Equiphase observation basis for reconstruction of forward Brillouin dynamics

Abstract

Activation-driven resonant systems are commonly measured through intensity spectra, where superposed activation-synchronized and resonant contributions can distort intrinsic Lorentzian responses into Fano-like spectra. Forward Brillouin scattering (FBS) is a typical optomechanical example, in which Kerr-induced cross-phase modulation (XPM) interferes with resonant FBS-induced XPM and limits reliable extraction of guided-acoustic resonance dynamics. Here, we introduce a reference-phase-anchor-based equiphase observation basis (EPOB) to reconstruct FBS dynamics. By defining a controlled observation phase in the measured XPM response field, EPOB fixes the Kerr-induced XPM as a deterministic phase basis and enables controlled quadrature projection of the complex Lorentzian FBS response. Using a coherent-activation-based Sagnac interferometer, we experimentally reconstruct the real and imaginary components, as well as the full complex transient FBS dynamics. For substance identification, EPOB resolves the fundamental trade-off between two response regimes. The activation stage provides strong signals corrupted by Kerr interference, whereas the decay stage delivers spectrally clean but much weaker signals. The decay-stage response also degrades much more rapidly with linewidth broadening. Consequently, existing grating-free liquid FBS sensors remain limited to a spatial recognition length of ∼80 cm, despite the millimeter-scale capability demonstrated in air. We further validate EPOB by distinguishing air, ethanol, and water using an 8-cm fiber, achieving an order-of-magnitude improvement in spatial recognition capability. These results establish EPOB as an observation-basis framework for reconstructing weak resonant dynamics in systems where deterministic activation-synchronized and resonant responses coexist.