Observation of Kerr nonlinearity and Kerr-like nonlinearity induced by terahertz generation in LiNbO$_3$

Femtosecond laser pulses interacting with LiNbO3 has been widely applied in intense terahertz generation, excitation and imaging of phonon polaritons and modulating light. It is of great importance to study the nonlinearities induced by femtosecond laser pulses in LiNbO3. Here, we demonstrate that both Kerr nonlinearity and Kerr-like nonlinearity induced by terahertz wave occur under the interaction between laser pulses and LiNbO3 using optical pump-probe techniques. We show that the contribution of Kerr-like nonlinearity to pump-probe spectra varies with the interaction length because of the phase mismatching between terahertz wave and laser pulse. We also observed the excitation of the low frequency phonon polaritons. Experimental results are in consistent with theoretical calculation.