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Tilted Bragg grating refractometers are ideal devices for sensing applications. They work by diffracting light from a confined core mode into a series of well-defined cladding modes that are sensitive to the refractive index of an adjacent fluid. Using the Cauchy integral method, we find the modes of a ridge waveguide refractometer. To gain good agreement with the experiment, the method requires us to take into account the dispersion and the 2-D geometry of the waveguide. The resulting modes are then used to predict the coupling dips in the reflection spectrum. Comparison with experimental measurements verifies the ability of this method to accurately determine the mode structure in the waveguide and, with minimal calibration, the refractive index of the adjacent fluid with error less than 2 &#x00D7;10<sup>-4</sup>.

Complete Mode Structure Analysis of Tilted Bragg Grating Refractometers in Planar Waveguides Toward Absolute Index Measurement