By comparing optical signals travelling through a sensing and a reference arm, interferometric photonic sensors achieve remarkable sensitivities and detection limits using sim- ple single-wavelength laser sources. Sensors based on bimodal waveguides can, in principle, provide the same advantages without requiring a reference arm, by comparing the propagation of two modes travelling through a single sensing waveguide. However, typical implementations of bimodal sensors face two challenges: (i) the abrupt mode excitation and recombination at the sensor input and output is inefficient, unbalanced in power and produces spurious reflections that can mask small sensing signals, (ii) the sinusoidal nature of the output signal can lead to ambiguities in the readout. Here we present a spiralled bimodal refractive index sensor with full mode conversion, multiplexing and demultiplexing and a coherent phase detection, providing an unambiguous linear phase readout with a compact and robust layout. Our sensors have been designed for a 1550 nm central wavelength, fabricated on a silicon nitride platform and validated with bulk sensing experiments, achieving a limit of detection of 1.67 · 10^−7 RIU.