Eigenvalue problem of open inhomogeneous dielectric waveguide

Authors

  • E. V. Guseva National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev http://orcid.org/0000-0003-1968-7036
  • M. S. Gorb National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev

DOI:

https://doi.org/10.20535/RADAP.2014.56.42-54

Keywords:

inhomogeneous dielectric waveguide, eigenvalue problem, finite element method, open waveguide excitation, microwave imaging

Abstract

Introduction. Algorithm for solving eigenvalue problem of open inhomogeneous dielectric waveguide is presented. Open waveguide divided into two regions. Inner inhomogeneous region is discretized using node–edge finite elements. Fields in outer unbounded homogeneous region expanded into cylindrical harmonics. The final nonlinear eigenvalue problem is solved using inverse iteration procedure.
Results. Calculated surface waves of circular inhomogeneous object. Literature overview on the excitation of open waveguide is presented.
Conclusions. Above algorithm allow to determine the discrete spectrum of waves in open inhomogeneous waveguide

Author Biographies

E. V. Guseva, National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev

Cand. of Sci (Techn.), Assoc. Prof.

M. S. Gorb, National Technical University of Ukraine, Kyiv Politechnic Institute, Kiev

M.S., Postgraduate student

References

Перелік посилань

Барыбин А. А. Электродинамика волноведущих систем. Теория возбуждения и связи волн / Барыбин А. А. – М. : ФИЗМАТЛИТ, 2007. – 512 с. – ISBN: 978–5–9221–0740–2.

Okechukwu F.E. Medical imaging / Okechukwu F.E. – Croatia.: Intech Publisher, 2011. – 400 p. – ISBN 978–953–307–774–1.

Allilomes P.C. A Nonlinear Finite–Element Leaky–Waveguide Solver / P.C. Allilomes, G.A. Kyriacou // IEEE Trans. MTT. – 2007. – Vol. 55, №7. – pp.1496–1510.

Allilomes P. C. A FEM analysis of open boundary structures using edge elements and a cylindrical harmonic expansion / P.C. Allilomes, G.A. Kyriacou, E.Vafiadis, J.N. Sahalos // Electromagnetics. – 2004. – Vol. 24, № 1–2. – pp. 69–79.

Никольский В.В. Электродинамика и распространение радиоволн / В.В. Николь-ский, Т.И. Никольская. – М. : Наука. Гл. ред. физ–мат. лит., 1989. – 544с. – ISBN: 5–02–014033–3.

Zhu Y. Multigrid finite element methods for electromagnetic field modeling / Y. Zhu, A.C. Cangellaris. – USA: Wiley–Intersciencer, 2006. – 400 p. – ISBN: 10 0–471–74110–8.

Volakis J.L. Finite Element Method for Electromagnetics / J.L Volakis, A. Chatterjee, L.C. Kempel. – New York: IEEE PRESS, 1998. – 344p. – ISBN: 0–7803–3425–6.

Jin J. The finite element method in electromagnetics. Sc.Ed. / Jin J. – New York: Wiley–Interscience, 2002. – 753p. – ISBN: 0–471–43818–9.

Reddy C.J. Finite element method for eigenvalue problems in electromagnetics / C.J. Reddy, M.D. Deshpande, C.R. Cockrell, F.B. Beck // NASA, Langley Res. Center, Hampton, VA, Tech.Rep., 1994. – 28p.

Баландин М.Ю. Векторный метод конечных элементов / М.Ю. Баландин, Э.П. Шурина. – Новосибирск: НГТУ, 2001. – 69с.

Peolsi G. Quick Finite Elements for Electromagnetic Waves. Sc.Ed. / G. Peolsi, R. Coccioli, S. Selleri. – Boston, London: Artech House, 2009. – 289p. – ISBN: 978–1–59693–345–3.

Lee J.F. Full–Wave Analysis of Dielectric Waveguides Using Tangential Vector Finite Elements / J.F. Lee, D.K. Sun, Z.J. Cendes // IEEE Trans.MTT. – 1991. – Vol. 39, №8. – pp. 1262–1271.

Jin J. Theory and computation of electromagnetic fields / J. Jin. – New Jersey: John Wiley & Sons, 2010. – 572p. – ISBN: 978–0–470–53359–8.

