First-principle study of two-photon absorption in Fe₃O₄

Utilizing the length gauge and the electron density operator, we calculate the two-photon absorption (2PA) coefficient of Fe₃O₄ based on a full ab initio band structure. The pure two-photon interband transitions and those modulated by intraband transitions have been separated explicitly to determine their impact on the 2PA spectrum. A single main absorption peak instead of two will present in the spectrum by including the hybridization of inter- and intra-band transitions, which can be identified easily in future experimental studies. In addition, we find that in almost the whole 2PA-active spectral range, circularly polarized light can be absorbed with a much lower threshold power than the linearly polarized one. But the linearly polarized light is more easily to be manipulated. One can control the magnitude and resonance frequency of the 2PA coefficient by simply adjusting the polarization angle of the incident light. Our findings will deepen the understanding of the 2PA phenomenon in Fe₃O₄ nanoparticles.