Complex Conductivity Dependent Goos-Hanchen Shifts Through Metallic Surface

We investigate complex conductivity dependent tiny lateral Goos-Hanchen shifts in a four-level conductive medium. The joint combination of density matrix formalism and Maxwell's equations are exploited to derive formula for the conductivity dependent Goos-Hanchen shift. Eight types of phase refractive indices are noted which are associated to reflection, transmission and their corresponding Goos-Hanchen shifts for a single plane incident wave. We observe strong dependency of the Goos-Hanchen shifts on complex conductivity and the incident angle. Positive and negative shifts in reflected and transmitted beams are investigated with forward and backward currents and a maximum of +/- 4 lambda lateral shift is noted with complex conductivity. The results achieved may show significant applications in nano-processor technology and conductive sensor devices.