Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method

Efficient calculation of the light diffraction in free space is of great significance for tracing electromagnetic field propagation and predicting the performance of optical systems such as microscopy, photolithography, and manipulation. However, existing calculation methods suffer from low computational efficiency and poor flexibility. Here, we present a fast and flexible calculation method for computing scalar and vector diffraction in the corresponding optical regimes using the Bluestein method. The computation time can be substantially reduced to the sub-second level, which is 10⁵ faster than that achieved by the direct integration approach (~hours level) and 10² faster than that achieved by the fast Fourier transform method (~minutes level). The high efficiency facilitates the ultrafast evaluation of light propagation in diverse optical systems. Furthermore, the region of interest and the sampling numbers can be arbitrarily chosen, endowing the proposed method with superior flexibility. Based on these results, full-path calculation of a complex optical system is readily demonstrated and verified by experimental results, laying a foundation for real-time light field analysis for realistic optical implementation such as imaging, laser processing, and optical manipulation.