The finite-difference time-domain (FDTD) method is used as rigorous electromagnetic analysis model to calculate the field for a diffractive microlens (DML). The FDTD is used for the entire solution rather than using a near- to far-field propagation method to obtain the far-field energy distribution; thus, all the results are vector based. We derived a formula to calculate the magnitude of electric field, which is time dependent and can be used to graphically show the light wave propagation and focusing process through a DML. Both the comparison and the integral methods are presented to obtain wave amplitude in full solution space, and the distribution of light energy behind a DML is illustrated based on the wave amplitude. The formula of diffractive efficiency of the DML is derived from a time-averaged Ponyting vector, which can indicate the propagation direction of light energy. Application of these formulations in the analysis of a DML example demonstrates the high accuracy and efficiency of our method.
"Analysis of a diffractive microlens using the finite-difference time-domain method," Journal of Micro/Nanolithography, MEMS, and MOEMS 9(3), 033004 (1 July 2010). https://doi.org/10.1117/1.3469817