“…+ H dipole ), which describes the light-coupled component of the interacting material-radiation field system, is composed of the Hamiltonians of the interacting radiation field and the electric dipole moment of the radiative transition, given in the dipole approximation as: [50][51][52] state energies, g ðiÞ os is the linear coupling between the radiation field and the local electron density (i.e., n j ¼ c y 2ð2Þ c 2 ), M (i) s is the electric dipole matrix element associated with the transition between the two electronic levels, c y 1ð2Þ and c 1(2) are the creation and annihilation operators for a hole in electronic levels 1 and 2, a y j and a j are the creation and annihilation operators for a phonon with transition frequency o (i) s = (e 2 À e 1 )/h , N s is the total number of modes in the laser cavity associated with the modulation frequency o (i) s , the subscript s denotes the particular vibration mode that is excited, and the superscript i denotes whether or not this vibration mode is an intramolecular mode (i = 1) or an intermolecular mode (i = 2). In what follow, we only consider modulation frequencies o s that are tuned to the characteristic frequency of an intramolecular C-C stretching vibration o 0 = 215 meV (which is an optical vibration mode), [23][24][25]38,53,57,58 and drop the superscript i.…”