Hermite-Gaussian-Talbot carpets

In this Letter, we demonstrate the generation of Hermite-Gaussian-Talbot carpets (HGTC) based on the interference of a Hermite-Gaussian (HG) beam array with constant successive separation (shift). Despite the acceleration of HG beams during propagation, their symmetric structure ensures that the self-imaged carpets are generated in straight lines perpendicular to the propagation direction, at particular distances, multiples of the famous Talbot distance z_T. By considering the separation as a multiple or a fraction of the Hermite-Gaussian beam width, the calculated Talbot distance z_T is expressed as a function of the beam parameters, such as the Rayleigh length. The same carpets are also observed in planes situated at different fractions of z_T, but with different frequency appearances. An interesting feature of these carpets is that the dimension of one cell of the beam array remains constant in each period (period fraction). We believe that such novel, to our knowledge, carpets will be useful in photonics for creating lattices and optical potentials.