Using spectroscopic ellipsometry, the refractive index and absorption versus wavelength of the ferroelectric antiferromagnet Bismuth Ferrite, BiFeO_3 is reported. The material has a direct band-gap at 442 nm wavelength (2.81 eV). Using optical second harmonic generation, the nonlinear optical coefficients were determined to be d_15/d_22 = 0.20 +/- 0.01, d_31/d_22 = 0.35 +/- 0.02, d_33/d_22 = -11.4 +/- 0.20 and |d_22| = 298.4 +/- 6.1 pm/V at a fundamental wavelength of 800 nm.
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