To obtain sub-wavelength focusing of light by using all-dielectric materials, we propose a new concept for the design of inhomogeneous refractive index profile with random distributions of elements occupying the unit cells of photonic crystals (PCs). Light focusing phenomenon is both systematically and quantitatively analyzed at different operating frequencies and we show that focusing ability of randomly generated GRIN like photonic medium pushes the limit of diffraction and allows light beam to focus into a spot size below λ/2. Numerous designs are iteratively generated with the same Gaussian probability function in order to investigate novel optical characteristics of the medium in both frequency and time domains.
We have specifically examined sub-wavelength focusing abilities of the designed random PC structures. Obtained results show that at long wavelength regime, the proposed configuration can achieve strong sub-subwavelength focusing effect. Due to different dielectric material density orientations, both off-centered and directional radiation patterns can be generated. The proposed idea of merging randomness with engineering index distribution yields rich light manipulation capabilities. Sub-wavelength focusing of light holds great potential in various applications such as nanolithography, optical microscopy, and optical precision measurements and data storage.