Vortex states are interesting fundamental quantum states whilst also finding many uses in photon optics. In 2010, propagating electron vortices were experimentally produced for the first time leading to the emergence of the field of electron phase shaping. This thesis details the production of electron states containing orbital angular momentum which produce a C-shaped intensity in the focal plane. This C-shaped intensity has a diameter of approximately 10 nm and can be used to lithographically pattern nanometre scale split rings. The broken rotational symmetry also allows rotations to be viewed. The design theory and orbital angular momentum analysis of the C-shaped states is presented. Experimental results of the first production of C-shaped electrons are then shown. The C-shaped electron beams have been applied to lithographic patterning and future potential applications of C-shapes for both electrons and photons are discussed. Photons have been shown to be able to couple total angular momentum,both spin and orbital contributions, to the orbital motion of two dimensional plasmon modes in chiral structures. The similar transfer of orbital angular momentum between propagating electron and plasmon modes has not yet been shown. This thesis provides the design of two dimensional spiral structures to support plasmon oscillations containing orbital angular momentum. Simulated electromagnetic fields show the addition of a spiralling boundary can allow eigenmodes with orbital angular momentum. In addition, the first analysis and electron energy loss experimental investigation of free space electron states containing OAM with flat chiral thin film structures supporting two dimensional surface plasmon modes is presented, showing some initial evidence of an energy signal dependent on the sign of topological charge.