- Open Access
Scattering singularities of a resonant cavity containing plasma
APS Open Sci. 1, 000132 – Published 11 September, 2026
DOI: https://doi.org/10.1103/5d6b-yljs
Abstract
The influence of plasma on the evolution of scattering singularities in microwave cavities remains largely unexplored, despite its importance for controlling reflectionless plasma excitation. In this work, we investigate the evolution of scattering singularities in a plasma-loaded microwave cavity. To analyze this complex interaction, a numerical model describing an experimental cavity containing a plasma tube is developed. This model enables the tracking of singularity evolution across various plasma configurations and explains the underlying physical mechanisms. Our results demonstrate that significant changes in the imaginary frequency of these singularities occur under two specific conditions: high collision frequency associated with optimal electron densities or high electron densities associated with optimal collision frequency. Furthermore, in the collisionless regime, we show that the variation of the real frequency increases due to the excitation of a transverse plasmonic resonance inside the plasma tube.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (57)
- G. Oliveri, D. Werner, and A. Massa, Reconfigurable electromagnetics through metamaterials—A review, Proc. IEEE 103, 1034 (2015).
- O. Sakai and K. Tachibana, Plasmas as metamaterials: A review, Plasma Sources Sci. Technol. 21, 013001 (2012).
- M. Barbuto, A. Monti, S. Vellucci, M. G. H. Alijani, T. Giagnacovo, G. Laghi, F. Capelli, M. Grande, O. Gazeli, I. Katsantonis, J. Yan, K. Kourtzanidis, R. Filippone, G. D. Iorio, A. D. Iorio, M. Kafesaki, M. Gherardi, A. Toscano, and F. Bilotti, Modeling and characterization of plasma tubes as building blocks for reconfigurable and programmable metasurfaces, Adv. Electron. Mater. 11, e00605 (2025).
- J. Sokoloff, O. Pascal, T. Callegari, R. Pascaud, F. Pizarro, L. Liard, J. Lo, and A. Kallel, Non-thermal plasma potentialities for microwave device reconfigurability, C. R. Phys. 15, 468 (2014).
- R. Pascaud, F. Pizarro, O. Pascal, T. Callegari, and L. Liard, Theoretical and numerical study of a plasma-based frequency tunable microstrip antenna, in Proceedings of the 8th European Conference on Antennas and Propagation (EuCAP 2014) (IEEE, The Hague, Netherlands, 2014), pp. 1545–1546.
- V. Laquerbe, R. Pascaud, A. Laffont, T. Callegari, L. Liard, and O. Pascal, Towards antenna miniaturization at radio frequencies using plasma discharges, Phys. Plasmas 26, 033509 (2019).
- K. Kourtzanidis, D. M. Pederson, and L. L. Raja, Electromagnetic wave energy flow control with a tunable and reconfigurable coupled plasma split-ring resonator metamaterial: A study of basic conditions and configurations, J. Appl. Phys. 119, 204904 (2016).
- S. Varault, B. Gabard, J. Sokoloff, and S. Bolioli, Plasma-based localized defect for switchable coupling applications, Appl. Phys. Lett. 98, 134103 (2011).
- W. R. Sweeney, C. W. Hsu, and A. D. Stone, Theory of reflectionless scattering modes, Phys. Rev. A 102, 063511 (2020).
- A. H. Alhulaymi, N. Pyvovar, P. del Hougne, O. D. Miller, and A. D. Stone, Coherent control of wave scattering via minimal-parameter tuning of complex spectra, arXiv:2510.13035.
- A. Krasnok, D. Baranov, H. Li, M.-A. Miri, F. Monticone, and A. Alú, Anomalies in light scattering, Adv. Opt. Photon. 11, 892 (2019).
- J. Erb, D. Shrekenhamer, T. Sleasman, T. Antonsen, and S. Anlage, Control of the scattering properties of complex systems by means of tunable metasurfaces, Acta Phys. Pol. A 144, 421 (2023).
- J. Sol, A. Alhulaymi, A. D. Stone, and P. del Hougne, Reflectionless programmable signal routers, Sci. Adv. 9, eadf0323 (2023).
- M. F. Imani, D. R. Smith, and P. del Hougne, Perfect absorption in a disordered medium with programmable meta-atom inclusions, Adv. Funct. Mater. 30, 2005310 (2020).
