We experimentally demonstrate several physical concepts necessary for the future development of dielectric laser accelerators—photonic elements that utilize the inelastic interaction between electrons and the optical near fields of laser-illuminated periodic nanostructures. To build a fully photonic accelerator, concatenation of elements, large energy gains, and beam steering elements are required. Staged acceleration is shown using two spatio-temporally separated interaction regions. Further, a chirped silicon grating is used to overcome the velocity dephasing of subrelativistic electrons with respect to its optical near fields, and last, a parabolic grating geometry serves for focusing of the electron beam.