A generalization for Fresnel's coefficients (transmission and reflection) in semi- bounded plasma waveguides and the effect of plasma temperature on them

Document Type : Full length research Paper


Department of Laser and photonics , Faculty of Physics, University of Kashan, Kashan, Iran


In this paper, propagation of electromagnetic waves in a cylindrical waveguide with two different regions and with circular cross-section is investigated. The incident wave in symmetric mode TM0j is sent from the first media to the second media which the first is a filled loss-free dielectric semi-bounded metallic waveguide. The second region of the waveguide is a metallic waveguide with a plasma rod which is isolated by a thin dielectric layer from the metallic wall of the waveguide. The considered plasma rod in the waveguide is assumed in warm approximation. The generation of the new modes for reflected and transmitted waves investigated and by using the mode matching technique, the reflection and transmission coefficients are obtained as a function of the temperature of plasma charged carriers. It is shown that the reflected and transmitted waves have phase difference with respect to the incident wave. The graphs of reflection and transmission coefficients and so the graphs of their phase difference for some elementary modes in terms of the variations of the plasma temperature are presented.


Main Subjects

 [1] D.S. Jones, Methods in electromagnetic wave propagation, Wiley-IEEE Press, 2nd Edition, (1994).  ISBN: 978-0780311558.
[2] D. Cheng, Field and Wave Electromagnetics, 2nd Edition Addison-Wesley (1989). ISBN:978-0201128192.
[3] A.A. Kishk, Electromagnetic Waves Propagation in Complex Matter, InTech First, (2011). ISBN: 978-953-307-445-0.
[4] C.H. Papas, Theory of electromagnetic wave propagation", McGraw Hill, New York, (1965). ISBN: 0486656780.
[5] R.E. Collin, Foundations for microwave engineering, Wiley-IEEE Press, (2001). ISBN: 978-0-780-36031-0.
[6] D.A. Goldberg, L.J. Laslett, R.A. Rimmer, Modes of elliptical waveguides: A correction, IEEE Trans. Microwave Theory Tech., 38 (1990) 1603–1608. https://doi.org/10.1109/22.60005.
[7] C. Rajyaguru, T. Fuji, H. Ito, N. Yugami, Y. Nishida, Observation of ultrahigh energy electrons by resonance absorption of high-power microwaves in a pulsed plasma, Physical Review E 64 (2001) 016403. https://doi.org/10.1103/PhysRevE.64.016403.
[8] J. Hopwood, D.K. Reinhard, J. Asmussen, Charged particle densities and energy distributions in a multipolar electron cyclotron resonant plasma etching source, Java. Sci. Technol. A 8 (1990) 3103. https://doi.org/10.1116/1.576592.
[9] L. Liao, D.R. Lim, A.M. Agarwal, X. Duan, K.K. Lee, L.C. Kimerling, Optical transmission losses in polycrystalline silicon strip waveguides: Effects of waveguide dimensions, thermal treatment, hydrogen passivation, and wavelength, Electronic Materials 29 (2000) 1380–1386. https://doi.org/10.1007/s11664-000-0122-4.
[10] J.F. Drake, P.K. Kaw, Y.C. Lee, G. Schmid, Parametric instabilities of electromagnetic waves in plasmas, The Physics of Fluids 17 (1974) 778. https://doi.org/10.1063/1.1694789.
[11] D.R. Smith, D. Schurig, Electro-magnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors, Physical Review Letters 90 (2003) 077405. https://doi.org/10.1103/PhysRevLett.90.077405.
[12] R.B. White1, F.F. Chen, Amplification and absorption of electromagnetic waves in over dense plasmas, Plasma Physics 16 (1974) 565-587. https://doi.org/10.1088/0032-1028/16/7/002.
[13] J.P. Palastro, T.M. Antonsen, S. Morshed, A. G. York, H.M. Milchberg, Pulse propagation and electron acceleration in a corrugated plasma channel, Physical Review E 77 (2008) 036405. https://doi.org/10.1103/PhysRevE.77.036405.
