以數值方法分析奈米懸浮液中的光學自聚焦效應

Abstract

本論文以數值方法探討在奈米懸浮液中的光學自聚焦現象，模擬高斯光束在10%奈米懸浮液的非線性介質中的傳播行為，以其光腰的大小觀察自聚焦現象。光束在懸浮著奈米尺寸粒子之液體中傳播時，該粒子受到光束的散射力作用開始運動，並因此重新分佈。由於粒子的折射率與液體的折射率不同，此二種物質所形成的折射率分佈影響光束的傳播行為，光束可由發散變成聚焦。 在先前文獻中[3][4]，藉由實驗量測粒子的移動距離能推算其運動速度約為30μm/s，所改變的折射率為2。0×10−4，並觀察到入射光與奈米懸液作用一段時間後的聚焦結果。即便在實驗上可以觀察到粒子受力移動及光束自聚焦的現象，但此現象的動態變化及理論方面仍需要進一步的分析。 因此，本文提出一種以數值模擬並分析奈米懸液中的光學自聚焦現象的方法，該方法包括光束傳播法(BPM)用於模擬光在非均相的折射率分佈中的傳播行為，以及有限差分法處理作為描述流體的運動的Navier-Stokes方程式。其中，將奈米懸浮液視為固態粒子與液態流水的二相混合物，以粒子與液體之間的速度差作為動量交換，使得受散射力作用而運動的粒子帶動周圍的流體並產生流場。 此方法計算奈米懸液之流速、重新分佈的折射率，以及光束大小之動態結果，觀察出粒子在光的傳播方向上因速度的不同而形成堆積，並提昇局部的折射率∆n約為10−4，使得高斯光束的光腰隨時間變窄的自聚焦現象。

This thesis presents research on the optical self-focusing effect in suspension of nanoparticles with numerical methods. The simulating scenario is associated with a Gaussian laser with the wavelength at 532 nm and the waist of 20 μm launched into a cell of suspension with 10% Polystyrene nanoparticles to observe the optical self-focusing phenomenon. The implementation of the simulation comprises the beam propagation method (BPM) and finite-difference Navier-Stokes equation, and the computations are made by using Python. The BPM is adopted to address the light propagating in an inhomogeneous medium, and the Navier-Stokes equation is adopted to solve the motion of fluid dynamics in suspension. The nanoparticles drag the fluid to flow forth due to the optical scattering force, and the velocity differences between the nanoparticles and the fluid contribute to the exchange of momentum in the mixture of the fluid phase and particulate phase, which characterizes the relation between the light and fluid dynamics. The simulation deals with the dynamical flow field of the suspension, redistributed refractive index and the beam shape, and the results indicate that the condition of self-focusing in suspension is based on the nanoparticles accumulating along with direction where the beam is propagating, which further changes the distribution of refractive index to the order ∼ 10−4.