Fig. 1: Energy scheme for four non-consecutive harmonics and intense NIR field.

a Scheme of energy levels of the photoelectrons released by the absorption of one photon from the four non-consecutive harmonics H6, H7, H9 and H10 and the absorption or emission of (up to five) NIR photons. Ip indicates the ionisation potential of the atom. b Photoionisation pathways leading to the population of the sideband \({S}_{6,7}^{(-)}\) and contributed by the harmonics H6 and H7. Due to the number of NIR photons involved, the population oscillates at frequency 3ωNIR. c Photoionisation pathways leading to the population of the sideband \({S}_{7,9}^{(--)}\) and contributed by the harmonics H6, H7 and H9. Due to the number of NIR photons involved, the population oscillates at frequencies 3ωNIR and 6ωNIR as a result of the paths contributed by the harmonics H6-H7 and H7-H9). The subscripts in the sideband notation indicate the harmonic orders closest in energy to the given sideband. The superscripts (− , + ) and (− − , − , 0, + , + + ) are used to distinguish sidebands in order of increasing energy between adjacent and non-adjacent harmonics, respectively. Only transitions involving the exchange of up to five NIR photons are shown for simplicity.