Skip to main content
SpringerLink
Log in

Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

  • Elementary Particles and Fields
  • Theory
  • Published:
Physics of Atomic Nuclei Aims and scope Submit manuscript

Abstract

Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell’s equations is made to obey “inclined” boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of “entanglement” of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lüneburg lens.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis (Fizmatgiz, Leningrad, 1962; Interscience, New York, 1964).

    Google Scholar 

  2. Z. A. Vlasova, Tr.MIAN SSSR 53, 16 (1959).

    MathSciNet  MATH  Google Scholar 

  3. L. E. El’sgol’ts, Differential Equations and Variational Calculus (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  4. S. I. Vinitsky and L. I. Ponomarev, Sov. J. Part. Nucl. 13, 557 (1982).

    Google Scholar 

  5. I. V. Puzynin, T. D. Boyadzhiev, S. I. Vinitsky, et al., Phys. Part. Nucl. 38, 70 (2007).

    Article  Google Scholar 

  6. S. I. Vinitsky, A. A. Gusev, and O. Chuluunbaatar, Vestn. SPb. Univ., Ser. Fiz. Khim., No. 3, 111 (2010).

  7. O. Chuluunbaatar, A. A. Gusev, S. I. Vinitsky, and A. G. Abrashkevich, Comput. Phys. Commun. 180, 1358 (2009).

    Article  ADS  MATH  Google Scholar 

  8. O. Chuluunbaatar, A. A. Gusev, S. I. Vinitsky, and A. G. Abrashkevich, Comput. Phys. Commun. 179, 685 (2008).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. A. A. Gusev et al., arXiv: 1005.2089 [cond-mat.meshall].

  10. O. Chuluunbaatar, M. S. Kaschiev, V. A. Kaschieva, and S. I. Vinitsky, Lect. Notes Comp. Sci. 2542, 403 (2003).

    Article  MathSciNet  Google Scholar 

  11. O. Chuluunbaatar et al., Proc. SPIE 6165, 61650B (2006).

    Article  Google Scholar 

  12. O. Chuluunbaatar et al., Proc. SPIE 6165, 61650C (2006).

    Article  Google Scholar 

  13. O. Chuluunbaatar et al., J. Phys. B 39, 243 (2006).

    Article  ADS  Google Scholar 

  14. O. Chuluunbaatar et al., Proc. SPIE 6537, 653706 (2007).

    Article  Google Scholar 

  15. O. Chuluunbaatar et al., J. Phys. A 41, 295203 (2008).

    Article  MathSciNet  Google Scholar 

  16. A. A. Gusev, O. Chuluunbaatar, S. I. Vinitsky, et al., J. Phys. Conf. Ser. 248, 012047 (2010).

    Article  ADS  Google Scholar 

  17. A. A. Gusev et al., Phys. At. Nucl. 73, 331 (2010).

    Article  Google Scholar 

  18. V. L. Derbov et al., Izv. Sarat. Univ., Ser. Fiz. 10, 4 (2010).

    Google Scholar 

  19. A. A. Gusev, O. Chuluunbaatar, S. I. Vinitsky, et al., Phys. Atom. Nucl. 75, 1210 (2012).

    Article  ADS  Google Scholar 

  20. O. Chuluunbaatar, A. A Gusev, V. L. Derbov, P. M. Krassovitskiy, and S. I. Vinitsky, Phys.At. Nucl. 72, 768 (2009).

    Article  Google Scholar 

  21. S. I. Vinitsky et al., Lect. Notes Comp. Sci. 5743, 334 (2009).

    Article  ADS  Google Scholar 

  22. A. A. Gusev et al., Lect. Notes Comp. Sci. 6244, 106 (2010).

    Article  ADS  Google Scholar 

  23. S. I. Vinitsky, V. L. Derbov, V.M. Dubovik, et al., Sov. Phys. Usp. 33, 403 (1990).

    Article  ADS  Google Scholar 

  24. A. Gusev, V. Andreev, V. Derbov, et al., Proc. SPIE 5773, 119 (2005).

    Article  ADS  Google Scholar 

  25. A. Gusev, V. Andreev, V. Derbov, et al., in Proceedings of 7th Workshop on Computer Algebra in Scientific Computing, St. Petersburg, Russia, Jul. 12–19, 2004, Ed. by V. G. Ganzha, E. W. Mayr, and E. V. Vorozhtsov (Technische Universitat München, Garching, 2004), p. 233.

    Google Scholar 

  26. V. P. Karassiov, V. L. Derbov, and S. I. Vinitsky, Proc. SPIE 2098, 164 (1994).

    Article  ADS  Google Scholar 

  27. V. L. Derbov, B. L. Markovski, and S. I. Vinitsky, Laser Phys. 2, 775 (1992).

    Google Scholar 

  28. Topological Phases in Quantum Theory. Proceedings, International Seminar, Dubna, USSR, Sept. 2–4, 1988, Ed. by B. L. Markovski and S. I. Vinitsky (World Sci., Singapore, 1989).

    Google Scholar 

  29. B. Z. Katsenelenbaum, Theory of Irregular Waveguides with Slowly Varying Parameters (Akad. Nauk SSSR, Moscow, 1961) [in Russian].