[14] H. Okuda, H. Sasada, Significant deformations and propagation variations of Laguerre–Gaussian beams reflected and transmitted at a dielectric interface, Optical Society of America A 25 (2008)881-890. https://doi.org/10.1364/JOSAA.25.000881.
[15] T.D. Wu, K.S. Chen, J. Shi, A.K. Fung, A transition model for the reflection coefficient in surface scattering, IEEE Transactions on Geoscience and Remote Sensing, 39 (2001) 2040 - 2050. https://doi.org/10.1109/igarss.1998.702218.
[16] D.R. Smith, S. Schultz, P. Markoš, C.M. Soukoulis, Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Physical Review B 65 (2002) 195104. https://doi.org/10.1103/PhysRevB.65.195104.
[17] T.Y. Alekhinan, A.V. Tyukhtin, Electromagnetic field of a charge intersecting a cold plasma boundary in a waveguide, Physical Review E 83 (2011) 066401. https://doi.org/10.1103/PhysRevE.83.066401.
[18] A.V. Tyukhtin, Determination of the particle energy in a waveguide with a thin dielectric layer, Physical Review Accelerators and Beams 15 (2012) 102801. https://doi.org/10.1103/PhysRevSTAB.15.102801.
[19] T.Y. Alekhinan, A.V. Tyukhtin, Self-acceleration of a charge intersecting a boundary surface in a waveguide, Physical Review Accelerators and Beams 16 (2013) 081301. https://doi.org/10.1103/PhysRevSTAB.16.081301.
[20] A.A. Grigoreva, A.V. Tyukhtin, V.V. Vorobev, T.Y. Alekhinan, S. Antipov, Mode Transformation in a Circular Waveguide with a Transverse Boundary Between a Vacuum and a Partially Dielectric Area, IEEE Transaction on microwave theory and techniques 64 (2016) 3441– 3448. https://doi.org/10.1109/tmtt.2016.2602267.
[21] W. Gai, P. Schoessow, B. Cole, R. Konecny, J. Norem, J. Rosenzweig, J. Simpson, Experimental demonstration of wake-field effects in dielectric structures, Physical Review Letters 61 (1988) 2756. https://doi.org/10.1103/PhysRevLett.61.2756.
[22] C. Li, W. Gai, C. Jing, J.G. Power, C.X. Tang, A. Zholents, High gradient limits due to single bunch beam breakup in a collinear dielectric Wakefield accelerator, Physical Review Accelerators and Beams 17, (2014) 091302. https://doi.org/10.1103/PhysRevSTAB.17.091302.
[23] G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, Elsevier India, 7edition (2012).                                ISBN:978-0123846549.
[24] D. Jackson, Classical electrodynamics. New York: John Wiley, 3rd Edition (1998).           ISBN: 978-0471309321.
[25] G. Conciauro, M. Guglielmi, R. Sorrentino, Advanced Modal Analysis: CAD Techniques for Waveguide Components and Filters, New York, NY, USA: Wiley, (2000).                             ISBN:978-0-471-97069-9.
[26] U. Papziner, F. Arndt, Field theoretical computer-aided design of rectangular and circular iris coupled rectangular or circular waveguide cavity filters, IEEE Trans. Microw. Theory Tech 41 (1993) 462–471. https://doi.org/10.1109/22.223746.
[27] R.V. Haro-Báez, J. Córcoles, J.A. Ruiz-Cruz, J.R. Montejo, J.M. Garaiand Rebollar, Higher-Order Mode Electromagnetic Analysis of a Material Sample between Two Flanged Coaxial Probes for Broadband Modelling of Dielectric Measurement Setups. Advances in Mathematical Physics 2019 (2019). https://doi.org/10.1155/2019/6404812.
[28] A.A. Rukhadze, A.F. Alexandrov, L.S. Bogdankevich, Principles of plasma electrodynamics, Springer-Verlag Berlin Heidelberg (1966).                                                                          ISBN: 978-3-642-69249-9.
[29] F.E Chen, Introduction to plasma physics and controlled fusion, Springer (1974). ISBN:978-3-319-22308-7.
[30] N.A. Krall, Principles of Plasma Physics, McGraw-Hill, New York, (1973). ISBN: 978-0070353466.
[31] D.M. pozar, Microwave engineering. Wiley, New York ,(2012). ISBN: 978-0-470-63155-3