High-order harmonic generation of soft X-rays by carbon nanotubes

HIGH-ORDER HARMONIC GENERATION OF SOFT X-RAYS BY CARBON NANOTUBES 

The approach to the formulation of the SRs for the HHGS presented in Section 5 is based on the dipole approximation with respect to both the incident and the emitted waves. As such, it is not valid for the spatially extended target systems, such as CNTs. Therefore, let us first present a 

According to classical electrodynamics, the intensity of nth harmonic, /(n.k) HHG processes is associated with the corresponding Fourier component of the time-dependent electron flux J (r, t) [32]  

When dealing with micro- or mesoscopic systems behaving according to the laws of quantum mechanics, one has to use the quantum mechanical expression for the electron flux (current-density operator) [33], 

Consider, for instance, the time-periodic, spatially dependent vector-potential of an incident electromagnetic field, propagating along the z-axis. The Floquet expression for the vector potential of the nth harmonic emitted in the incident field propagation direction (z) is given by 

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High-order harmonic generation of soft x-rays by carbon nanotubes 409... 

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