The effect of Hamiltonian symmetry on generation of odd and even harmonics

The present work shows that even for very high fields for which perturbation theory breaks down the even peaks in harmonic generation (HG) spectra are suppressed for a model Hamiltonian which is symmetric with respect to the reflection of coordinate space combined with translation of time by half period of the field. The proof presented utilizes the combination of Floquet theory and complex coordinate method. Numerical examples are included, which illustrate that even harmonics appear only when the above mentioned symmetry property of the Hamiltonian is broken.