- G. C. Alexandropoulos, N. Shlezinger, and P. del Hougne, Reconfigurable intelligent surfaces for rich scattering wireless communications: Recent experiments, challenges, and opportunities, IEEE Commun. Mag. 59, 28 (2021).
- P. del Hougne, K. B. Yeo, P. Besnier, and M. Davy, Laser Photon. Rev. 15, 2000471 (2021).
- M. Dupre, P. del Hougne, M. Fink, F. Lemoult, and G. Lerosey, Wave-field shaping in cavities: Waves trapped in a box with controllable boundaries, Phys. Rev. Lett. 115, 017701 (2015).
- P. del Hougne, K. B. Yeo, P. Besnier, and M. Davy, Coherent wave control in complex media with arbitrary wavefronts, Phys. Rev. Lett. 126, 193903 (2021).
- J. Sol, D. R. Smith, and P. del Hougne, Meta-programmable analog differentiator, Nat. Commun. 13, 1713 (2022).
- F. T. Faul, L. Cronier, A. Alhulaymi, A. D. Stone, and P. del Hougne, Agile free-form signal filtering and routing with a chaotic-cavity-backed non-local programmable metasurface, Adv. Sci. 12, 2500796 (2025).
- K. Chang and J. Wiley, Encyclopedia of RF and Microwave Engineering (Wiley, Hoboken, New Jersey, 2005).
- J. Su, Y. Li, X. Li, P. Yao, Y. Liu, M. Ding, and W. Tang, A novel microwave plasma reactor with a unique structure for chemical vapor deposition of diamond films, Diam. Relat. Mater. 42, 28 (2014).
- J. Asmussen, R. Mallavarpu, J. R. Hamann, and H. C. Park, The design of a microwave plasma cavity, Proc. IEEE 62, 109 (1974).
- A. Lacoste, F. Dias, C. Boisse-Laporte, and P. Leprince, Experimental study of energy coupling and plasma breakdown in a pulsed high frequency resonant cavity, J. Appl. Phys. 89, 3108 (2001).
- V. Mazières, O. Pascal, R. Pascaud, L. Liard, S. Dap, R. Clergereaux, and J.-P. Boeuf, Space-time plasma-steering source: Control of microwave plasmas in overmoded cavities, Phys. Rev. Appl. 16, 054038 (2021).
- V. Mazieres, R. Pascaud, L. Liard, S. Dap, R. Clergereaux, and O. Pascal, Plasma generation using time reversal of microwaves, Appl. Phys. Lett. 115, 154101 (2019).
- V. Mazieres, R. Pascaud, O. Pascal, R. Clergereaux, L. Stafford, S. Dap, and L. Liard, Spatio-temporal dynamics of a nanosecond pulsed microwave plasma ignited by time reversal, Plasma Sources Sci. Technol. 29, 125017 (2020).
- V. Mazières, A. A. Ibrahim, C. Chauvière, P. Bonnet, R. Pascaud, R. Clergereaux, S. Dap, L. Liard, and O. Pascal, Transient electric field shaping with the linear combination of configuration field method for enhanced spatial control of microwave plasmas, IEEE Access 8, 177084 (2020).
- T. Delage, J. Sokoloff, O. Pascal, V. Mazieres, A. Krasnok, and T. Callegari, Plasma ignition via high-power virtual perfect absorption, ACS Photon. 10, 3781 (2023).
- B. Fromont, R. Pascaud, A. Saucourt, V. Mazières, J. De Rosny, M. Fink, N. Lebbe, O. Pascal, J. Sokoloff, L. Liard, and T. Delage, Microwave sink using plasma-based localized surface plasmons, Phys. Rev. Appl. 24, 014020 (2025).
- B. Fragge, J. Sokoloff, O. Rouzaud, O. Pascal, and M. Orain, A versatile set-up to study plasma/microwave sources for liquid fuel ignition, Eur. Phys. J. Appl. Phys. 92, 30903 (2020).
- Note that the final model parameters, later determined and reported in Table 1, have been used in Fig. 3.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/5d6b-yljs for detailed cavity geometry.
- M. Feulner, F. Seufert, A. Müller, G. Hagen, and R. Moos, Influencing parameters on the microwave-based soot load determination of diesel particulate filters, Top. Catal. 60, 374 (2017).
