Reflection and transmission coefficients for an electromagnetic wave are usually computed using the frequency representation: a monochromatic plane wave decomposition [1-2]. Even though this method is a powerful tool, the physical meaning can be hidden by some mathematical complexity coming from Fourier integrals, complex analysis and matrix manipulation. Furthermore, the Maxwell equations, when the fields are only dependent on x and t, are very simple and can be solved using elementary calculation [3]. It will be shown that the physical propagation mechanism, which includes initial conditions, transmission and reflection, can be completely built up within the space-time, rather than in the frequency domain. This would shed a new light on traditional well known results.