Modeling of a diffractive micro-lens by an effective medium method

The rigorous vector-based simulation methods for subwavelength diffractive lenses are methods of growing importance. In this paper, we introduce a rigorous vector-based method to compute the electromagnetic propagation. It includes the Finite-Difference Time-Domain (FDTD) for the near field simulation, and the Radiation Spectrum Method (RSM) for the far field propagation. This approach is then proposed to design effective medium cylindrical diffractive lenses. This kind of component, made up of binary features that behave as an effective medium, can achieve an higher diffraction efficiency than conventional diffractive optical elements. The layout design of the component is realised thanks to the FDTD simulation by estimating the phase difference introduced by subwavelength binary gratings. Then, the whole modeling of the component, whose minimum feature size can be smaller than 100 nm, is done with the RSM algorithm. Because of their subwavelength, aperiodic, finite and high spatial frequencies characteristics, these devices conception methods prevent the use of scalar modeling or coupled wave theory. The proposed method overcomes these limitations. First, the principle of the rigorous vector-based method is introduced. Then, we present the design of the subwavelength structures by means of the FDTD method, followed by the design of the subwavelength element. Finally, the simulation method of the subwavelength lens by use of the FDTD method for the near field propagation and the RSM for the far field calculation is also presented. Finally, we discuss the comparison between a subwavelength lens and its multilevel counterpart.