Phase analysis of coherent radial-breathing-mode phonons in carbon nanotubes: Implications for generation and detection processes

In time-resolved pump-probe spectroscopy of carbon nanotubes, the fundamental understanding of the optical generation and detection processes of radial-breathing-mode (RBM) phonons has been inconsistent among the previous reports. In this study, the tunable-pumping/broadband-probing scheme was used to fully reveal the amplitude and phase of the phonon-modulated signals. We observed that signals detected off resonantly to excitonic transitions are delayed by π/2 radians with respect to resonantly detected signals, which demonstrates that RBM phonons are detected through dynamically modulating the linear response, not through adiabatically modulating the light absorption. Furthermore, we found that the initial phases are independent of the pump detuning across the first (E11) and the second (E22) excitonic resonances, evidencing that the RBM phonons are generated by the displacive excitation rather than stimulated Raman process.