Fig. 4: Feynman diagrams of the leading electrodynamic interactions that contribute to SEHRS.

a, The 12 possible interactions when the two incident photons are annihilated at the nanohelix and a Raman-shifted photon is emitted at the CV molecules. Time progresses upwards. The Au nanohelix is represented by the vertical gold-coloured world line on the left in each case, its thickness signifying bulk response. The world line for the CV is represented by the black line on the right, its final state in purple exhibiting vibrational excitation. The input photons are shown as black wavy lines and the signal output photon as red, and each radiation field–matter interaction is shown as a green dot. The horizontal dashed line represents dynamic coupling in the near-zone limit. Line intervals between interaction dots on either side represent virtual states. b, The six possible permutations of annihilated and emitted photons. ii–vi illustrate different cases, with the same temporal ordering in which at least one of the input photon annihilations takes place within the CV, with iv–vi further distinguished by the emitted photon originating from the nanohelix. c, Leading forms of mixed-multipole counterparts to b(i). Here, the green dot signifies an E1 interaction, orange M1 and blue E2. For clarity, the M1 and E2 interactions are highlighted with an asterisk and a triangle, respectively. Similar counterparts exist for each of the remaining subpanels within b.