Poynting Vector Spin in Gyromagnetic Medium and its Impact on Backward Power Flow in Waveguiding Structures

TL;DR

The paper analyzes the complex Poynting-vector dynamics in a $\hat{z}$-biased gyromagnetic ferrite to reveal a gyrotropy-induced transverse reactive power ($P_y$) that spins the instantaneous Poynting vector ($P_{IPV}$) around a time-invariant component, mathematically captured by the complex Poynting vector $P_{CTAPV}$. A Stokes-parameter framework is developed, with $S_0=|P_x|^2+|P_y|^2$, $S_1=|P_x|^2-|P_y|^2$, $S_2=2|P_x||P_y|\cos\phi$, and $S_3=2|P_x||P_y|\sin\phi$, to quantify both the spin ($S_3$) and the relative real versus reactive power balance ($S_1$) for TE modes where $S_2=0$. By analyzing bulk ferrite and ferrite-filled waveguides, the work shows a gyrotropy-dependent crossover $y_c=(a/\pi)\tan^{-1}(\mu' k_x/(\kappa' k_y))$ where Re$(P_x)=0$, and demonstrates how increased $\kappa'$ shifts the Stokes plot into regions corresponding to backward power flow and asymmetric surface currents with $Z_{wave}$ diverging at $y_c$. The results offer a framework for tunable, nonreciprocal waveguiding and surface-wave control in gyromagnetic media, with potential extensions to gyroelectric and magnetically biased plasmas.

Abstract

This paper investigates the reactive power and spin of instantaneous Poynting vector in the bulk of gyromagnetic medium. It is shown that the gyromagnetic medium introduces a spin in the Poynting vector. The spin of the instantaneous Poynting vector and the relative strengths of the real and reactive power components are quantified using the Stokes plot method. Using this technique we investigate the presence of backward power propagation in a ferrite-filled waveguide. We present an analytical expression to locate the crossover point separating the forward and backward power propagation, where the real power propagation has a null. We further show that this backward power propagation leads to corresponding opposing surface currents on a waveguide plate of the ferrite-filled waveguide, while the potential difference between the two plates remain symmetric.

Figures (9)

• Figure 1: Flow chart describing the steps involved in the computation of isofrequency surfaces and the corresponding Poynting vector.
• Figure 2: (a) Graphical illustration of the time-varying behavior of the IPV. The real and imaginary components of the CTAPV over the 3D IFSs are shown in (b,c) corresponding to the elliptical regime at $7$ GHz, and (d,e) corresponding to the hyperbolic regime at $11$ GHz. Panels (b) and (d) correspond to the real part of the CTAPV and (c) and (e) correspond to the imaginary part.
• Figure 3: Variation of Stokes parameters $S_1$ and $S_3$ over the Poincaré circle corresponding to the variation of $\kappa^\prime$ from $0$ to $2$. We have $\mu^\prime=2$ for this propagation scenario along $\hat{x}$-axis.
• Figure 4: (a) Geometry of the dielectric-filled rectangular waveguide. (b) Longitudinal real and (c) transverse reactive components of the CTAPV. (d) Stokes plot over the Poincaré sphere for wave propagation across the dielectric-filled waveguide at $7$ GHz. (e) Dispersion curve corresponding to the dielectric-filled waveguide. Stokes plot representations at frequencies $\omega_1$ ($f_1=6.38$ GHz), $\omega_2$ ($f_2=7$ GHz) and $\omega_3$ ($f_3=9.4$ GHz).
• Figure 5: Flow chart describing the steps involved in the computation of fields and Poynting vector in a ferrite-filled waveguide, biased transverse to the direction of propagation.