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Odd-even harmonics emitted from a laser-target system imprint rich, subtleinformation characterizing the system's dynamical asymmetry, which is desirableto decipher. In this Letter, we discover a simple universal relation betweenthe odd-even harmonics and the asymmetry of the THz-assisted laser-atomicsystem -- atoms in a fundamental mid-IR laser pulse combined with a THz laser.First, we demonstrate numerically and then analytically formulize the harmoniceven-to-odd ratio as a function of the THz electric field, the source of thesystem's asymmetry. Notably, we suggest a scaling that makes the obtained ruleuniversal, independent of the parameters of both the fundamental pulse andatomic target. This universality facilitates us to propose a general pump-probescheme for THz waveform sampling from the even-to-odd ratio, measurable withina conventional compact setup.

Universality in odd-even harmonic generation and application in terahertz waveform sampling