The use of dielectric microstructures driven by solid state lasers to accelerate charged particles or to transversely deflect them is a growing area of scientific interest with an international collaboration of researchers working to develop this concept. Many experimental efforts and new designs use a planar symmetric geometry with sub-micron apertures for the particle beam. We provide a general theoretical framework for the electromagnetic fields in this type of geometry, including derivation of the TE and TM modes supported, and examine the transverse force components exerted on the beam, which may be used for focusing or for deflection of the particles. Show Partial Abstract