UDC 535.13: 535.326: 535.36: 621.37

A model of a multilayer smoothly-irregular integrated-optical waveguide in the zero vector approximation: theory and numerical analysis

 

A. A. Egorov ¹, K. P. Lovetskii ², A. L. Sevastianov ², L. A. Sevastianov ²

¹ A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Vavilov Street 38, Moscow, 119991, Russia

² Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow 117198, Russia

 

The paper is received on March 20, 2019

 

Abstract. In this paper, we analyzed waveguide modes and their characteristics in the framework of the adiabatic mode model and the modified averaging method. The obtained results are compared with the results of other authors in the framework of the matrix model of comparison waveguides, which is obtained from the zero approximation of the adiabatic mode model by replacing tangential boundary conditions on non-horizontal sections of the waveguide layers sections with horizontal projections of the boundary conditions (neglecting the vertical contributions to the exact boundary conditions). Accounting for real boundary conditions is the basis of our proposed new method for calculating the dispersion ratios and fields of a smoothly irregular integrated optical waveguide. A brief description of the algorithm for calculating the dispersion dependence in the matrix model of reference waveguides is given. It is shown that the thickness profile of the additional waveguide layer of a thin-film generalized Luneberg waveguide lens obtained by the comparison waveguide method exactly coincides with the thickness profile of the additional waveguide layer of the thin-film waveguide Luneberg lens obtained by Southwell. An algorithm for calculating the vertical distribution of fields in a matrix model of reference waveguides is described. In addition, an algorithm for calculating the vertical distribution of the electromagnetic field of guided modes in the zero and first approximations of the adiabatic mode method is described. The dispersion dependences of the smooth-irregular four-layer integrated-optical waveguide, that is, a thin-film generalized Luneberg waveguide lens, are calculated. Synthesized thin-film generalized Luneberg waveguide lens. It is shown that there is practically no discrepancy between our data in the matrix model of the comparison waveguide method and the Southwell data. Graphs of the vertical distribution of fields in the zero vector approximation to the thin-film generalized Luneberg waveguide lens are presented.

Key words: electrodynamics, waveguide, dispersion relation, modes, waveguide Luneburg lens, computer simulation, numerical modeling.

References

1.     Egorov A.A., Lovetskii K.P., Sevastianov A.L., Sevastianov L.A. Integral’naya optika: teoriya i kompyuternoe modelirovanie. Monografiya. [Integrated Optics: Theory and Computer Modelling. Monography]. Moscow, People Friendship University of Russia Publishing house, 2015 (In Russian).

2.     Shevchenko V.V. Plavnye perekhody v otkrytykh volnovodakh [Continuous Transitions in Open Waveguides]. Moscow: Nauka Publ., 1969. (In Russian)

3.     Sevastianov L.A., Egorov A.A. The theoretical analysis of waveguide propagation of electromagnetic waves in dielectric smoothly-irregular integrated structure. Optics and Spectroscopy, 2008, Vol. 105, No. 4, pp. 576-584.

DOI https://doi.org/10.1134/S0030400X08100123

4.     Egorov A.A., Sevast'yanov L.A. Structure of modes of a smoothly irregular integrated-optical four-layer three-dimensional waveguide.  Quantum Electronics, 2009, Vol. 39, No. 6, pp. 566-574.

DOI https://doi.org/10.1070/QE2009v039n06ABEH013966

5.     Egorov A.A., Sevastianov L.A., Sevastyanov A.L., Stavtsev A.V. Propagation of the monochromatic electromagnetic waves in irregular waveguides. A brief introduction to an analysis in the case of smooth or statistic irregularities. Bulletin of PFUR. Series Mathematics. Computer science. Physics, 2010, No. 1, pp. 67-76.

6.     Egorov A.A., Lovetskiy K.P., Sevastianov A.L., Sevastianov L.A. Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalised waveguide Luneburg lens in the zero-order vector approximation. Quantum Electronics, 2010, Vol. 40, No. 9, pp. 830-836.

DOI https://doi.org/10.1070/QE2010v040n09ABEH014332

7.     Egorov A.A., Sevastyanov A.L., Ayryan E.A., Lovetskii K.P., Sevast'yanov LA. Zero approximation of vector model for smoothly-irregular optical waveguide.  Matematicheskoe modelirovanie – Mathematical Simulation, 2010, Vol. 22, No. 8, pp. 42-54. (In Russian)

8.     Sevastyanov L.A., Egorov A.A, Sevastyanov A.L. Method of Adiabatic Modes in Studying Problems of Smoothly Irregular Open Waveguide Structures. Physics of Atomic Nuclei. 2013, Vol. 76, No. 2. pp. 224-239.

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

9.     Egorov A.A., Sevast'yanov L.A., Sevast'yanov A.L. Method of adiabatic modes in research of smoothly irregular integrated optical waveguides: zero approximation. Quantum Electronics, 2014, Vol. 44, No. 2, pp. 167-173.

DOI https://doi.org/10.1070/QE2014v044n02ABEH015303

10.            Egorov A.A., Andler G., Sevastyanov A.L., Sevastyanov L.A. On some properties of smoothly irregular waveguide structures critical for information optical systems. Distributed Computer and Communication Networks. DCCN 2018. 21st International Conference, DCCN 2018, Moscow, Russia, September 17–21, 2018, Proceedings. Editors Vladimir M. Vishnevskiy, Dmitry V. Kozyrev. Part of the Communications in Computer and Information Science book series. 2018, Vol. 919, pp. 387-398. Springer, Cham. DOI https://doi.org/10.1007/978-3-319-99447-5

11.            Taflove A., Hagness S.C. Computational Electrodynamics. The Finite Difference Time Domain Method. 2d.ed. Artech, London, 2000.

12.            Luneburg R.K. Mathematical theory of optics. University of California Press, 1966.

13.            Morgan S.P. General solution of the Luneburg lens problem.  J. Appl. Phys., 1958, Vol. 29, No. 9, pp. 1358-1368.

14.            Southwell W.H. Inhomogeneous optical waveguide lens analysis.  JOSA. 1977, Vol. 67, No. 8, pp. 1004-1009.

15.            Southwell W.H. Index profiles for generalized Luneburg lenses and their use in planar optical waveguides.  JOSA. 1977, Vol. 67, No. 8, pp. 1010-1014.

16.           Snyder A.W. and Love J.D. Optical Waveguide Theory. Chapman and Hall, New York, 1983.

17.           Marcuse D. Light Transmission Optics. Van Nostrand, New York, 1972.

18.           Robert G. Hunsperger, Integrated Optics. Theory and Technology Springer-Verlag, New York, 1984.

19.           Egorov A.A., Sevastyanov L.A., Sevastyanov A.L. Research of electrodynamic properties of a planar thin-film Luneburg lens.  Zhurnal Radioelektroniki - Journal of Radio Electronics, 2008, ¹ 6. Available at: http://jre.cplire.ru/jre/jun08/4/text.pdf

20.           Fehlberg E. Low-order Classical Runge-Kutta formulas with stepsize control. NASA Technical Report R-315.

21.           Tikhonov A.N.,  Arsenin V.Ya. Solutions of Ill-Posed Problems, 3rd ed.  Halsted, New York, 1977.

 

For citation:

A. A. Egorov, K. P. Lovetskii, A. L. Sevastianov, L. A. Sevastianov. A model of a multilayer smoothly-irregular integrated-optical waveguide in the zero vector approximation: theory and numerical analysis. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 3. Available at http://jre.cplire.ru/jre/mar19/11/text.pdf

DOI  10.30898/1684-1719.2019.3.11