Focusing and phase compensation of paraxial Hermite-Gaussian and Laguerre-Gaussian beams by a negative refractive index material slab

According to angular spectrum representation, formalisms describing paraxial Hermite-Gaussian and Laguerre-Gaussian beams propagating through an isotropic negative refractive index material (NIM) slab are presented. Focusing and phase compensation of paraxial Hermite-Gaussian and Laguerre-Gaussian beams by the slab are investigated. The phase difference of beams caused by Gouy phase shift in air can be compensated by the inverse Gouy phase shift in NIM, thus the phase difference between the object plane and the image equals to zero in certain matching conditions. If conditions of focusing and phase compensation are satisfied simultaneously, intensity and phase distribution at object plane can be reconstructed at the image plane.