Theoretical analysis of Talbot distance in hyperbolical medium

The self-imaging (Talbot) effect in hyperbolic mediums is analyzed theoretically. In these mediums, the transverse and longitudinal permittivity components have opposite signs. We propose a general solution about the Talbot distance in these mediums. Approximations are given for both deep sub-wavelength gratings and gratings with periods much larger than the incident wavelength. Based on these approximations, formulas for the Talbot distance in different cases are given and demonstrated. The Talbot effect in hyperbolic medium can be used to achieve super resolution, thus enabling applications such as photolithography.