negative refraction based on supermode theory in metal waveguide arrays

We investigate the phenomenon of negative refraction (nr) in metallic waveguide arrays (mwgas) by illuminating partial waveguides. some waveguides in mwgas are sheltered and the other waveguides are opened; only these opened waveguides can be illuminated by the incident wave. these illuminated waveguides will be independently excited surface plasmon polariton (spp) supermodes at the entrances, which will propagate along the waveguides of mwgas. the total field is the superposition of the excited spp supermodes, which is varied with transmission distance. at certain places in mwgas, the total field is enhanced and the nr phenomenon is formed. we find that nr phenomenon not only was under the control of incidence angle, but also was governed by the number of illuminating waveguides, which become more prominent when the number of illuminating waveguide increases. the spp supermode theory is applied to explain this nr phenomenon. the result by the supermode theory is validated by the numerical simulations of the finite-difference time-domain method.