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Because the commonly adopted viewpoint that the Keldysh parameter $\gamma $determines the dynamical regime in strong field physics has long beendemonstrated to be misleading, one can ask what happens as relevant physicalparameters, such as laser intensity and frequency, are varied while $\gamma$ iskept fixed. We present results from our one- and fully three-dimensionalquantum simulations of high-order harmonic generation (HHG) from various boundstates of hydrogen with $n$ up to 40, where the laser intensities and thefrequencies are scaled from those for $n=1$ in order to maintain a fixedKeldysh parameter $\gamma$$< 1$ for all $n$. We find that as we increase $n$while keeping $\gamma $ fixed, the position of the cut-off scales in welldefined manner. Moreover, a secondary plateau forms with a new cut-off,splitting the HHG plateau into two regions. First of these sub-plateaus iscomposed of lower harmonics, and has a higher yield than the second one. Thelatter extends up to the semiclassical $I_p+3.17U_p$ cut-off. We find that thisstructure is universal, and the HHG spectra look the same for all $n\gtrsim 10$when plotted as a function of the scaled harmonic order. We investigate the$n$-, $l$- and momentum distributions to elucidate the physical mechanismleading to this universal structure.

High-order harmonic generation from Rydberg states at fixed Keldysh parameter