Broadband Green's function computing technique that employs low wavenumber extraction, obtains fast frequency independent modal band solutions and achieves fast convergence of modal expansions, is used to model and design electromagnetic wave behavior of signals in artificial materials with periodic structures, including metamaterials, photonic crystals, and phononic crystals, which are used for smart microwave devices, photonic devices, and acoustic devices. The Broadband Green's function is a general response function for artificial materials and is used to model bandgaps, bandpasses, impurities, defects, displacements of scatterers, and to formulate integral equations for periodic scatters in a finite volume. Designs of metamaterials, photonic crystals, and phononic crystals enable controlling the waves through bandpasses, bandgaps, surface states, polarizations, defects, absorption, enhancement, refraction, substrates, and guidance. The Broadband Green's function technique is used in computer simulations to analyze wave behavior over a broad frequency range, which improves design optimization of smart microwave and photonic devices.