# Optical Effects Induced by Bloch Surface Waves in One-Dimensional Photonic Crystals
## 5 The BSW-Induced Magneto-Optics  
Magneto-optical effects, for example the Faraday and Kerr effects, are actively used to control the light polarization and intensity [44]. The magnitude of these effects is small, but it can be significantly enhanced near narrow optical resonances in the structures [45; 46; 47; 48; 49; 50; 51]. An appropriate resonant optical state for this purpose is the Bloch surface wave in magneto-photonic crystals (MPCs). The possibility of using BSWs at the MPC to control the parameters of the light polarization was studied in [52; 53]. The paper [52] is devoted to a numerical study of the Faraday rotation at the spectral position of the BSW resonance and to the research of the BSW magneto-optical switching in MPCs. The concept of using the BSW in MPCs to control all parameters of light polarization through the external magnetic field application was proposed and experimentally demonstrated in the paper [53]. In these studies, the structures of the MPC, consisting of alternating quarter-wave layers of iron yttrium garnet and fused quartz, were considered. The thickness of the upper layer was selected specifically in accordance with the conditions of the BSW excitation in the structure. For the experimental study, the MPC structure was fabricated by ion-beam sputtering of Bi-substituted yttrium iron garnet (Bi:YIG) and fused quartz targets onto a substrate made of gadolinium gallium garnet. The sample was annealed after deposition of each pair of layers. Numerical studies were carried out using Berreman's \(4\times 4\) transfer matrix approach [54; 55]. The reflectance and the Faraday rotation angle of the light reflected from the MPC, depending on the angle of incidence and the wavelength, were numerically studied. In the experiment, spectra of the reflectance and Faraday rotation angle were measured using the optical reflectance spectroscopy technique. The sample of the MPC was illuminated by the radiation of a halogen lamp. Light passed through a polarizer to set the required polarization of light. The MPC was illuminated through a glass prism in the Kretschmann scheme of total internal reflection. A magnetic field with strength of about 1 kOe was created at the sample using a permanent magnet. Light reflected from the sample was detected with a spectrometer. To determine the polarization of the reflected light, an analyzer was placed in front of the detector and the dependence of reflectance on the angle of the analyzer was measured. The Faraday rotation angle was calculated as half of the phase difference, obtained from approximation of data with Malus' law for opposite directions of the magnetic field. The parameters of the MPC were chosen in such a way that if \(s\)-polarized light illuminates the sample behind the light line, the BSW appears in the photonic band gap. If the incident light has the \(p\)-polarization, the waveguide mode (WGM) is excited in the same spectral range. Both the experimentally measured and numerically calculated spectra of the Faraday rotation have Fano-shaped resonance at the spectral position of the BSW excitation. The shape of Fano resonance in a Faraday rotation spectrum depends on the relative spectral positions of the resonances of the BSW and WGM. While the incident angle increases, positions of the BSW and the WGM resonances become closer and finally pass through one another. During this process, the Fano resonance in Faraday rotation spectra changes from an asymmetric shape to a symmetric one. Thus, the Faraday rotation spectra depend not only on the BSW resonance in the structure, but also on the interaction between the BSW and the WGM modes. The Fano-shaped resonances in the Faraday rotation spectra can be interpreted by considering the general properties of the WGM and BSW. The reflected light phase changes as a function of the wavelength near the resonances of the WGM and BSW. The phase changes slow at the WGM spectral position because of low \(Q\)-factor of the resonance, and have a sharp jump at the BSW resonance, where the \(Q\)-factor is high.