In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipo
le-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited feature at the line center. Applicability to precision measurement is discussed.
