Recent works have established that electron beam driven wakefield not only can serve as a viable source for coherent narrow band terahertz radiation but also as a future candidate for high gradient compact linear accelerators. It has also been pointed out that concentric cylindrical dielectric structures, while being very efficient in extracting the energy of the drive beam, which leads to GeV/m gradient level, are susceptible to excitation of transverse modes which give unwanted trajectory kicks and cause beam breakup instabilities. At the same time, temporary high field induced dielectric conductivity was observed in the same system where in response to high field, charge carriers were injected to the conduction band of the dielectric resulting in anomalous dissipation of the wake. Evidence of this point shall be presented in this thesis. First, in order to address the issue of deflection modes, a solution was proposed to use slab structures. Exploiting the Cartesian symmetry, and the wakefield response thereof, a dielectric wakefield system, where both the structure and the beam are flat, may achieve zero net transverse deflection forces. Second, in order to confine high field to the vacuum region away from the dielectric, thus avoiding all high field related problems, photonic band gap materials may be used. Also known as photonic crystals, these structures give rise to defect modes which are confined only to the defect (vacuum) region. Further shaping of the vacuum/dielectric interface, for example by periodic corrugation, not only reduces the field across the interface on the dielectric side by $1/\epsilon$ as consequence of boundary condition, but also brings about further options of tailoring the field. Motivated by these issues, in this thesis, through a series of relevant analytic calculations, simulations, and experiments, the possibility of using Cartesian symmetric, photonic structures for dielectric wakefield will be assessed.