Focusing of light beyond the diffraction limit by randomly distributed graded index photonic medium

Sub-wavelength focusing of light holds great potential in various applications of science and engineering, including nanolithography, optical microscopy, optical measurements, and data storage. In the present paper, we propose a new concept to obtain sub-wavelength focusing of light by using structures composed of all-dielectric materials. The approach utilizes the design of an inhomogeneous refractive index profile with random distributions of individual elements occupying the unit cells of two-dimensional photonic crystals (PCs). Light focusing phenomenon is both systematically and quantitatively analyzed at different selected frequencies and we show that the randomly generated graded index (GRIN)-like photonic medium provides light focusing in air with a spot size below λ/3, where λ is the wavelength of light. The numerically obtained minimum spot size is equal to 0.260λ. Gaussian probability function is used to implement numerous random designs to investigate the optical characteristics of the photoni...

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