Photonic band structures of colloidal crystals measured with angle-resolved reflection spectroscopy

We acquired angle- and polarization-resolved reflection spectra from a colloidal crystal made of polystyrene spheres along the two perpendicular directions corresponding to the LU and LW directions in the first Brillouin zone of an fcc lattice. Dispersion relations between the reflection peak positions and the wave vectors of the incident light were obtained from the measured spectra and compared with calculated photonic band structures. For the first stop band region in the spectra, the behavior of the reflection peak due to Bragg diffraction agreed with the calculated band structure and revealed some differences induced by the polarization and crystalline orientations. The spectral features observed in the higher energy regions also revealed these differences. In addition, dispersion relationships between the peak positions and the wave vectors were obtained from the results of fitting each spectrum with several Gaussian curves, compared with the calculated photonic band structures. The relationships obtained for the LU direction almost matched the calculated band structure, while the relationships obtained for the LW direction revealed the features of the mixed band structure calculated for the two perpendicular directions. These results indicate that angle- and polarization-resolved reflection spectroscopy has the potential to experimentally analyze the photonic band structures of actual photonic crystals.