arXiv2023
High-order harmonics are ubiquitous in nature and present in electromagnetic, acoustic, and gravitational waves. They are generated by periodic nonlinear processes or periodic high-frequency pulses. However, this periodicity is often inexact, such as that in chirped (frequency-swept) optical waveforms or interactions with nonstationary matter - for instance, reflection from accelerating mirrors. Spectra observed in such cases often contain complicated sets of harmonic-like fringes, uninterpretable or even misinterpretable via standard Fourier analysis. Here, we propose the concept of alloharmonics, i.e. spectral interference of harmonics with different orders, fully explaining the formation of these fringes (from Greek $\ddot{{\alpha}}{\lambda}{\lambda}{\omicron}{\varsigma}$: \'allos, "other"). Like atomic spectra, the complex alloharmonic spectra depend on several integer numbers and bear a unique imprint of the emission process, such as the driver period and its time derivatives, which the alloharmonic theory can decipher. We demonstrate laser-driven alloharmonics experimentally in the extreme ultraviolet spectral region and extract nonperiodicity parameters. We analyze previously published simulations of gravitational waves emitted by binary black hole mergers and demonstrate alloharmonics there. Further, we predict the presence of alloharmonics in the radio spectra of pulsars and in optical frequency combs, and propose their use for measurement of extremely small accelerations necessary for testing gravity theories. The alloharmonics phenomenon generalizes classical harmonics and is critical in attosecond physics, frequency comb generation, pulsar studies, and future gravitational wave spectroscopy.