since the ring has inner and outer radii and while the r value is typically between the values of inner and outer radiuses of the ring the exact value of r depends on the waveguide structure since the effective refractive index of the waveguide mode depends on the magnetic field the wavelength position of the exemplary valleys in the transmission will also depend on the value and direction of the applied magnetic field due to the nonreciprocity of the effect in the case of a perfectly circular ring the sensitivity to the in plane component of the external magnetic field will be very small if the external magnetic field is uniform across the ring area since the axially symmetric segments of the ring will cancel the effects of each other however such a resonant structure will be highly sensitive to the nonuniformity of the in plane projection of the external magnetic field and thus can be used as a magnetic field gradient sensor the effect of the component of magnetization perpendicular to the ring uniform or not however will add up from all the segments of the ring and will thus be stronger than that from the in plane uniform components thus waveguide ring or disc resonators can be used as sensors of uniform magnetic fields perpendicular to the plane of the substrate fig5 is a schematic illustrative drawing of a ring or disk resonator 65 66 made in the form of a non magnetically active resonator structure on top of a magnetically active disk of yig or high verdet constant glass 62 the mo film 62 is supported on a substrate 61.