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 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 the Research Institute of Measuring Systems n.a. Yu.E. Sedakov 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 General Designer of the Research Institute of Measuring Systems n.a. Yu.E. Sedakov

The article provides a rigorous formulation of the spectral method for calculating the dispersion characteristics of the waves of open dielectric waveguides with arbitrary function of the dielectric filling over the transverse coordinate. By comparison with the spectral method, it has been checked the ray method for the application validity for the analysis of open dielectric waveguides. Comparison of the ray method with a modified Galerkin method has been performed for the example of the strip waveguide. The limits of applicability of the ray method for the analysis of such a structure have been defined. It has been shown that for the case when the geometric dimensions of the waveguide is much larger than the wavelength the ray field presentation method is quite effective. The modified Galerkin method revealed a lack of critical frequencies of the basic wave. That is, the dispersion characteristic of the basic wave gradually approach the horizontal axis. The ray method can not detect such a feature. The difference between the results obtained using the modified Galerkin method and the ray method is the more significant the higher the type of wave. Both methods give good agreement only at high frequencies. At low frequencies, the investigated methods provide both quantitative and qualitative difference between the dispersion characteristics of the waves of a strip dielectric waveguide.

 

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. Sotskaja L.I., Sotskijj A.B. Metod integralnogo uravnenija v teorii slabonapravljajushhikh neodnorodnykh opticheskikh volnovodov // ZHTF. 2002. T. 72. № 12. S. 1-8.
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.