Full-scatter vector field analysis of an overmoded and periodically-loaded cylindrical structure for the transportation of THz radiation

TL;DR

The paper addresses the challenge of transporting diffraction-prone THz pulses over long distances using overmoded iris-line waveguides. It develops a full-scatter vector-field theory that yields closed-form spectral coefficients for all mode reflections and transmissions at discontinuities, leveraging Lorentz reciprocity and Schelkunoff equivalence to handle nonuniform cross-sections. The approach generalizes prior forward-scatter and thin-screen limits, enables thicker-screen analysis, and provides efficient scattering-matrix implementations to predict both transient entrance behavior and steady-state output under various source excitations. The results show good agreement with established limits (e.g., Vainstein) and forward-scatter theory, validating the method’s accuracy and highlighting its practical utility for THz transport design and optimization in large, overmoded cylindrical structures.

Abstract

Highly overmoded and periodically loaded structures, such as the iris-line waveguide, offer an attractive solution for the efficient transportation of diffraction-prone THz pulses over long distances (hundreds of meters). This paper presents the full-scatter field theory that allows us to analytically derive all the spectral (modal) coefficients on the discontuities of the iris line. The spectral analysis uses vector fields, superseding scalar field descriptions, to account for diffraction loss as well as polarization effects and ohmic loss on practical conductive surfaces. An advanced application of Lorentz's reciprocity theory, using a generalized guided-field configuration, is developed to reduce complexity of the mode-matching problem over nonuniform sections. The used technique is quite general and applies to a wide class of structures, as it only assumes a paraxial incidence (i.e. a parabolic wave equation) along the axis of the structure. It removes the traditional assumption of very thin screens, allowing for the study of thicker screens in the high-frequency limit, while formulating the problem efficiently by scattering matrices whose coefficients are found analytically. The theory agrees with and expands previously established techniques, including Vainstein's asymptotic limit and the forward-scatter approximation. The used formulation also facilitates accurate visualization of the transient regime at the entrance of the structure and how it evolves to reach steady state.

Figures (14)

• Figure 1: A sketch showing the geometry of the iris line and the definition of key dimensions: (a) a three-dimensional sketch of the structure, without the enclosing vacuum chamber, (b) a cross-section, including the vacuum chamber. We seperate the problem domain into two types of regions (subdomains): we call the regions with narrower radius ($r\leq a$) "waveguide" regions (indicated by a circle with the letter w in the figure), whereas regions with larger radius ($r\leq r_0$) are "cavity" regions (indicated by a circle with the letter c in the figure). The red dashed lines in the figure represent the planes for the "step-in" discontinuities (when traveling from a cavity to a waveguide region) and the "step-out" discontinuities (when traveling from a waveguide to a cavity region).
• Figure 2: A sketch demonstrating Schelkunoff's theorem. The original problem has a source and a field that fills the structure, passing through the aperture (opened in a conductive diaphragm, as indicated by the thick black lines). This original problem is replaced by an equivalent problem, whereby the original source is removed and an equivalent current source $\mathbf{J}=\hat{n}\times\mathbf{H}_{0}\delta(z)$ is placed in the aperture's plane. The equivalent current density $\mathbf{J}$ will produce scattered fields $(\tilde{\mathbf{E}}^-,\tilde{\mathbf{H}}^-)$ to the left, and $(\tilde{\mathbf{E}}^+,\tilde{\mathbf{H}}^+)$ to the right.
• Figure 3: An example of step-in discontinuity with a TM incidence. For clarity, only the $E$ fields are explicitly shown in this figure. The integration surfaces on the right and left hand sides of the volume $V$ are denoted by $S_1$ and $S_2$, and are immediately adjacent to each side of the plane $z=0$ (note that the figure is showing exaggerated distances between the surfaces $S_1,S_2$ and $z=0$ for clarity). Here, a single mode is incident ($\mathbf{E}^{in,c}_{\text{TM}\ell}$), a field is reflected back into the waveguide region ($\mathbf{E}^-_1$), and a field is transmitted onto the cavity region ($\mathbf{E}^+_1$), as given by (\ref{['E1-']}) and (\ref{['E1+']}). The reflected and transmitted fields can be in both TE and TM in general. Analogous geometries, fields, and surfaces can be constructed for the step-out discontinuity and TE/TM incidences.
• Figure 4: When constructing the equivalent problem, by starting from the original problem (a), filling the aperture with a perfect electric conductor (b), and then replacing the aperture by an equivalent current $\mathbf{J}_1$ (c), it is important to distinguish between the surface current $\mathbf{J}_\text{sh.}$ due to the "shoulders" of the step-in structure, which will always be there, and the current $J_1$ that models only the aperture. Only the latter is the source concerned for generating the scattered fields, $(\mathbf{E}^\pm_1,\mathbf{H}^\pm_1)$, as in Schelkunoff's theorem (see Appendix \ref{['Appx1']}).
• Figure 5: Validating the match of each transverse field ($E_r$ and $E_\phi$) on the left-hand side and right-hand side of a step-in discontinuity, for TM incidence. The plot used the results in (\ref{['B- stepIn1']}), (\ref{['A- stepIn2']}), (\ref{['B+ stepIn3']}), and (\ref{['A+ stepIn4']}) for the field expansions, which were limited to 300 terms and plotted for an example structure that has $r_0/a=2$.