Angular properties of refractive index sensor based on reflection interferometer

The angular properties of sensor, implemented in Kretschmann's scheme, where the optimized for oblique incidence of light thin-film reflection interferometer acts as a sensing element, are described in the paper. Analytical equations, defining the sensor's properties for $S$ and $P$ polarization states at working wavelength in vicinity of working angle of incidence, are provided, as well as approximate equations for main parameters of sensor: sensitivity, angular full width at half maximum, contrast and figure of merit. The possibility to vary the named parameters by choosing appropriate metal and dielectric layers of the structure is shown. For an example, the numerical calculations are made for one of special cases, optimized for $S$ polarization state, as having larger figures of merit. The dependencies of angular properties on number of layers and base thickness are demonstrated. It is shown, that angular measurements with this method are theoretically capable of infinite figures of merit, and in practice they are only limited by losses in layered structure and beam divergency. The recommendations for experimental realization of method are given.