  Realizing optical analogues of quantum phenomena in atomic, molecular, or
condensed matter physics has underpinned a range of photonic technologies. Rabi
splitting is a quantum phenomenon induced by a strong interaction between two
quantum states, and its optical analogues are of fundamental importance for the
manipulation of light-matter interactions with wide applications in
optoelectronics and nonlinear optics. Here, we propose and theoretically
investigate purely optical analogues of Rabi splitting in integrated
waveguide-coupled resonators formed by two Sagnac interferometers. By tailoring
the coherent mode interference, the spectral response of the devices is
engineered to achieve optical analogues of Rabi splitting with anti-crossing
behavior in the resonances. Transitions between the Lorentzian, Fano, and Rabi
splitting spectral lineshapes are achieved by simply changing the phase shift
along the waveguide connecting the two Sagnac interferometers, revealing
interesting physical insights about the evolution of different optical
analogues of quantum phenomena. The impact of the device structural parameters
is also analyzed to facilitate device design and optimization. These results
suggest a new way for realizing optical analogues of Rabi splitting based on
integrated waveguide-coupled resonators, paving the way for many potential
applications that manipulate light-matter interactions in the strong coupling
regime.
