Electron dynamics in grating-type dielectric laser accelerators: particle transfer function, generalized acceleration/deflection gradients and Panofsky-Wenzel theorem

The notions of acceleration gradient and deflection gradient are generalized to phasor quantities (complex-valued functions) in the context of dielectric laser acceleration (DLA). It is shown that the electromagnetic forces imparted on a near-resonant particle traversing a unit cell of a grating-type DLA can be conveniently described by generalized acceleration and deflection gradients. A~simple formulation of the Panofsky-Wenzel theorem in terms of the generalized gradients is given. It is shown that all particle transfer properties of a DLA unit cell can be derived from a single, complex-valued function, the generalized acceleration gradient.