We have theoretically demonstrated Rabi-like splitting and self-referenced refractive index sensing in hybrid plasmonic-1D photonic crystal structures. The coupling between Tamm plasmon and cavity photon modes are tuned by incorporating a low refractive index spacer layer close to the metallic layer to form their hybrid modes. Anticrossing observed in the dispersion validates the strong coupling between the modes and causes Rabi-like splitting, which is supported by coupled mode theory. The Rabi-like splitting energy decreases with increasing number of periods (N) and refractive index contrast ({eta}) of the two dielectric materials used to make the 1D photonic crystals, and the observed variation is explained by an analytical model. The angular and polarization dependency of the hybrid modes shows that the polarization splitting of the lower hybrid mode is much stronger than that of the upper hybrid mode. Further investigating the hybrid modes, it is seen that one of the hybrid modes remains unchanged while other mode undergoes significant change with varying the cavity medium, which makes it useful for designing self-referenced refractive index sensors for sensing different analytes. For {eta}=1.333 and N=10 in a hybrid structure, the sensitivity increases from 51 nm/RIU to 201 nm/RIU with increasing cavity thickness from 170 nm to 892 nm. For a fixed cavity thickness of 892 nm, the sensitivity increases from 201 nm/RIU to 259 nm/RIU by increasing {eta} from 1.333 to 1.605. The sensing parameters such as detection accuracy, quality factor, and figure of merit for two different hybrid structures ([{eta}=1.333, N=10] and [{eta}=1.605, N=6]) are evaluated and compared. The value of resonant reflectivity of one of the hybrid modes changes considerably with varying analyte medium which can also be used for refractive index sensing.
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