Reconfigurable High-Efficiency Power Dividers Using Waveguide Epsilon-Near-Zero Media for On-Demand Splitting

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors propose two dynamically tunable power dividers using waveguide ENZ media by precisely modulating the internal magnetic field intensity and the widths of the output waveguides. However, the implementation details of the rotatable copper plates (e.g., driving mechanism and the impact of rotation accuracy on performance) are not sufficiently elaborated, which may affect the practical feasibility of the proposed design. Before made a decision, the authors should response the following questions.

1. The reflection coefficient of the Equation (1) assumes that the cross-sectional area of the ENZ channel approaches zero, but in the actual design, the channel width is 2 mm. The potential impact of this approximation on the results needs to be discussed.
2. In the second paragraph of Section 2, there are errors in the subscript notation.
3. Please give a detailed description of the mechanism for tunable power allocation with rotatable copper plates. In practical applications, once the structure is manufactured, the performance of the device is fixed which will be very difficult to achieve the tunable power allocation.
4. The manuscript claims high transmission efficiency but lacks comparative analysis with results from other relevant literature.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript proposed two configurable constructions of power dividers using ENZ media PTFE. Via either mechanically rotatable Cu plates, or variable cross-sectional areas, these two engineering approaches ensure dynamically controllable power division. Full wave simulations of power, s-parameters, transmission efficiency were demonstrated to evaluate the device performance. This is a short, straightforward paper and demonstrates theoretical values for future practical applications. I suggest major revision and expect the authors to refine the draft by answering the following questions.

1. Please consider changing title to “… for On-demand splitting” because “on-demand-split” is an adjective.
2. Please elaborate on which method you use and the model constructions for the simulation results, for example, FEM COMSOL?
3. In fig. 2 (c), the Port 1 power is ~0 W/m instead of the 1 W/m as claimed in the description?

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, the authors present reconfigurable microwave power splitters based on ENZ tunnel structures. The authors investigated two different realizations in their paper: (i) a mechanically tunable splitter that uses a rotatng copper plate to vary the effective channel width and (ii) an electronicaly tunable splitter that utilizes PIN diodes integrated into the SIW loop to direct power towards multiple output ports. Both designs employed ENZ unique field-uniformity property which allows energy to be redistrbuted with minimal reflection when specific matching conditions are met. This work included theoretical formulations, full-wave simulations and parametric studies. Also, they showed adjustable splitting ratios and various statse such as 1:1, 1:2 and complete redirection to a single port and reported transmission efficiencies above 90%. In summary, the paper highlights the potential of ENZ-based structures to enable compact and flexible power-dividing components and after revieiwng this paper I provided my feedback and evaluation in the following.

1. In this structure, the mechanical plate controls “effective entrance widths” b1 and b2 but no quantitative perturbation model links rotation angle "theta" to sub-channel modal admittance. Can you derive/fit an explicit Y(theta) relation and use it to predict S-parameters?
2. At 3 GHz, and assuming Sigma_copper = 6×10^7 S/m, the skin depth is around 1.2 um. So you can expect current crowding along long circumferential paths. Consequently, the ENZ tunnel fields will be changed. Can this non-uniform distribution change the results?
3. The mechanical design places PTFE-filled ports on an air-filled ENZ ring. What is the exact mode-matching formulation at the ENZ–dielectric junction? Do you require stepped transformers or flares to suppress evanescent-to-propagating conversion in the structure?
4. The biasing systme is not discussed in the paper. Is it possible to route DC feeds and RF chokes without spoiling ENZ homogeneity or introducing parasitic slots? It would be helpful if you could provide a complete bias network scehmatic/layout.
5. In your theory, you assumed field homogeneity inside the ENZ region. However, both the splitter plate and the entrance discontinuities create strong local perturbations. How do you cnsider this in your model?
6. In the SIW design, you adopted "a’" from Equation (5) under the condition W <= lambda_g/20, but with epsilon=2.2 at 3 GHz a back-of-the-envelope give lambda_g/20 = 3.3 mm while your via pitch is W = 5 mm. So, please verify the actual lambda_g in your geometry and demonstrate that leakage and sidewall stopband remain acceptable.
7. In all states (includng near out of band where higher modes may leak through the loop), the authors should quantify port-to-port isolation. Therefore, please report S23/S24/S34 with and without the internal barrier plate (mechaincal) and with each diode state (electrical) and explain any angle-dependent or state-dependent crosstalk.
8. The authors stated that magnetic feilds at the SIW outputs are “in phase and of equal amplitude” even when the power split is 2:1. That seems inconsistent because equal |H| with different cross-sections means different Poynting flux only via area, not via modal ampltude at the ports. The normalization of fields at ports and the sampling of amplitudes should be clarified.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In this manuscript, the authors present two designs to realize dynamically tunable power dividers using waveguide ENZ media. The first design varied the power ratio between the two output ports through mechanical tuning, and the second design achieves dynamic modulation of both the number of output ports and the power ratio by controlling the PIN diodes. Both theoretical analysis and simulation results verify the feasibility of these two designs. The paper is well-organized and clearly written. Overall, I suggest the acceptance of this paper to be published after minor revision.

