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Video abstract for the article 'Macroscopic optical response and photonic bands' by J S Pérez-Huerta, Guillermo P Ortiz, Bernardo S Mendoza and W Luis Mochán (J S Pérez-Huerta et al 2013 New J. Phys. 15 043037). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/15/4/043037/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. Although materials are never homogenous, as they have structure at least at the atomic level, it is a universal practice to describe their optical response as if they were uniform. The microscopic inhomogeneities have such a small length-scale, compared to the wavelength of light, that their texture may be hidden within a macroscopic response. Recently, the optical properties of artificial crystals fabricated by alternating ordinary materials with different response functions have been produced and their optical properties have been studied. Somewhat exotic properties have been found, such as photonic bands and gaps analogous to those describing electrons within crystals, negative refraction, extreme anisotropy, cloaking behavior, etc. Main results. In this paper we show that these novel materials may also be described in terms of a macroscopic dielectric response, even when their intrinsic lengthscales are comparable to the wavelength of light. In this case, one has to account fully for retardation effects, originated in the finite time taken by the field to travel across a unit cell. Retardation yields non-locality, meaning that the system responds at a given position to the field that acts some distance away, and it manifests itself through the spatial dispersion of the dielectric function epsilonM(ω, k), which depends independently on both the frequency ω and the wavevector k. Wider implications. We developed a very general and efficient scheme to calculate epsilonM and we showed that the photonic band structure may be obtained and classified using our macroscopic formulation.