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

Using a quantum-mechanical three-step model, we present numerical calculations of the high-order harmonic generation from four polyatomic molecules. Ethylene (C2H4) serves as an example where orbital symmetry directly affects the harmonic yield. We treat the case of methane (CH4) to address the high-order 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-order harmonic signal. This example illustrates the importance of adding coherently the amplitude contributions from the individual degenerate orbitals. Finally, we study the high-order harmonic generation from propane (C3H8) and butane (C4H10). These two molecules, being extended and far from spherical in structure, produce harmonics with nontrivial orientational dependencies. In particular, propane can be oriented so that very high-frequency harmonics are favored, and thus the molecule contains prospects for the generation of uv attosecond pulses