G. S. Malyshev - Post-graduate Student of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev E-mail: physics@nntu.nnov.ru S. B. Raevskij - Honored Scientist of RF, Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev A. Yu. Sedakov - Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Director of FRPC - Measuring System Research Institute n.a. Yu.Ye. Sedakov - (Nizhny Novgorod) A. A. Titarenko - Dr.Sc. (Eng.), Associate Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Deputy Chief Designer of FRPC - Measuring System Research Institute n.a. Yu.Ye. Sedakov - (Nizhny Novgorod)

The article provides a rigorous formulation of the spectral method of calculating the dispersion characteristics of the waves of open dielectric waveguides (ODW) with an arbitrary function of the dielectric filling over the transverse coordinates. The method of partial areas (MPA) is considered in relation to the analysis of multilayer round ODW. The advantages and disadvantages of two calculation methods for ODW have been considered in the article. The main factors influencing on the speed of calculations by two methods have been specified. These methods are used to calculate the dispersion characteristics of waves in the three-layer round ODW and in the gradient fiber with a triangular refractive index profile. Comparison of the results of calculation of the dispersion characteristics of the waves of round ODW produced by the spectral method and the method of partial areas, has shown that performance of considered methods is comparable. When calculating the dispersion characteristics of the fundamental wave of the circular gradient ODW, the spectral method has great speed compared with MPA. Moreover the MPA makes it possible to obtain a rigorous solution only for multilayer ODW with a round cross-section. The spectral method is suitable for calculation of the ODW with arbitrary cross section and allows to reveal the whole waves spectrum for a given frequency range.

 

1. Raevskijj S.B., Titarenko A.A. Raschet otkrytykh prodolno reguljarnykh diehlektricheskikh volnovodov s proizvolnym poperechno neodnorodnym secheniem // Radiotekhnika i ehlektronika. 2009. № 11. S. 1285-1299.
2. Neganov V.A., Osipov O.V., Raevskijj S.B., JArovojj G.P. EHlektrodinamika i rasprostranenie radiovoln. M.: Radiotekhnika. 2007.
3. Raevskijj S.B., Titarenko A.A. Metod ehlektrodinamicheskogo rascheta prjamougolnykh zakrytykh volnovodov s proizvolnym diehlektricheskim zapolneniem // Antenny. 2007. Vyp. 2 (117). S. 4-11.
4. Gradshtejjn I.S., Ryzhik I.M. Tablicy integralov, summ, rjadov i proizvedenijj. M.: Fizmatgiz. 1963.
5. Unger KH.G. Planarnye i volokonnye opticheskie volnovody. M.: Mir. 1980.
6. Belanov A.S., Dianov E.M., Krivenkov V.I. Dispersija v svetovodakh so slozhnym profilem pokazatelja prelomlenija // Doklady akademii nauk. 1999. T. 364. № 1. S. 37-41.
7. Abramovic M., Stigan I. Spravochnik po specialnym funkcijam. M.: Nauka. 1979.