Anyone care about ferrite-based metamaterial?

Recently, I've read paper entitled by "Left-handed transmission characteristics of rectangular waveguide periodically loaded with ferrite", and I want to repeat the dispersion relation shown in fig.2, but I meet the chanllenge to solve the transcendental equation (5), which is deduced from the mode-matching method analysis. And I've check the deduction process from equation(1) to equation(5), and I programmed it in matlab, but I could not yet repeat the results shown in fig.2. Hope anyone who is interested in this paper's work can discuss with me.

I'm up by myself......! :(