Electron energy losses from thin silver films

Generation of entangled waveguided photon pairs by free electrons

“…Although energetic free electrons are typically assumed to undergo weak light-matter interactions that probe only the linear optical response, actual EELS measurements contain contributions due to multiple excitation events, which were observed in the first experimental evidence of the existence of surface plasmons ( 45 ), while subsequent theoretical work showed that coherent states with a Poissonian population of plasmon modes are created by interaction with the free electrons ( 36 , 46 , 47 ). In particular, to second-order and neglecting quantum-coherence effects, the total EELS distribution signal is described by Γ( k ∥ , ω) = Γ (1) ( k ∥ , ω) + Γ (2) ( k ∥ , ω) (with units of time × distance), where the second term, quantifying the probability of exciting two light quanta (i.e., double loss events), with net energy and momentum matching those transferred from the electron, is given by the self-convolution of the linear EELS probabilitynormalΓ(2)(k∥,normalω)=∫-∞∞dk∥′‍∫0normalωdω′ normalΓ(1)(k∥−k∥′,normalω−normalω′) normalΓ(1)(k∥′,normalω′)…”

“…Poissonian population of plasmon modes are created by interaction with the free electrons (36,46,47). In particular, to second-order and neglecting quantum-coherence effects, the total EELS distribution signal is described by Γ(k ∥ , ω) = Γ (1) (k ∥ , ω) + Γ (2) (k ∥ , ω) (with units of time × distance), where the second term, quantifying the probability of exciting two light quanta (i.e., double loss events), with net energy and momentum matching those transferred from the electron, is given by the self-convolution of the linear EELS probability In what follows, we neglect triple and higher-order processes, which contribute negligibly under the conditions here considered (see fig.…”