Evolution of a finite Olver beam propagating in a right handed and double negative index slab system

In this work, we investigate the evolution of a first order finite Olver beam and a zeroth order one (finite Airy beam) propagating in a right handed and double negative index cascaded slab system based on the transfer matrix and generalized Huygens-Fresnel integral equation. It is discovered that the incident finite Olver beam could reappear on the output cross section by using a periodic slab system with a negative index material as long as nl= −nr, L = R; for nl≠−nr, the bigger abs(nl) is, the longer the needed unit length L to achieve an original beam intensity reproduction, and vice versa; the relations between the negative refractive index and the double negative material unit length are also quantitative explored by using the Origin Lab. It is expected that the derived analytical formulae and conclusions can provide a convenient and effective way for studying the evolution of a finite Olver beam propagating in multilayered structures, especially for periodic and quasi-periodic slab systems.