高斯光束计算平板波导自由传输区远场分布及其修正

Calculation of the Far Field Pattern from a Planar Waveguide Using a Modified Gaussian Beam Approximation

对近轴近似条件下求解亥姆霍兹方程得到的高斯光束显式传播公式做了分析 ,同时 ,基于基尔霍夫衍射理论 ,在菲涅耳近似的条件下给出了相应的高斯光束在远场的传播公式 ,在此基础上 ,对近轴近似条件做出了定量分析 ,给出了这个近似条件引入的误差 ,提出了一种计算高斯光束远场分布的修正方法 ,并采用有限差分光束传播方法 (FD BPM)来检验各种方法的准确性。把这种修正方法应用到平面光集成波导器件 ,如阵列波导光栅 (AWG)、蚀刻衍射光栅 (EDG)等器件的设计和模拟中 ,可以大大降低工作的复杂性 ,同时可以得到精确的结果。

Conventional formula for a Gaussian beam propagating in a homogeneous slab waveguide can be derived by solving the Helmoholtz equation with the paraxial approximation. Based on the Kirchhoff diffraction theory, a more accurate formula is derived. The quantitative error of the conventional formula is analyzed and a modification is given to improve the accuracy. The accuracy of the modified formula is verified by a numerical simulation with finite difference-beam propagation method (FD-BPM). The modified formula can be used to simplify the design and simulation for integrated photonic devices such as arrayed waveguide grating (AWG) and etched diffraction grating (EDG).