Second harmonic generation microscopic observations of a multiferroic $BiFeO3$ single crystal

Anisotropy of the optical second harmonic generation (SHG) in a multiferroic $BiFeO3$ single crystal is observed by an SHG microscope. Polarization dependences of SH intensities are measured in several polarization configurations of the incident and SH waves to determine the magnitude and sign of polar $i$-type SHG tensor components. To obtain proper values of these SHG tensors, the effects of the interference term and wave number mismatch are taken into account in these analyses. $d24$ component is 15 times larger than $d32$ and this result is essentially different from the thin film case.