T , etc. are lists of particle dipoles, quadrupoles, and higher order moments, E 0 ≡ [E 0 , . . . , E 0 ] T is the incident field repeated N times, and the M mn blocks are tensors that couple the m th field gradient felt by particles to the n th moment. In a triply-periodic geometry, we can express M mn,ij , the ij block of each M mn , as