Optical temporal interference model for investigation and manipulation of non-integer high-order harmonic generation

High-precision optical frequency measurement serves as a cornerstone of modern science and technology, enabling advancements in fields ranging from fundamental physics to quantum information technologies. Obtaining precise photon frequencies, especially in the ultraviolet or even extreme ultraviolet regimes, is a key goal in both light–matter interaction experiments and engineering applications. High-order harmonic generation (HHG) is an ideal light source for producing such photons. In this work, we propose an optical temporal interference model (OTIM) that establishes an analogy with multi-slit Fraunhofer diffraction (MSFD) to manipulate fine-frequency photon generation by exploiting the temporal coherence of HHG processes. Our model provides a unified physical framework for three distinct non-integer HHG generation schemes: single-pulse, shaped-pulse, and laser pulse train approaches, which correspond to single-MSFD-like, double-MSFD-like, and multi-MSFD-like processes, respectively. Arbitrary non-integer HHG photons can be obtained using our scheme. Our approach provides a new perspective for accurately measuring and controlling photon frequencies in fields such as frequency comb technology, interferometry, and atomic clocks.