基于高斯光束与射线追踪的短波波场计算算法

短波通信中几何光学理论难以计算焦散波场的传播问题,提出一种基于高斯光束的短波传播计算算法.首先,采用高斯光束法将产生高频波场的波源分解为若干个高斯光束;然后,通过射线追踪法与拉格朗日公式计算每个高斯光束,通过沿光束中心射线的ODE(常微分方程)计算曲率与光束宽度等定量;最终,采用泰勒展开式决定中心射线附近光束的贡献度,将接收点附近的高斯光束进行加权求和,获得接收端的波场.实验结果表明,本算法可有效地计算焦散的短波传播,并且与几何光学法的误差极为接近.

High frequency wave field computational algorithm based on Gaussian beam and ray tracing

Geometrical optics theory is unable to solve the problem of computing the wave propagation problem of wave field with caustics, a Gaussian beam based high frequency wave propagation computational algorithm is proposed. Firstly, the Gaussian beam method is adopted to decompose the wave source of high frequency wave field into Gaussian beams; Then, each Gaussian beam is computed by ray tracing and Lagrangian formulation, and the values for width and curvature are computed by solving the ODE(Ordinary Differential Equations) of the central rays of the beams; lastly, the contributions of the beams concentrated close to their central rays are determined by Taylor expansion, the wave field of receiver point is computed by a weighted sum of beams near the receiver point. Experimental results show that the proposed algorithm can compute the high frequency propagation with caustics efficiently, and releases a similar error compared with geometrical optics method.