The Bragg Frequency Convertor: A Meeting Between Spatial and Temporal Periodicities For Selective Parametric Frequency Translation

Abstract: This study introduces the Bragg Frequency Convertor, a spatial-temporal-periodic grating that extends the concept of conventional Bragg gratings into the dynamic domain to achieve pure parametric frequency conversion. By time-modulating either the high-index or low-index layers of a quarter-wave Bragg grating, we demonstrate selective and directional frequency conversion: Modulation of the high-index layers selectively yields down-conversion, whereas modulation of the low-index layers leads to up-conversion. Such a pure frequency conversion emerges from the synergistic interplay of spatial and temporal periodicities. The output is thus dominated by the converted frequency, with the carrier and undesired time harmonics suppressed. We derive a coupled-mode theory explaining such a layer-dependent phase matching and validate it with full-wave simulations, showing tunable conversion efficiency via modulation phase. The advance presented here lies in recognizing the conventional Bragg grating not as a passive partner but as an enabling scaffold: its intrinsic spatial periodicity is exploited to impose the precise spectral constraints required for efficient temporal modulation and the generation of pure parametrically converted signals. This work establishes temporal Bragg gratings as a versatile platform for reconfigurable and spurious-free frequency conversion, with applications in optical systems, signal processing, spectral engineering, and quantum photonics.