Paraxial forward-scatter field analysis for a THz pulse traveling down a highly overmoded iris-line waveguide

Highly overmoded iris-line structures carry desirable features for the efficient transportation of THz radiation over long distances. Previous studies have analyzed the iris line, modeled approximately as a long open-resonator structure with thin screens, using methods such as Vainstein’s impedance boundary condition or perturbative mode matching. The aim in those methods was to seek the eigensolution that represents the dominant (least lossy) propagation mode in a long iris-line structure at a steady state. In this paper, a forward-traveling wave analysis is presented, wherein a short THz pulse paraxially traverses the oversized structure cell by cell, including the transient regime. The iris line’s periodic discontinuities are analyzed in terms of forward-wave orthogonal mode decompositions, which are then used to build a “forward-scatter” model (matrix) for each cell. The presented approach predicts a diffraction loss behavior that agrees with that of the eigensolution found by the previous analytical methods for a long waveguide at the steady state but adds the ability to analyze waveguides of finite lengths, showing transients as they evolve and settle to the dominant mode down the line, and offers numerical implementation speeds that are typically an order-of-magnitude faster than those previously reported for the mode-matching method. This approach may also be easily extended to analyze iris lines with mechanical imperfections (e.g., misalignments or aperiodic defects), allowing for investigations of performance sensitivity against manufacturing tolerances.

Figure 1

(a) The iris-line geometry in three dimensions, showing the screens without the enclosing chamber at the outer radius. (b) A cross section in the iris line, showing the enclosing chamber.

Figure 2

One cell of the iris line and regions of solution.

Figure 3

A qualitative sketch of a short THz pulse traveling through the oversized cell, with indicative forward and backward mode expansions at each boundary plane within the cell. For clarity, the pulse (in red) is shown at different moments in time. At $t_0$, a forward-traveling wave is incident onto the cell. At $t_1$, the wave reaches the first discontinuity and we generally have a forward mode and a backward scattered-mode expansion in region 1, along with a forward scattered–mode expansion in region 2 (due to the shortness of the pulse, no backward reflections exist yet in region 2). At $t_2$, the forward wave continues through region 2, and at $t_3$, the second discontinuity is met: again, we generally have forward and backward scattered-mode expansions in region 2 and only a forward scattered–mode expansion in region 3. At $t_4$, forward traveling waves propagate in region 3 toward the cell’s exit, and the cycle repeats through the next cells. A key assumption made in the forward-scatter high-frequency analysis under consideration (see the main text) is that we can expand the wave in forward modes only, ignoring the backward reflections as a first approximation, which turns out to be a good approximation at the high-frequency limit.

Figure 4

Comparison of the rhs (green color line) with the lhs (dashed black line) of Eq. (28) for $E_r$ and Eq. (29) for $E_{\varphi }$, with the upper limit of the sums truncated at 300 terms and the $(A_n,B_n)$ values substituted from the results in (42) and (35). In this plot, we took $r_0/a=2$ as an example.

Figure 5

Comparison of the rhs (green color line) with the lhs (dashed black line) of Eq. (43) for $E_r$ and Eq. (44) for $E_{\varphi }$, with the upper limit of the sums truncated at 300 terms and the $(A_n,B_n)$ values substituted from the results in (48) and (52). In this plot, we took $r_0/a=2$ as an example.

Figure 6

Comparison of the rhs (green color line) with the lhs (dashed black line) of Eq. (53) for $E_r$ and Eq. (54) for $E_{\varphi }$, with the upper limit of the sums truncated at 300 terms and the $(A_n,B_n)$ values substituted from the results in (62) and (70). In this plot, we took $r_0/a=2$ as an example.

Figure 7

Comparison of the rhs (green color line) with the lhs (dashed black line) of Eq. (71) for $E_r$ and Eq. (72) for $E_{\varphi }$, with the upper limit of the sums truncated at 300 terms and the $(A_n,B_n)$ values substituted from the results in (80) and (88). In this plot, we took $r_0/a=2$ as an example.

Figure 8

A sketch illustrating how the different sections of the cell are modeled using different transmission matrices in the numerical analysis.

Figure 9

Transients along the iris line (sampled at the indicated irises) for the ${\mathrm{TM}}_{11}$ excitation case. The plots show the magnitude of the field component $E_r$, without (top) and with (bottom) normalization with respect to the amplitude on the axis $r=0$. Heavy trace lines in the plot highlight the field profiles at the first iris and last iris of the line, while dashed lines highlight the first two eigenmodes of the iris line (denoted $J_{01}$, $J_{02}$).

Figure 10

Transients along the iris line (sampled at the indicated irises) for the ${\mathrm{TE}}_{11}$ excitation case. The plots show the magnitude of the field component $E_r$, without (top) and with (bottom) normalization with respect to the amplitude on the axis $r=0$. Heavy trace lines in the plot highlight the field profiles at the first iris and last iris of the line, while dashed lines highlight the first two eigenmodes of the iris line (denoted $J_{01}$, $J_{02}$).

Figure 11

Transients along (sampled at the indicated irises) the iris line for the matched $J_0(2.4r/a)$ source case. The plots show the magnitude of the field component $E_r$, without (top) and with (bottom) normalization with respect to the amplitude on the axis $r=0$. Heavy trace lines in the plot highlight the field profiles at the first iris and last iris of the line, while dashed lines highlight the first two eigenmodes of the iris line (denoted $J_{01}$, $J_{02}$).

Figure 12

Transients along the iris line (sampled at the indicated irises) for the backed-off Gaussian excitation case. The plots show the magnitude of the field component $E_r$, without (top) and with (bottom) normalization with respect to the amplitude on the axis $r=0$. Heavy trace lines in the plot highlight the field profiles at the first iris and last iris of the line, while dashed lines highlight the first two eigenmodes of the iris line (denoted $J_{01}$, $J_{02}$).

Figure 13

Plot of the data shown in Table 2.