Abstract | Optical detection and manipulation of material orders is one of the cornerstones of modern technologies. Well-known examples are the detection of inversion symmetry breaking using the second harmonic generation and time-reversal breaking using the magneto-optical Kerr effect, and the control of magnetization precession using the inverse Faraday effect. In this talk, I will discuss how to extend the capability of optical detection and manipulation, by using several nonlinear optical effects. I will focus on the detection and manipulation of chiral and real-space helical structures, including the detection of magnetic toroidal moment using the nonreciprocal directional dichroism, the detection of structural chirality of twisted bilayers using the layer circular photogalvanic effect, and the control of structural chirality in 1T-TiSe2 using chiral lights. I will further demonstrate that those effects have similar geometric origins, i.e. they are related to Berry curvature and quantum metric tensors, which characterize the geometry of the Hilbert space on the Brillouin zone. Finally, I will show their unique features.
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