Faraday effect of 1-D magnetic photonic crystals for normal and parallel incidence to the periodic direction

We calculated the Faraday rotation of one-dimensional (1-D) magnetic photonic crystals (MPCs), which are based on the dielectric Ti$_{2}$O$_{3}$ and Al$_{2}$O$_{3}$, and the magnetic Bi:YIG, by employing 4 x 4 transfer-matrix method for the general case that the linearly polarized incident beam is parallel to their periodic direction, as mostly studied for the 1-D MPCs. Furthermore, even for a special case of normal incidence, the calculation of Faraday rotation was also carried out for such discontinuous thin films with a 1-D array structure and the existence of rotation was proved, which had been scarcely studied yet. The magneto-optical Faraday effects obtained for these two cases are compared and discussed in detail.