# Optical Effects Induced by Bloch Surface Waves in One-Dimensional Photonic Crystals
## 2 Reflectance  
Optical properties of the BSW are quite similar to the ones inherent in surface plasmon-polaritons in metal films. BSWs are most widely studied in one-dimensional photonic crystals (distributed Bragg reflectors). A typical SEM image of a one-dimensional photonic crystal is shown in the Figure 1a. The BSWs propagate along the vacuum/photonic crystal interface in the photonic-band-gap spectral range, and exponentially decay in the directions perpendicular to the surface plane [22]. Depending on the photonic crystal structure, the BSWs can have a polarization sensitivity and be excited only by TE-polarized light. The dispersion law of BSWs lies behind the air light line [24]. This is clearly seen, for example, in Figure 1c presenting calculated spectral-angular dependence of reflectance response of the  
Figure 1: (**a**) Typical SEM image of one-dimensional photonic crystal, consisting of 6 SiO\({}_{2}\)/Ta\({}_{2}\)O\({}_{5}\) bilayers at the quartz substrate (from bottom to top); (**b**) Schematic of the Kretschmann configuration for the Bloch surface waves (BSW) coupling and detection; (**c**) Calculated normalized reflectivity map R(\(\theta,\lambda\)) of the 1D photonic crystal illuminated in the Kretschmann configuration. Darker regions indicate lower reflectance. BSW dispersion curve is indicated by the arrow and SEW acronym. Reprinted with permission from [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], Proceedings of SPIE 7356, 73560E (2009) [23]. considered photonic crystal. The BSW resonance appears as the narrow dip in reflectance and the BSW dispersion curve is shown as a dark line located inside the first photonic band gap beyond the critical angle. As soon as the BSW dispersion curve approaches the critical angle for which the total internal reflection occurs, it becomes wider until it disappears. As in the case of the SPP, the BSW requires special excitation schemes. Prism schemes of the attenuated total internal reflection in the Otto or Kretschmann geometry, or schemes based on matching the wave-vector lengths of the BSW and the incident light by means of a diffraction grating, can be used. The prism scheme in the Kretschmann geometry is shown in Figure 1b. A sample of a photonic crystal is attached to a 45-degree BK7-glass prism using an immersion fluid that ensures the matching of the refractive indices of materials of the prism and the substrate of the photonic crystal. The light is brought into the prism at an angle of incidence \(\theta\). In the case of the synchronism condition \(k_{BSW}=k_{0}n_{p}\sin\theta\), where \(k_{BSW}\), \(k_{0}\) are the wave vectors of the BSW and light in air, respectively, and \(n_{p}\) is the refractive index of the prism, the BSW is excited on the surface of the photonic crystal and air boundary. The excitation can be detected either by the spectra or angular dependences of the reflectance, or by the BSW scattering on the surface roughness. A typical dependence of the reflectance of a photonic crystal on the angle of incidence in the Kretschmann geometry is shown in the Figure 2.  
The angle of total internal reflection of light is marked as a light line. A minimum relative to the BSW excitation is observed at angles of incidence behind the light line. An interesting fact is that the BSW resonance is not always clearly manifested in the reflection spectra. If the thickness of the photonic crystal is too large, coupling of the incident light to the BSW can be ineffective and the depth of the minimum is small, since a small part of the incident light is coupled to the BSW. In another case, when the thickness of the photonic crystal is insufficient, coupling becomes too strong, the BSW leakage radiation goes back into the prism and the minimum in the reflectance spectrum also does not appear. In this case, additional losses can be introduced into the system, for example, by covering the surface of a photonic crystal by a fluorescent dye [23; 25].