  Dielectric microstructures have generated much interest in recent years as a
means of accelerating charged particles when powered by solid state lasers. The
acceleration gradient (or particle energy gain per unit length) is an important
figure of merit. To design structures with high acceleration gradients, we
explore the adjoint variable method, a highly efficient technique used to
compute the sensitivity of an objective with respect to a large number of
parameters. With this formalism, the sensitivity of the acceleration gradient
of a dielectric structure with respect to its entire spatial permittivity
distribution is calculated by the use of only two full-field electromagnetic
simulations, the original and adjoint. The adjoint simulation corresponds
physically to the reciprocal situation of a point charge moving through the
accelerator gap and radiating. Using this formalism, we perform numerical
optimizations aimed at maximizing acceleration gradients, which generate
fabricable structures of greatly improved performance in comparison to
previously examined geometries.
