We have utilized the finite-difference approach to explore electron-tunneling properties in gapped graphene through various electrostatic-potential barriers ranging from Gaussian to a triangular envelope function in comparison with a square potential barrier. The transmission coefficient is calculated numerically for each case and applied to the corresponding tunneling conductance. It is well known that Klein tunneling in graphene will be greatly reduced in gapped graphene. Our results further demonstrate that such a decrease of transmission can be significantly enhanced for spatially-modulated potential barriers. Moreover, we investigate the effect from a bias field applied to those barrier profiles, from which we show that it enables the control of electron flow under normal incidence. Meanwhile, the suppression of Klein tunneling is found more severe for a non-square barrier and exhibits a strong dependence on bias-field polarity for all kinds of barriers. Finally, roles of a point impurity on electron transmission and conductance are analyzed with a sharp peak appearing in electron conductance as the impurity atom is placed in the middle of a square barrier. For narrow triangular and Gaussian barriers, however, the conductance peaks become significantly broadened, associated with an enhancement in tunneling conductance.

The effects of induced optical polarization by Dirac electrons in graphene on the hybridization of radiative and evanescent fields are found. Such effects result in a localized polarization field which significantly modifies an incident surface-plasmon-polariton (SPP) field. This yields a high sensitivity to local dielectric environments and provides an investigative tool for molecules or proteins selectively bound with carbons. A scattering matrix is utilized with varied frequencies in the vicinity of the surface-plasmon (SP) resonance for the increase, decrease, and even a full suppression of the polarization field, which enables accurate effective-medium theories to be constructed for Maxwell-equation finite-difference time-domain methods. Moreover, double peaks in the absorption spectra for hybrid SP and graphene-plasmon modes are significant only with a large conductor plasma frequency, but are overshadowed by a round SPP peak at a small plasma frequency as the graphene is placed close to the conductor surface. These resonant absorptions facilitate polariton-only excitations, leading to polariton condensation for a threshold-free laser.