Simulating resonance-mediated two-photon absorption enhancement in rare-earth ions by a rectangle phase modulation

Improving the up-conversion luminescence efficiency crucial in several related application areas. In this work, of rare-earth ions via the multi-photon absorption process is we theoretically propose a feasible scheme to enhance the resonance-mediated two-photon absorption in Er3＋ ions by shaping the femtosecond laser field with a rectangle phase modulation. Our theoretical results show that the resonance-mediated two-photon absorption can be decomposed into the on-resonant and near-resonant parts, and the on-resonant part mainly comes from the contribution of laser central frequency components, while the near-resonant part mainly results from the excitation of low and high laser frequency components. So, the rectangle phase modulation can induce a constructive interference between the two parts by properly designing the modulation depth and width, and finally realizes the resonance-mediated two-photon absorption enhancement. More- over, our results also show that the enhancement efficiency of resonance-mediated two-photon absorption depends on the laser pulse width （or laser spectral bandwidth）, final state transition frequency, and intermediate and final state absorption bandwidths. The enhancement efficiency modulation can be attributed to the relative weight manipulation of on-resonant and near-resonant two-photon absorption in the whole excitation process. This study presents a clear physical insight for the quantum control of resonance-mediated two-photon absorption in the rare-earth ions, and there will be an important significance for improving the up-conversion luminescence efficiency of rare-earth ions.