Ben–Shan Liao Nonlinear Rayleigh–Ritz iterative method for solving large scale nonlinear eigenvalue problems / B. Zhaojun, Lie–Quan Lee., Kwok Ko // Taiwanese journal of mathematics. – 2010. – Vol. 14, №3. – pp.869–883.

Bai Z. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide / Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, H.Vorst. – Philadelphia: SIAM, 2000. – 410p.

Voss H. An Arnoldi method for nonlinear eigenvalue problems / H. Voss // BIT Numerical Mathematics. – 2004. – №44. – pp. 387–401.

Вайнштейн Л. А. Электромагнитные волны / Л.А. Вайнштейн. – М. : Радио и связь, 1988. – 440 с. – ISBN: 5–256–00064–0.

Маненков А.Б. Возбуждение открытых однородных волноводов / А.Б. Манен-ков // Известия Вузов. Радиофизика. – 1970. –Том 13, №5. – с.739–748.

Goubau G. On the excitation of surface waves / G. Goubau // Proceedings of the IRE. – 1952. –Vol. 40, №7. – p.865–868.

Collin R.E. Field theory of guided waves. Sec. Ed / Collin R.E. – New York. : Wiley Interscience, 1991. – 852p. – ISBN: 0–87942–237–8.

Dudley D.G. Linear source in a circular tunnel / D.G. Dudley, S.F. Mahmoud // IEEE Trans. AP. – 2006. – Vol. 54, №7. – p. 2034–2047.

Yip G.L. Launching Wave Efficiency of the HE11 surface wave mode on a dielectric rod / G.L. Yip // IEEE Trans. MTT. – 1970. – Vol. 18, №12. – p. 1033–1041.

Yip G.L. Launching Efficiency of the HE11 surface wave mode on a dielectric tube / G.L. Yip, T. Auyeung // IEEE Trans. MTT. – 1974. – Vol. 22, №1. – p. 6–14.

Safaai–Jazi A. Scattering from an Arbitrarily Located Off–Axis Inhomogeneity in a Step–Index Optical Fiber / A. Safaai–Jazi, G.L. Yip // IEEE Trans. MTT. – 1980. – Vol. 28, №1. – p.24–32.

Duncan J.W. The efficiency of excitation of a surface wave on a dielectric cylinder / J.W. Duncan // IRE Trans. MTT. – 1959. – Vol. 7, №2. – p.257–268.

Hanham S.M. High efficiency excitation of dielectric rods using a magnetic ring current / S.M. Hanham, T.S. Bird // IEEE Trans. AP. – 2008. – Vol. 56, №6. – p. 1805–1808.

Каценеленбаум Б.З. Симметричное возбуждение бесконечного диэлектрическо-го цилиндра / Б.З. Каценеленбаум // Журнал Технической Физики. – 1949. – Том 19, № 10. – с.1168–1181.

Каценеленбаум Б.З. Несимметричные колебания бесконечного диэлектрическо-го цилиндра / Б.З. Каценеленбаум // Журнал Технической Физики. – 1949. – Том 19. – №10. – с.1182–1191.

Person P.L. A simple mesh generator in Matlab / P.L. Person., G. Strang. – Режим доступу: http://persson.berkeley.edu/distmesh

References

Barybin А. А. (2007) Elektrodinamika volnovedushchikh sistem. Teorija vozbuzhdenija i svjazi voln [Electrodynamics of waveguide system. Excitation and mode coupling theory]. Moscow, 512 p.

Okechukwu F.E. (2011) Medical imaging. Croatia, Intech Publisher, 400 p.

Allilomes P.C. and Kyriacou G.A. (2007) A Nonlinear Finite–Element Leaky–Waveguide Solver. IEEE Trans. MTT. Vol.55, No 7, pp. 1496–1510.

Allilomes P. C., Kyriacou G., Vafiadis E., Sahalos J.N. (2004) A FEM analysis of open boundary structures using edge elements and a cylindrical harmonic expansion. Electromagnetics. Vol.24, No 1, pp.69–79.

Nikolskiy V.V. and Nikolskaya T.Y. (1989) Elektrodinamika i rasprostranenie radiovoln [Electrodynamics and wave propagations]. Moscow, 544p.

