Laser-driven acceleration in dielectric photonic band gap structures can provide gradients on the order of GeV/m. The small transverse dimension of the structure, on the order of the laser wavelength, presents interesting wakefield-related issues. Higher order modes can seriously degrade beam quality, and a detailed understanding is needed to mitigate such effects. On the other hand, wakefields also provide a direct way to probe the interaction of a relativistic bunch with the synchronous modes supported by the structure. Simulation studies have been carried out as part of the effort to understand the impact on beam dynamics, and to compare with data from beam experiments designed to characterize candidate structures. In this paper, we present simulation results of wakefields excited by a sub-wavelength bunch in optical photonic band gap structures. Show Partial Abstract