Improved First Rayleigh Sommerfeld Method for investigating microlens array with long focal depth and small f-number

In recent years, with the developments of the micro-photolithography, micro-optical elements with small characteristic size and highly refinement are available. These micro-optical elements with a sub-wavelength structure can realize multi-function, such as a microlens array with a long focal depth and high transverse resolution, and it has been extensively studied owing to its potential applications. With the decrease of the characteristic size of faster focusing microlens array, the scattering or coupling effect of the light waves becomes much stronger. Therefore, rigorous Maxwell's electromagnetic theory should be adopted to analyze the focusing performance along both the longitudinal and transverse directions of faster focusing microlens array. However, rigorous numerical methods cost a lot of computing times and memories. Thus, it is impossible to perform optimal design of the faster focusing microlens array by rigorous methods. A simpler and faster, even somewhat less accuracy, design approach is needed. Various approximate scalar methods have been developed under some assumptions and approximations, which are inadequate, especially, in the analysis of various microlens with small f-number less than f/1.0 and small feature size. In this presentation, an improved First Rayleigh Sommerfeld Method (IRSM1) is applied to analyze the focusing performance of dual- and tri- cylindrical microlens arrays with long focal-depth and small f-number for the TE polarization. The real extended focal depth, the diffraction efficiency, the spot size, and the real position of the focal plane of the microlens array with different f-numbers and preset extended focal depths are calculated by the IRSM1, rigorous boundary element method (BEM) and original Rayleigh Sommerfeld method (ORSM1), respectively. The accuracies of the IRSM1 and the ORSM1 are evaluated along the longitudinal direction. The results indicate that the IRSM1 can be used for analyzing the cylindrical microlens array with long focal depth and small f-number, but the ORSM1 is fully failure for those microlens arrays with small f-number. This investigation can provide valuable information for optical engineers and might be used for further guiding the designs of the micro-optical elements for realizing longitudinal optical field modulation.