Enhancement of the Electric Field and Diminishment of the Group Velocity of Light in Dielectric Multilayer Systems: A General Description

We present analytical formulae for light propagation through a multilayer of dielectric media as a function of the "total charge" and the "accumulated charge" that we propose by the transfer-matrix method. We redefine the concept of the total charge introduced by Liu et al. [J. Phys. Condens. Matter. 29, 455303 (2017)] and newly define the accumulated charge to determine the magnitude of electric field inside the multilayers analytically. In addition, we derive an analytical expression for the group velocity of light in each layer. The purpose of this work is to predict which kind of sequence would provide the strongest amplification of the electric field inside the multilayer as well as to find the sequence that gives the lowest group velocity. We find that the symmetric alternating sequence gives the best amplification of the electric field and the lowest mean group velocity compared with the other sequences.