Flat Dielectric Waveguides of the Terahertz Range and Diffraction Antennas on Their Basis

Introduction. The existing CAD tools of electrodynamic modeling used to analyze complex waveguide structures of the microwave range employ the finite element method. However, in the terahertz range, determining the channeling properties of layered dielectric waveguides becomes a difficult task. This is primarily related to the construction of a partition grid of the layered structure and the need to take into account the behavior of the electromagnetic field at the boundaries of media with different relative permittivity. In this work, we use the principles of the finite element method to solve the problem of finding a propagation constant in a flat multilayer dielectric waveguide, and show how to reduce the number of elements when setting optimal boundary conditions. Based on the obtained computational model, the possibility of constructing diffraction antennas operating in the THz range is considered.

Aim. Construction of a computational model for calculating a flat dielectric waveguide by the finite element method, determination of the dispersion characteristics of the analyzed structure in the THz range. Discussion of the possibility of constructing a diffraction antenna on a dielectric structure in various designs.

Materials and methods. A computational mathematical model for the analysis of a complex layered structure is based on Maxwell's equations and the finite element method using boundary conditions for tangential and normal components of the electromagnetic field.

Results. A numerical analysis of the dispersion characteristics of structures with complex dielectric filling is carried out; variants of diffraction antennas for use in the THz range are considered.

Conclusion. The created mathematical models made it possible to numerically evaluate the channeling properties of dielectric structures in the THz range, on the basis of which diffraction antennas can be constructed.

1. Schwartz G. C., Srikrishnan K. V. Handbook of Semiconductor Interconnection Technology. 2nd ed. Boca Raton, CRC Press, 2006, 536 p.

2. Zi S., Chistyakov Yu. D. Tekhnologiya SBIS [ULITC Technology]. Moscow, Mir, 1986, vol. 1, 404 p.; vol. 2, 453 p. (In Russ.)

3. Marchuk G. I. Metody vychislitel'noi matematiki [Methods of Computational Mathematics]. Moscow, Nauka, 1980, 536 p. (In Russ.)

4. Grinev A. Yu. Chislennye metody resheniya prikladnykh zadach elektrodinamik [Numerical Methods for Solving Applied Problems of Electrodynamics. Textbook]. Moscow, Radio engineering, 2012, 336 p. (In Russ.)

5. Rektorys K. Variational Methods in Mathematics, Science and Engineering. Berlin, Springer, 1977, 571 p.

6. Nikolsky V. V. Variatsionnye metody dlya vnutrennikh zadach elektrodinamiki [Variational Methods for Internal Problems of Electrodynamics]. Moscow, Nauka, 1967, 460 p. (In Russ.)

7. Declou J. Metod konechnykh elementov [The Finite Element Method]. Trans. from French. Moscow, Mir, 1976, 95 p. (In Russ.)

8. Zenkevich O. Metod konechnykh elementov v tekhnike [The Finite Element Method in Engineering]. Moscow, Mir, 1975, 541 p. (In Russ.)

9. Zienkiewicz O., Morgan K. Finite Elements and Aapproximation. New York, John Wiley & Sons, 1983, 328 p.

10. Segerlind L. Applied Finite Element Analysis. New York, John Wiley & Sons, 1976, 442 p.

11. Austrell P., Dahlblom O., Lindemann J., Olsson A., Olsson K.-G., Persson K., Pettersson H., Ristinmaa M., Sandberg G., Wernberg P.-A. CALFEM: A Finite Element Toolbox. Ver. 3.4. Sweden; Structural Mechanics, LTH, 2004, 285 p.

12. Hutton D. V. Fundamentals of Finite Element Analysis. 1st ed. New York, McGraw Hill, 2003, 640 p.

13. Le K. H. Finite Element Mesh Generation Methods: A Review and Classification. ComputerAided Design. 1988, vol. 20, iss. 1, pp. 27–38. doi: 10.1016/0010-4485(88)90138-8

14. Moaveni S. Engineering Fundamentals: An Introduction to Engineering. 3th ed. Toronto, Thomson Learning, 2008, 634 p.

15. Shäfer M. Computational Engineering – Introduction to Numerical Methods. Berlin, Springer-Verlag, 2006, 321 p. doi: 10.1007/3-540-30686-2

16. Stasa F. L. Applied Finite Element Analysis for Engineers. New York, CBS Publishing, 1985, 659 p.

17. Fairweather G. F., Rizzo J., Shippy D. J., Wu Y. S. On the Numerical Solution of TwoDimensional Potencial Problems by an Improved Boundary Integral Equations Method. J. Computational Phisics. 1979, vol. 31, iss. 1, pp. 96–112. doi: 10.1016/0021-9991(79)90064-0

18. Frey P. J., George P.-L. Mesh Generation. Application to Finite Elements. 2nd ed. London, ISTE Publishing Company, 2008, 814 p. doi: 10.1002/9780470611166