- S. Walter, P. Schwanzer, G. Hagen, H.-P. Rabl, M. Dietrich, and R. Moos, Soot monitoring of gasoline particulate filters using a radio-frequency-based sensor, Sensors 23, 7861 (2023).
- J. Li, A. Astafiev, A. Kudryavtsev, C. Yuan, and X. Wang, The possibility of measuring electron density of plasma at atmospheric pressure by a microwave cavity resonance spectroscopy, IEEE Trans. Plasma Sci. 49, 1001 (2021).
- Y. P. Raizer, in Gas Discharge Physics, edited by J. E. Allen (Springer, Berlin, Germany, 1997), Vol. 2.
- J. Yao, C. Yuan, S. Eliseev, A. Kudryavtsev, and Z. Zhou, Longitudinal structure and plasma parameters of an entire DC glow discharge as obtained using a 1D fluid-based model with non-local ionization, Plasma Sources Sci. Technol. 29, 075003 (2020).
- Under our conditions, no striations should appear in the positive column (PC), and the density profile along the tube in the PC remains constant.
- M. A. Lieberman and A. J. Lichtenberg, Principles of plasma discharges and materials processing, MRS Bull. 30, 899 (1994).
- S. Muhl and A. Perez, The use of hollow cathodes in deposition processes: A critical review, Thin Solid Films 579, 174 (2015).
- D. R. Biggs and M. A. Cappelli, Tunable microwave pulse generation using discharge plasmas, Appl. Phys. Lett. 109, 124103 (2016).
- L. Zhang and J.-T. Ouyang, Experiment and simulation on one-dimensional plasma photonic crystals, Phys. Plasmas 21, 103514 (2014).
- The purpose of this model is not to provide quantitatively predictive simulations, but rather to capture the underlying physics of the cavity's first resonant modes.
- H. Haus and W. Huang, Coupled-mode theory, Proc. IEEE 79, 1505 (1991).
- Y. Ra'di, A. Krasnok, and A. Alú, Virtual critical coupling, ACS Photon. 7, 1468 (2020).
- T. Delage, O. Pascal, J. Sokoloff, and V. Mazieres, Experimental demonstration of virtual critical coupling to a single-mode microwave cavity, J. Appl. Phys. 132, 153105 (2022).
- Note that, for simplicity, the frequency used to compute the ratio corresponds to the resonance frequency of the mode in the case, where .
- At and , the critical electron density, see later in Sec. 3b, is .
- O. Klein, S. Donovan, M. Dressel, and G. Grüner, Microwave cavity perturbation technique: Part I: Principles, Int. J. Infrared Millimeter Waves 14, 2423 (1993).
- For these two configurations, the frequency range studied differs, and the relative difference between the critical electron density values associated with the minimum and maximum frequencies of each range is in the first case, compared to only in the second.
- J. Shohet and C. Moskowitz, Eigenvalues of a microwave-cavity-lossy-plasma system, J. Appl. Phys. 36, 1756 (1965).
- E.-K. Souw, Plasma density measurement in an imperfect microwave cavity, J. Appl. Phys. 61, 1761 (1987).
- M. A. W. van Ninhuijs, K. A. Daamen, J. G. H. Franssen, J. Conway, B. Platier, J. Beckers, and O. J. Luiten, Microwave cavity resonance spectroscopy of ultracold plasmas, Phys. Rev. A 100, 061801 (2019).
- N. Daneshfar, The study of scattering-to-absorption ratio in plasmonic nanoparticles for photovoltaic cells and sensor applications, Plasmonics 16, 2017 (2021).
- Plasmonic resonance intensifies the electromagnetic field diffused by the plasma, resulting in an infinite increase in polarizability . Based on the polarizability expression for our configuration (two cylinders with different permittivities) given by Daneshfar [55], we determined the permittivity of the plasma that satisfies . For each electron density, we calculated the required wave frequency to obtain this permittivity value. For , this frequency is 2.63 GHz, which is close to the resonance frequency shown in Fig. 6.
- It is also worth emphasizing that this collisionless case is the only configuration for which the pole and zero do not exhibit a similar trajectory in the complex plane. As can be inferred from Eqs. (3) and (4), this behavior originates from a modification of the external decay rate. This underscores the significant role of the plasmonic resonance, which induces a reorganization of the field distribution within the cavity. A detailed analysis of this effect will be the subject of future work.