Por Daniel Passos (CFTC, Lisbon University).

The nonlinear conductivities, or susceptibilities, are response functions that encapsulate the nonlinear optical properties of materials observed under sufficiently intense laser light [1]. They are involved in describing everything in perturbative nonlinear optics, from second harmonic generation to the Kerr effect, self-focusing and even the more recently proposed jerk current [2]. Despite their central importance, the calculation of these quantities for crystals remains a challenge, partly due to the complexity of the perturbation theory involved. Here, this complexity is examined and recent advances are reviewed, with focus on electronic nonlinearities under the independent particle approximation. The resolution of a decades-long debate concerning gauge invariance (or lack thereof) is presented, as well as two new methods of computation of nonlinear conductivities: a numerical algorithm based on a newly developed perturbation theory [3]; and a methodology for analytical derivations that follows from the standard length gauge perturbation theory [4,5].

References:
[1] Cotter, D., Butcher, P. N., (1991), Elements of nonlinear optics , Cambridge University Press
[2] Fregoso, B. M., Muniz, R. A., Sipe, J. E. (2021), Physical Review Letters, 121
[3] Ventura, G. B., Passos, D. J., Lopes, J. M. V. P., Lopes dos Santos, J. M. B., (2021), Comment on [2], Physical Review Letters, 126
[4] Passos, D. J., Ventura, G. B., Lopes, J. V. P., Lopes dos Santos, J. M. B., (2018), Physical Review B, 97
[5] Aversa, C., Sipe, J. E., (1995), Physical Review B, 52