Some theory of a dual-polarization interferometer for sensor applications

It is shown that by making straightforward approximations it is possible to simplify the analysis of the measurements of a well-established dual-waveguide interferometer for sensor applications. In particular we derive approximate algebraic formulae for the mode phase shifts that are measured in the interferometric sensor when a layer of the entity to be detected is deposited. Knowledge of the shifts of both the TE and TM mode phases allows the deduction of both the thickness and refractive index of a homogeneous deposited layer, and the formulae derived make that possible with significantly reduced numerical computation. More generally the algebraic formulae and the ease with which numerical results can be obtained for a wide range of layer parameter combinations provide opportunities to improve our understanding of device behaviour. In an application of the theory to a specific practical structure, the numerical results show that the ratio of the TE and TM mode phase shifts varies linearly with deposited layer refractive index but is only weakly dependent on layer thickness, as has been observed previously in some experiments. The numerical results are interpreted using the theory and a simple formula describing the linear dependence of phase shift ratio on deposited layer refractive index is derived.