We provide a methodology for the study of a photonic crystal microcavity and a quantum well (QW) in the strong coupling regime by finite difference in the time domain. Numerical results for an InP L7 photonic crystal microcavity coupled to an ideal QW are provided. A comparison of the time analysis processed by the discrete Fourier transform, the Padé approximant, and harmonic inversion is presented to optimize the computation time. We present a method to solve the uncertainty of the frequency spectrum depending on the starting time used in the spectral analysis. The influence of polarization anisotropy on strong coupling is studied. The Rabi splitting is exactly zero only when the induced polarization in the QW is aligned with a field component incompatible with the symmetry of the mode.