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Generation and Parametric Amplification of Few‐Cycle Light Pulses at Relativistic Intensities

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Abstract

This thesis is dedicated to the generation and amplification of intense, ultrashort light pulses. For a thorough understanding of the physical effects encountered when working with such pulses, the following chapter provides a mathematical description of the propagation and interaction of light.

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Notes

  1. 1.

    More precisely: there is only a small change of \(\varvec{\tilde{U}}\) within a distance of one wavelength \(\lambda = 2\pi /k\).

  2. 2.

    The mathematical requirement is that the difference between phase velocity \(v_\mathrm {p}=\frac{\omega }{k}\) and group velocity \(v_\mathrm {g}=\frac{\partial \omega }{\partial k}\) is small compared to the latter.

  3. 3.

    Not to be confused with the dispersion coefficient for the group delay \(D_1\) = GD\((\omega _0)\) which is the temporal delay of the carrier frequency \(\omega _0\) and hence a single value.

  4. 4.

    This substitution adds a factor of two due to the historical definition of \(d_\mathrm {eff}\) and another factor of two due to the permutation symmetry of \(\chi _{ijk}^{(2)}\). The relation between \(d_\mathrm {eff}\) and \(\chi _{ijk}^{(2)}\) will be further explained in Sect. 2.3.4.

  5. 5.

    For orthorhombic crystals the principle axes correspond to the crystallographic axes. For non-orthogonal crystal structures such as hexagonal or triclinic crystals, however, principle and crystallographic axes do not coincide.

  6. 6.

    For simplicity we consider in the following only linearly polarized beams.

  7. 7.

    For a derivation of Eq. (2.84) see Sect. A.2.2 in the appendix.

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  1. Laboratory for Attosecond Physics, Max-Planck-Institute for Quantum Optics, Garching, Bavaria, Germany

    Alexander Kessel

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Kessel, A. (2018). Fundamentals. In: Generation and Parametric Amplification of Few‐Cycle Light Pulses at Relativistic Intensities. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-92843-2_2

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