Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, and optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable second order nonlinear susceptibility chi ^(2) once an in-plane electric field is applied. chi^(2) can be electrically tuned from 0 to ~ {10^5 pm/V}, three orders of magnitude larger than the widely used nonlinear crystal AgGaSe2. We show that the unusually large chi^(2) arises from two different quantum enhanced two-photon processes thanks to the unique electronic spectrum of BLG. The tunable electronic bandgap of BLG adds additional tunability on the resonance of chi^(2), which corresponds to a tunable wavelength ranging from ~2.6 {mu}m to ~3.1 {mu}m for the up-converted photon. Combined with the high electron mobility and optical transparency of the atomically thin BLG, our scheme suggests a new regime of nonlinear photonics based on BLG.
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