The authors analyze transmission of a normally incident plane wave through a Ag/dielectric layered concentric ring structure using finite-difference time-domain (FDTD) analysis. The authors study the dependency of the transmission efficiency on the refractive index in slit. The numerical analysis indicates that the focusing beyond diffraction limit is found even at the extended focal length comparable to the distance of 7 lambda from exit plane using a circularly polarized coherent plane wave, lambda=405 nm. Especially, compared to Ag-only structure, the Ag/LiNbO3 structure exhibits over 2.85 orders of larger transmission power. Therefore, this Ag/dielectric layered lens has the potential for significantly the high resolution imaging and optical data storage.