Recently, a research team from Columbia University reports a hybrid technique of stimulated Raman excited fluorescence (SREF) with superb sensitivity and fine chemical specificity. Through stimulated Raman pumping to an intermediate vibrational eigenstate, followed by an upconversion to an electronic fluorescent state, SREF encodes vibrational resonance into the excitation spectrum of fluorescence emission. They demonstrated multiplexed SREF imaging in cells, breaking the "colour barrier" of fluorescence. And they also achieved all-far-field single-molecule Raman spectroscopy and imaging without plasmonic enhancement. DOI: 10.1038/s41566-019-0396-4
In most nonlinear optical problems, we work in a lab-fixed frame of reference, but the molecules comprising the system are oriented randomly with respect to that frame. In this situation, averaging molecular quantities over the random orientation is of interest. The problem reduces to calculating a tensor of averaged products of n direction cosines, typically found by expanding in "basic" (Kronecker and Levi-Civita) isotropic tensors. While ingenious this method has not been extended past rank n=8, where it already entails a coefficient matrix that occupies an entire page of typescript. We instead use a pedestrian approach: an integral over Euler angles, traditionally thought intractable for high n but which turns out not to be. From our general formula we obtain simple criteria to decide when a component is 0 and observe a connection to Wigner's D-matrix.