Planckian signatures in optical harmonic generation and supercontinuum

Many theories of quantum gravity, as string theory, loop quantum gravity, and doubly special relativity, predict the existence of a minimal length scale and outline the need to generalize the uncertainty principle. This generalized uncertainty principle relies on modified commutation relations that - if applied to the second quantization - imply an excess energy of the electromagnetic quanta with respect to $\hbar \omega$. Here we show that this "dark energy of the photon" is amplified during nonlinear optical process. Therefore, if one accepts the minimal length scenario, one must expect to observe specific optical frequencies in optical harmonic generation by intense laser fields. Other processes as four-wave mixing and supercontinuum generation may also contain similar spectral features of quantum-gravity. Nonlinear optics may hence be helpful to falsify some of the most investigated approaches to the unification of quantum mechanics and general relativity.