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with the same velocity make up a pure spin current without net spin polarization or magnetization. When the spins are parallel or anti-parallel to the moving direction, the spin current is a longitudi- nal one. A longitudinal spin current has a special symmetry property - chirality. An object, such as a hand or a helix, is chiral if it cannot be made identical to its mirror image by translation and rotation. The chirality of a longitudinal spin current is illustrated in Fig. 1 (b): If a spin’s micro- scopic current circulates its moving direction left-handedly, the mirror image does right-handedly, and vice versa. 

Noticing its chirality, we conceived the idea of measuring a longitudinal spin current using the chiral sum-frequency optical spectroscopy, which was recently developed as a standard tool to study molecular chirality [22–24]. In chiral sum-frequency, two input optical fields F$_{1}$ and F$_{2}$ (with frequencies !$_{1}$ and !$_{2}$ , respectively) and the induced polarization field P at frequency !$_{1}$ + !$_{2}$ form a left- or right-hand system. Fig. 1 (c) shows how a chiral sum-frequency process occurs in a chiral system. Considering a right-hand helix, a charge at position A will be driven to point B by an electric field F$_{1}$ which is along the X -axis, and then to point C by F$_{2}$ which is along the Y -axis. The confinement of the helix leads to a net displacement along the Z -axis. Thus the two input fields and the induced polarization ( F$_{1}$ ; F$_{2}$ ; P ) form a right-hand system. If the order of input fields is reversed ( F$_{2}$ applies before F$_{1}$ ), the charge would follow a trajectory like D ! E ! F , resulting in a polarization along the GLYPH<0> Z -axis, and ( F$_{2}$ ; F$_{1}$ ; P ) still form a right-hand system. Similarly, the sum-frequency in a left-hand helix is a left-hand chiral process. A sum- 

