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Aspects Of Attomicroscopy

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Attomicroscopy
As explained in the previous section, this approach is a promising way for generating isolated electron pulses last only few tens of femtosecond and hundreds of attosecond. This approach has striking advantages over the conventional compression techniques[51, 52, 97, 116], which can be summarized as follows: (I) The generated electron pulse duration is limited only by the gating laser pulse duration which could be in the order of attosecond time scale[20]. But, the nanostructure system where the photon-electron coupling takes place should has a broadband response over the spectral bandwidths of the gated pulse. (II) The extreme phase and synchronization stability (<1 fs) can be achieved between the pump and gating laser …show more content…

The temporal evolution of the electrons in the presence of the evanescent field can be described by a time-dependent Schrödinger equation including a light-matter coupling Hamiltonian with a classical electromagnetic field, whose solution can be found self-consistently by solving the Lippmann-Schwinger equation (Eq. (4) in ref (160)). Expanding the electron wave function in a basis of momentum eigenstates corresponding to gaining or losing a certain number of photons, the Lippmann-Schwinger equation can be solved, and the expansion coefficients are given in a recursive manner (Eq. (9) in ref (160)). With the expansion coefficients, the probabilities of electrons gaining/losing L photons can be computed from[160]
Ρ_L=∑_(N=|L|)^∞▒∑_(N`=|L|)^∞▒C_L^N (C_L^(N`) )^* exp⁡{- ((N+N`) 〖(τ⁄τ_p )〗^2)/(1+[((N+N`))⁄2] 〖(τ_e⁄τ_p )〗^2 )}/√(1+[((N+N`))/2] 〖(τ_e⁄τ_p )〗^2 ) (1) where N and N` are possible numbers of total scattering events,C_L^N’s are the expansion coefficients of the electron wave function in the basis of momentum eigenstates corresponding to gaining or losing a certain number of photons, τ the delay between the electron and “gating” optical pulses, τ_e the electron pulse duration, and τ_p the laser “gating” pulse duration.
The electron energy

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