Diffractive optical elements using the sub-wavelength scale pillar array structure

We propose the diffractive optical element using the sub-wavelength scale pillar array structure. The equivalent microscopic refractive index can be controlled by changing pillar width and the pillar lattice constant. Advantages of using the sub-wavelength scale structure to manipulate the equivalent index in such a manner are that the optical functional elements can be fabricated by a single-etch-step process, and that the anisotropic optical characteristics can be realized using isotropic materials. In this paper, we have designed and fabricated the Fresnel lens with sub-wavelength structure on the Si substrate. The equivalent refractive index, n_eff, as a function of the pillar width and the lattice constant was calculated by the EMT (Effective Medium Theory). The width of pillar at the n-th lattice point, a_n, was determined by n_eff and required the local optical length of the target diffractive optical element. The design wavelength, λ, was set at 1.6 μm, the lattice constant, Λ, was 0.45 μm, the pillar height, h, was 1.21 μm, and the refractive index of Si, n_si, was 3.48, respectively. These parameter values satisfied the sub-wavelength condition of λ > n_si Λ. The Fresnel lens with a focal length of 20 mm and the effective diameter of 1.8mm was designed and fabricated.