Rayleigh-Sommerfeld diffraction on a subwavelength scale: Theories and a resolution criterion

Abstract

Classical resolution criteria such as Rayleigh's and Sparrow's are based on the fringe structure produced by Fresnel diffraction or Fraunhofer diffraction. However, these two diffraction theories are based on the assumption of large-aperture scale and are thus incapable of describing the diffraction of subwavelength structure. We find a singularity near the incident wave vector ${k}_{0}$ in a subwavelength aperture by considering Rayleigh-Sommerfeld diffraction. The diffraction fringe structure disappears once the aperture scale is smaller than a threshold value. A two-point resolution criterion unrelated to the fringe structure is proposed based on the second-order derivative of the field structure. Numerical results indicate that, for the illumination wavelength of $\ensuremath{\lambda}=500\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, resolution of two 100-nm rectangular holes under near-field Rayleigh-Sommerfeld diffraction is improved by about 300 and 20% in the $x$ and $z$ directions, respectively, compared with the Sparrow criterion, while the lateral resolution limit is reduced to 35 nm.