Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory

A procedure for designing binary diffractive lenses by use of pulse-width-modulated subwavelength features is discussed. The procedure is based on the combination of two approximate theories, effective-medium theory and scalar diffraction theory, and accounts for limitations on feature size and etch depth imposed by fabrication. We use a closed-form expression based on zeroth-order effective-medium theory to map the desired superwavelength phase to the width of a binary subwavelength feature and to examine the requirements imposed by this technique on fabrication and on analysis. Comparisons are also made to more rigorous approaches. In making these comparisons, we show that a trade-off exists between the exactness of the mapping and the fabrication constraints on the minimum feature.