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Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

My focus in this thesis is high-order harmonic generation (HHG) by an intense ultrafast laser field.

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Notes

  1. 1.

    The influence of atoms or molecules on the external field is also included in this treatment.

  2. 2.

    In the derivation, \(e = -1\) in the atomic unit. This convention is different from what has been used by Lewenstein et al. [7], and this results in a sign change in front of \(E(t)\) and \(A(t)\).

  3. 3.

    The velocity operator in Lewenstein et al. [7] is \(\vec {v}=\vec {p}-\vec {A}(t)\). The discrepancy is due to the convention of \(e\) in the atomic unit.

  4. 4.

    In the calculation, the ground-state electronic wave function of an atom or a molecule can be obtained by using quantum chemistry codes such as GAMESS or GAUSSIAN [18].

  5. 5.

    The induced dipole moment is actually expressed in the molecular (or body-fixed) frame.

  6. 6.

    The propagation of laser pulse in an isotropic molecular medium is similar to that in an atomic medium. In general, the optical properties are anisotropic, so the laser evolution in a partially aligned molecular medium should also take the alignment effects into account.

  7. 7.

    See Appendix D for details.

  8. 8.

    This is also true for laser propagation in a partially aligned molecular medium.

  9. 9.

    If laser beam can be considered as a Gaussian beam, its spatial and temporal dependence is given approximately in Appendix D.3.

  10. 10.

    In [49, 50], the integral over \(\phi '\) in Eqs. (2.60) and (2.65) is incorporated into \(\rho (\theta ',\alpha )\).

  11. 11.

    \(\tilde{E}_{\text{ h }}(r,z',\omega )\) is expressed in the frequency domain, and its phase is also involved. Due to the different convention of Fourier transformation, this phase may need to change its sign before entering into the Eq. (2.67).

  12. 12.

    Note that the elements of an \(ABCD\) matrix are not expressed explicitly in Eq. (2.67), but the explicit expression can be found in Appendix D.2.

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  1. Department of Physics, Kansas State University, Manhattan, Kansas, USA

    Cheng Jin

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Jin, C. (2013). Theoretical Tools. In: Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01625-2_2

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