    Google Scholar 

  30. B. Z. Katsenelenbaum, Irregular Transmission Lines (Akad. Nauk SSSR, Leningrad, 1972) [in Russian].

    Google Scholar 

  31. V. V. Shevchenko, Continuous Transitions in Open Waveguides (Nauka, Moscow, 1969; Golem, Boulder, Colorado, 1971).

    Google Scholar 

  32. V. V. Shevchenko, Differ. Uravn. 15, 2004 (1979).

    MathSciNet  MATH  Google Scholar 

  33. N. S. Bakhvalov and G. P. Panasenko, Homogenization: Averaging Processes in Periodic Media (Nauka, Moscow, 1984; Kluwer, Dordrecht, 1989).

    Google Scholar 

  34. E. Di Giorgi and S. Spagnolo, Boll. Unione Mat. Ital., No. 8, 391 (1973).

  35. E. Sánchez-Palencia, Non-Homogeneous Media and Vibration Theory (Springer, Berlin, 1980; Mir, Moscow, 1984).

    MATH  Google Scholar 

  36. N. S. Bakhvalov, G. P. Panasenko, and A. L. Shtaras, in Advances in Science and Engineering, Ser. Modern Problems of Mathematics, Fundamental Directions, Vol. 34 (VINITI, Moscow, 1988), p. 215.

    Google Scholar 

  37. A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam, 1978).

    MATH  Google Scholar 

  38. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, and Kh. T. Ngoan, Usp. Mat. Nauk 34(5), 65 (1979).

    Google Scholar 

  39. V.M. Babich and V. S. Buldyrev, Asymptotic Methods in Short-Wavelength Diffraction Theory, Alpha Science Series on Wave Phenomena (Nauka, Moscow, 1972; Alpha Science International, Harrow, UK, 2009).

    Google Scholar 

  40. Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Nauka, Moscow, 1980; Springer-Verlag, Berlin, 1990).

    Google Scholar 

  41. L. A. Sevastianov and A. A. Egorov, Opt. Spectrosc. 105, 576 (2008).

    Article  ADS  Google Scholar 

  42. A. A. Egorov and L. A. Sevastianov, Quantum Electron. 39, 566 (2009).

    Article  ADS  Google Scholar 

  43. A. A. Egorov, A. L. Sevastyanov, E. A. Airyan, K. P. Lovetskii, and L. A. Sevastianov, Matem. Model. 22, 42 (2010).

    MATH  Google Scholar 

  44. A. A. Egorov, L. A. Sevastianov, and A. L. Sevastyanov, Zh. Radioelektron., No. 6, 1 (2008).

  45. A. A. Egorov, K. P. Lovetskii, A. L. Sevastyanov, and L. A. Sevastianov, QuantumElectron. 40, 830 (2010).

    ADS  Google Scholar 

  46. A. A. Egorov, K. P. Lovetskii, A. L. Sevastyanov, and L. A. Sevastianov, Issled. Rossii 010, 96 (2011); http://zhurnal.ape.relarn.ru/articles/2011/010.pdf

    Google Scholar 

  47. A. Egorov and L. Sevastyanov, SPIE Newsroom (2012), DOI:10.1117/2.1201111.003860.

  48. E. A. Ayryan, A. A. Egorov, L. A. Sevastianov, K. P. Lovetskiy, and A. L. Sevastyanov, Lect. Notes Comp. Sci. 7125, 136 (2012).

    Article  Google Scholar 

  49. A. S. Il’inskii, V. V. Kravtsov, and A. G. Sveshnikov, Mathematical Models of Electrodynamics (Vyssh. Shkola, Moscow, 1991) [in Russian].

  50. L. A. Vainshtein, Electromagnetic Waves (Radio i svyaz’, Moscow, 1988) [in Russian].

    Google Scholar 

  51. S. P. Morgan, J. Appl. Phys. 29, 1358 (1958); R. K. Luneburg, Mathematical Theory of Optics (Univ. of California Press, 1966).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. A. A. Samarskii and A. N. Tikhonov, Zh. Tekh. Fiz. 18, 959 (1948).

    Google Scholar 

  53. N. M. Krylov and H. H. Bogolyubov, Introduction to Nonlinear Mechanics (Akad. Nauk USSR, Kiev, 1937; Princeton Univ. Press, Princeton, 1947).

    Google Scholar 

  54. L. A. Sevastianov, in Proceedings of the Conference on Lasers in Science, Engineering, and Medicine (IRE RAN, Moscow, 1995), p. 72.

    Google Scholar 

  55. F. A. Berezin and M. A. Shubin, The Schrödinger Equation (Mosc. Gos. Univ., Moscow, 1983; Kluwer, Dordrecht, 1991).

    MATH  Google Scholar 

  56. M. V. Keldysh, Usp. Mat. Nauk 26(4), 15 (1971).

    MATH  Google Scholar 

  57. A. N. Bogolyubov, A. L. Delitsyn, and A. G. Sveshnikov, Comput.Math. Math. Phys. 38, 1815 (1998).

    MathSciNet  MATH  Google Scholar 

  58. A. L. Delitsyn, Comput. Math. Math. Phys. 51, 1771 (2011).

    Article  MathSciNet  Google Scholar 

  59. D. Markuze, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974; Mir, Moscow, 1974).

    Google Scholar 

  60. A. L. Sevastyanov, Candidate’s Dissertation in Physics and Mathematics (Peoples’ Friendship Univ. Russia, Moscow, 2010).