Below is a list of comments and suggestions:

1. What is the calculation of the TE10 cut-off frequencybased on?
2. Due to the low-loss characteristic of the ENZ media, the α_lossis zero, and the transmission efficiency exceeds 93% across the entire tuning range. However, the contribution of different loss mechanisms (such as conductor, dielectric, diode switching loss, etc.) is not analyzed. Please provide an analysis of the expected performance degradation due to these factors, including conductor loss, dielectric loss, diode switching loss, dimensional tolerances, and so on.
3. Is it possible to modulate the number of output ports and the continuous power ratio by combining the two design approaches?

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

This manuscript introduces two innovative designs for reconfigurable power dividers leveraging epsilon-near-zero (ENZ) waveguide media. The first design relies on magnetic field redistribution, while the second employs output waveguide cross-sectional modulation. The work is well-conceived, with the core concepts firmly supported by both theoretical analysis and comprehensive full-wave simulations. The manuscript is clearly written, and the presented results hold significant interest for researchers in microwave engineering, metamaterials, and reconfigurable devices. Overall, I consider this a high-quality contribution suitable for publication after minor revisions.

(1). The Introduction should be strengthened by citing seminal works on metamaterial-enabled power dividers and recent advances in wave manipulation [such as: Antoniades, M. A., and G. V. Eleftheriades. “A broadband series power divider using zero-degree metamaterial phase-shifting lines.” IEEE Microwave and Wireless Components Letters 15.11 (2005): 808-810; Guo, Z., et al. “Exceptional point empowered near-field routing of hyperbolic polaritons.” Science Bulletin 69.22 (2024): 3491-3495.]. The former represents a classical work on metamaterial-based broadband dividers, while the latter highlights recent progress in non-Hermitian and metamaterial-assisted field routing and dividers, which is closely related to the motivation of this paper.

(2). In the conclusion (or discussion section), it would be beneficial to provide a clearer comparison between the proposed ENZ-based dividers and conventional Wilkinson or other ENZ-based designs. Metrics such as insertion loss, bandwidth, tunability, and structural complexity should be briefly compared to highlight the advantages of this work.

(3). In Section 2, the derivation around Eqs. (1)–(4) is somewhat condensed. Please define all variables clearly (e.g., Ap, Hc) and provide brief physical interpretations. Adding annotations in Figure 1 corresponding to these variables would improve readability.

(4). Some sentences within the Introduction and Results sections exhibit slight redundancy. Streamlining these passages by removing repetitive phrasing would enhance the overall conciseness and flow of the manuscript.

(5). In Figure 4, consider adding arrows or schematic indicators to visually show how power distribution changes with copper plate rotation or diode switching. This would help readers outside the immediate field to better follow the mechanism.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have answered all my questions.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed my previous concerns, and the revised manuscript is now clearer, more coherent, and ready for publication.