Linearity of the Faraday-rotation-type ac magnetic-field sensor with a ferrimagnetic or ferromagnetic rotator film

We analyze the linearity and modulation depth of ac magnetic-field sensors or current sensors, using a ferrimagnetic or ferromagnetic film as the Faraday rotator and employing the detection of only the zeroth-order optical diffraction component from the rotator. It is theoretically shown that for this class of sensor the condition of a constant modulation depth and that of a constant ratio error give an identical series of curves for the relationship between Faraday rotation angle Θ and polarizer/analyzer relative angle Φ. We give some numerical examples to demonstrate the usefulness of the result with reference to a rare-earth iron garnet film as the rotator.