We propose an electro-optic time-lens (EOTL) model based on the coupled-mode theory. The model describes the
propagation of a femtosecond pulse in an electro-optical crystal with parabolic refractive index modulation by a
microwave. The proposed model integrates the second order dispersion approximation (β2 ≠ 0) and takes into
consideration the possible mismatch between the microwave phase velocity and the pulse group velocity. The coupled-mode
theory uses the Hermite-Gaussian functions which are the modes of an ideal electro-optic time-lens. The model
characterizes completely the performances of EOTL, including the aberrations, and it establishes the maximum velocity
mismatch for which the pulse profile propagates through the crystal without significant distortion. The theoretical model
is numerically implement considering the propagation of a short pulse in a Litium Niobate time-lens.