Gauge-field description of Sagnac frequency shift and mode hybridization in a rotating cavity

Active optical systems can give rise to intriguing phenomena and applications that are not available in conventional passive systems. Structural rotation has been widely employed to achieve non-reciprocity or time-reversal symmetry breaking. Here, we examine the quasi-normal modes and scattering properties of a dielectric disk under rotation. In addition to the familiar phenomenon of Sagnac frequency shift, we observe the the hybridization of the clockwise (CW) and counter-clockwise CCW) chiral modes of the cavity controlled by the rotation. The rotation tends to suppress one chiral mode while amplifying the other, and it leads to the variation of the far field. The phenomenon can be understood as the result of a synthetic gauge field induced by the rotation of the cavity. We explicitly derived this gauge field and the resulting Sagnac frequency shift. The analytical results are corroborated by finite element simulations. Our results can be applied in the measurement of rotating devices by probing the far field.