Theoretical studies of high-harmonic generation: Effects of symmetry, degeneracy and orientation

Using a quantum mechanical three-step model we present numerical calculations on the high-harmonic generation from four polyatomic molecules. Ethylene (C$_2$H$_4$) serves as an example where orbital symmetry directly affects the harmonic yield. We treat the case of methane (CH$_4$) to address the high-harmonic generation resulting from a molecule with degenerate orbitals. To this end we illustrate how the single orbital contributions show up in the total high-harmonic signal. This example illustrates the importance of adding coherently amplitude contributions from the individual degenerate orbitals. Finally, we study the high-harmonic generation from propane (C$_3$H$_8$) and butane (C$_4$H$_{10}$). These two molecules, being extended and far from spherical in structure, produce harmonics with non-trivial orientational dependencies. In particular, propane can be oriented so that very high-frequency harmonics are favorized, and thus the molecule contains prospects for the generation of UV attosecond pulses.