In the article [1] we calculated the polarization dependent second harmonic generation (SHG) response of a single 90-nm barium titanate (BaTiO₃) nanoparticle based on Eq. (3) and (4). The Eq. (3) is actually

We have recently discovered that the factors of 2 in the calculation of Eq. (3) were missing. We corrected the mistake and plotted the normalized polarization dependent SHG responses of BaTiO₃ nanoparticles at different orientations in Fig. 1 (a). The corresponding estimated SHG cross section of a 90-nm BaTiO₃ particle is 465 – 4,820 GM. It should be noted that Fig. 1 (a) shows the total SHG power radiated by the three dipole moment components, and the radiation pattern is not uniform in space. To consider the non-uniform SHG radiation pattern, we use a simplified model: assuming the SHG power radiated by the axial (Z-axis) dipole moment is hardly collected. By excluding the contribution of the axial dipole moment, the theoretical calculation of the SHG polar response is plotted in Fig. 1 (b). The experimental result matches with the theoretical calculation when θ = 20 degree. With this simplified model on the collection efficiency, we calibrated the measured SHG cross section as 23,910-29,510 GM. The greater measured SHG cross section suggests the object under the measurement was either a particle of 125-nm diameter or a cluster of two properly aligned nanoparticles of equivalent volume.

 

Fig. 1. Polarization dependent SHG response of an isolated BaTiO₃ nanoparticle. (a) Theoretical calculation of the normalized SHG polar response from a nanoparticle of various orientations. (b) Line: theoretical calculation of the normalized SHG polar response contributed from the transversal nonlinear polarizations of a nanoparticle of various orientations. Dots: experimental data. The black arrows in the polar diagrams indicate the projection of the c-axis of the nanoparticle on the XY plane.

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