Goos-Hänchen Shifts in Graphene with Spatially Modulated Potential

Using the energy spectrum of graphene with spatially modulated potential, we study the Goos-Hänshen shifts near extra Dirac points located at finite energy $\varepsilon=mπ$, with $m$ integer. On both sides of such points, we show that the Goos-Hänshen shifts can be negative as well as positive under various conditions. It is found that the shifts are strongly depending on the effects of the incident energy, potential height, incident angle and width of central region of unit cell. Such effects tell us that such width can be used to tune the shifts at the extra Dirac points.

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