of the optical field induced phase variation in the transverse plane used in most theoretical analysis is assumed to be isotropic based on Firth’s method. However, the diffusion-like equation should be modified when nematic liquid crystals are used. Unlike the previously used operating modes such as the hybrid-aligned films, the vertically aligned films or the liquid crystal light valve (LCLV) samples, we further consider the parallelly planar-aligned NLC films biased by a quasi-static electric field. To our knowledge, the electric field effect on the optical pattern formation phenomena has not been included in the earlier theoretical analysis. From our previous works, we know that the optical nonlinearity of such NLC films can be effectively modulated by suitably applying a quasi-static electric field. Therefore, considering the anisotropic properties of the nematic liquid crystals, we derive the governing diffusion-like equation for the optical field induced phase variation in the transverse plane. Furthermore, the threshold intensity distribution for the patterns to be formed is also derived by the results of the linear stability analysis (LSA) of the governing diffusion-like equation. By analyzing the anisotropic threshold intensity distribution we propose a possible method to obtain the roll and the hexagon patterns without canceling the anisotropic property of the threshold intensity. We successfully observe the roll and the hexagon patterns by simply controlling the input light intensity. Furthermore, from the theoretical analysis, we know that the anisotropic distribution of the threshold intensity results from the elastic anisotropy of the nematic liquid crystals. Hence, we analyze the issue of how the elastic anisotropy affects the optical pattern formation phenomena. From the results of the analysis of the effects of the elastic anisotropy, we further study the influence of the applied electric field. The nonlinearity of the system can, indeed, be modulated by the applied electric field through the modulation of the orientation of the liquid crystal molecules electrically. Therefore, a simple electric-method is achieved to obtain different optical patterns with a single input light intensity. The experimental results in our work qualitatively agree with the theoretical results well and the suggested pattern-forming properties in our theoretical analysis can be reasonably proved.