    Google Scholar 

  61. H. G. Unger, Planar Optical Waveguides and Fibres (Oxford Univ. Press, 1977; Mir, Moscow, 1980).

    Google Scholar 

  62. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983; Radio i svyaz’, Moscow, 1987).

    Google Scholar 

  63. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1995; Mir, Moscow, 1985).

    Google Scholar 

  64. A. A. Egorov, Quantim Electron. 34, 744 (2004).

    Article  ADS  Google Scholar 

  65. A. A. Yegorov, Opt. Eng. 44, 014601 (2005).

    Article  ADS  Google Scholar 

  66. A. A. Egorov, Radiophys. Quantum. Electron. 48, 57 (2005).

    Article  ADS  Google Scholar 

  67. A. A. Egorov, Quantum Electron. 41, 644 (2011).

    Article  ADS  Google Scholar 

  68. A. A. Egorov, Opt. Spectrosc. 112, 280 (2012).

    Article  ADS  Google Scholar 

  69. A. A. Egorov, Opt. Spectrosc. 109, 625 (2010).

    Article  ADS  Google Scholar 

  70. W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).

    Article  ADS  Google Scholar 

  71. A. P. Gorobets, A. N. Polovinkin, and A. R. Ravin, in Proceedings of the 12th International Conference on Mathematics, Computer, Education (Regulyar. Khaotich. Dinamika, Izhevsk, 2005), vol. 2, p. 667.

    Google Scholar 

  72. M. M. Vekshin, A. V. Nikitin, V. A. Nikitin, and N. A. Yakovenko, Optoelectron. Instrum. Data Process. 45, 70 (2009).

    Google Scholar 

  73. A. A. Egorov, Quantum Electron. 33, 335 (2003).

    Article  ADS  Google Scholar 

  74. A. A. Egorov, in Proceedings of ICO Topical Meeting on Optoinformatics/Information Photonics, St.-Petersburg, Russia, Sept. 4–7, 2006 (ITMO, St.-Petersburg, 2006), p. 236.

    Google Scholar 

  75. A. A. Egorov, in Proceedings of Scientific-Technical Conference on Optical Commutation and Optical Networks (TsNIIS, Moscow, 1990), p. 33.

    Google Scholar 

  76. A. P. Bogatov and I. S. Burmistrov, Quantum Electron. 29, 500 (1999).

    Article  ADS  Google Scholar 

  77. Kh. G. Vaskes, I. V. Cheremiskin, and T. K. Chekhlova, Sov. J. Quantum Electron. 22, 351 (1992).

    Article  ADS  Google Scholar 

  78. I. V. Cheremiskin and T. K. Chekhlova, Elektrosvyaz’, No. 2, 1 (2000).

  79. E.M. Dianov, Quantum Electron. 40, 1 (2010).

    Article  ADS  Google Scholar 

  80. A. Taflove and S. C. Hagness, Computational Electrodynamics. The Finite Difference Time Domain Method, 2nd. ed. (Artech, London, 2000).

    MATH  Google Scholar 

  81. I. Filikhin, S. G. Matinyan, J. Nimmo, and B. Vlahovic, Nanotech. 2, 1 (2011).

    Google Scholar 

  82. A. Lorke and R. J. Luyken, Physica B 256, 424 (1998).

    Article  ADS  Google Scholar 

  83. A. Lorke et al., Phys. Rev. Lett. 84, 2223 (2000).

    Article  ADS  Google Scholar 

  84. A. Fuhrer et al., Nature 413, 822 (2001).

    Article  ADS  Google Scholar 

  85. U. F. Keyser et al., Semicond. Sci. Technol. 17, L22 (2002).

    Article  ADS  Google Scholar 

  86. T. Kuroda et al., Phys. Rev. B 72, 205301 (2005).

    Article  ADS  Google Scholar 

  87. N. Stenger, M. Wilhelm, and M. Wegener, Phys. Rev. Lett. 108, 014301 (2012).

    Article  ADS  Google Scholar 

  88. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312(5781), 1780 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    L. A. Sevastianov & A. L. Sevastyanov

  2. Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    L. A. Sevastianov

  3. Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991, Russia

    A. A. Egorov

Authors
  1. L. A. Sevastianov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Egorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. L. Sevastyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Sevastianov.

Additional information

Original Russian Text © L.A. Sevastianov, A.A. Egorov, A.L. Sevastyanov, 2013, published in Yadernaya Fizika, 2013, Vol. 76, No. 2, pp. 252–268.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sevastianov, L.A., Egorov, A.A. & Sevastyanov, A.L. Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures. Phys. Atom. Nuclei 76, 224–239 (2013). https://doi.org/10.1134/S1063778813010134

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063778813010134

Keywords

Search

Navigation