The cauchy-riemann equations in determining the refractive index of microwave isolator of ferrite-metal strips in a waveguide

We present a full band microwave isolator in the X-band spectrum that features ferrite samples coated in uniformly spaced strips of metal wire. The objective is to use the wire strips to obtain effective negative permittivity levels at the desired frequencies within the spectrum, as well as to create negative permeability with the ferrite-wire configuration. In practice, we were capable of controlling the wire-covered ferrite samples by using an external field as small as 100 mT. The controllable permeability of ferrites in this experiment allowed us to create unidirectional wave propagation over the entire X-band frequency spectrum. This nonreciprocal circuit is a challenge to the traditional methods of defining refractive index, permittivity and permeability from the S-parameters of a vector network analyzer. We therefore propose a novel method to define the refractive index for nonreciprocal circuits.