Zhu Y. and Cangellaris A.C. (2006) Multigrid finite element methods for electromagnetic field modeling. USA, Wiley–Intersciencer, 400 p.

Volakis J.L., Chatterjee A. and Kempel L.C. (1998) Finite Element Method for Electromagnetics. New York, IEEE PRESS, 344p.

Jin J. (2002) The finite element method in electromagnetics. New York, Wiley–Interscience, 753p.

Reddy C.J., Deshpande M.D., Cockrell C.R. and Beck F.B. (1994) Finite element method for eigenvalue problems in electromagnetics. NASA, Langley Res.Center, Hampton, VA, Tech.Rep., 28p.

Balandin M.Yu. and Shurina E.P. (2001) Vektornyi metod konechnykh elementov. [Vector finite element method]. Novosibirsk, 69p.

Peolsi G., Coccioli R. and Selleri S. (2009) Quick Finite Elements for Electromagnetic Waves. Boston, London, Artech House, 289p.

Lee J.F., Sun D.K., Cendes Z.J. (1991) Full–Wave Analysis of Dielectric Waveguides Using Tangential Vector Finite Elements. IEEE Trans.MTT. Vol. 39, No 8, p. 1262–1271.

Jin J. (2010) Theory and computation of electromagnetic fields. New Jersey, John Wiley & Sons, 572p.

Ben-Shan Liao., Zhaojun Bai., Lie-Quan Lee and Kwok Ko. (2010) Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems. Taiwanese journal of mathematics. Vol. 14, No 3, pp.869–883.

Bai Z., Demmel J., Dongarra J., Ruhe A., Vorst H. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Philadelphia, SIAM, 2000. 410p.

Voss H. (2004) An Arnoldi method for nonlinear eigenvalue problems. BIT Numerical Mathematics. No 44, pp. 387–401.

Vayinshtein L. A. (1988) Elektromagnitnye volny [Electromagnetic waves]. Moscow, 440p.

Manenkov A.B. (1970) The excitation of open homogeneous waveguides. Radiophysics and Quantum Electronics. Vol 13, No 5, pp. 578-586.

Goubau.G. (1952) On the excitation of surface waves. Proceedings of the IRE. Vol. 40, No 7, p.865-868.

Collin R.E. Field theory of guided waves. New York, Wiley Interscience, 1991, 852p.

Dudley D.G., Mahmoud S.F. (2006) Linear source in a circular tunnel. IEEE Trans. AP. Vol. 54, No 7, p.2034-2047.

Yip G.L. (1970) Launching Wave Efficiency of the HE11 surface wave mode on a dielectric rod. IEEE Trans. MTT. Vol.18, No 12, p. 1033-1041.

Yip G.L., Auyeung T. (1974) Launching Efficiency of the HE11 surface wave mode on a dielectric tube. IEEE Trans. MTT. Vol. 22, No 1, p.6-14.

Safaai-Jazi A., Yip.G.L. (1980) Scattering from an Arbitrarily Located Off-Axis Inhomogeneity in a Step-Index Optical Fiber. IEEE Trans. MTT. Vol. 28, No 1, p.24-32.

Duncan.J.W. (1952) The efficiency of excitation of a surface wave on a dielectric cylinder. IRE Trans. MTT. Vol. 7, No 2, p.257-268.

Hanham S.M., Bird T.S. (2008) High efficiency excitation of dielectric rods using a magnetic ring current. IEEE Transaction On Antennas and Propagation. Vol. 56, No 6, p. 1805-1808

Kacenelenbaum B.Z. (1949) Symetrichnoe vozbuzhdenie beskonechnogho dielektrycheskogo cilindra [Symmetrical excitation of dielectric rod]. Zhurnal Tekhnicheskoi Fiziki. Vol 19, No 10, pp. 1168–1181.

Downloads

Published

2014-03-06

How to Cite

Гусєва, О. and Горб, М. (2014) “Eigenvalue problem of open inhomogeneous dielectric waveguide”, Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, 0(56), pp. 42-54. doi: 10.20535/RADAP.2014.56.42-54.

Issue

No. 56 (2014)

Section

Electrodynamics. Microwave devices. Antennas

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).