Adjustment of In-Phase Mode in Circulators Using Turnstile Junctions

The adjustment of the counter-rotating modes of waveguide circulators using weakly magnetized turnstile junctions is fairly well understood, but some uncertainty about the definition of the in-phase mode still remains. The purpose of this paper is to remedy this situation by experimentally evaluating the in-phase eigenvalue s₀ for different filling factors and radial wavenumbers of the in-phase resonator. This is done by using the unitary condition to derive four possible relationships between the in-phase and counter-rotating eigenvalues s₀ and s₁, and the scattering variable S₁₁, and using one or another of them to form s₀. The situation for which s₀ is in anti-phase to s₁ corresporrds to the first classic circulation condition of this class of device and is also derived.