Computationally efficient long-distance free-space optical simulation using a continuous-scaling angular spectrum method.

We propose a continuous-scaling angular spectrum (CSAS) method for efficient long-distance free-space optical (FSO) propagation simulation. By combining multistep propagation with continuously updated sampling intervals, the method maintains a constant sampling size and avoids the large computational grids required by conventional angular spectrum (AS) approaches. Under an aperture-limited framework, only the spatial-frequency components contributing to the received optical power (ROP) are preserved, and a low-frequency energy ratio is introduced to quantify the relevant spectral content. Numerical simulations and a 4.3 km outdoor FSO experiment demonstrate that CSAS provides consistent ROP estimation compared with conventional AS, while significantly reducing computational cost. At a propagation distance of 4.3 km, the proposed method achieves approximately 98% reduction in computation time without degrading power estimation performance. The results indicate that CSAS offers an efficient propagation framework for long-distance FSO systems, particularly for scenarios involving multi-step turbulence modeling and system-level evaluation.