On the representation of electromagnetic fields in closed waveguides using four scalar potentials

Abstract

The investigation of the electromagnetic field in a regular waveguide filled with a homogeneous substance reduces to the study of two independent boundary value problems for the Helmholtz equation. In the case of a waveguide filled with an inhomogeneous substance, a relationship arises between the modes of these two problems, which in numerical experiments can not always be fully taken into account. In this paper, we will show how to rewrite the Helmholtz equations in the “Hamiltonian form” to express this connection explicitly. In this case, the problem of finding monochromatic waves in a waveguide with arbitrary filling will be reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The results of numerical experiments on finding normal waves, realized in the computer algebra system Sage, are presented.

Keywords:

• Waveguide
• Maxwell’s equations
• normal modes
• partial radiation conditions
• Galerkin method
• Kantorovich method
• Sage
• Sagemath

Acknowledgements

The calculations in this article are performed in the computer algebra system Sage [49].

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The publication was prepared with the support of the “RUDN University Program 5-100”. The work was partially supported by Russian Foundation for Basic Research [grants number 15-07-08795], [grants number 16-07-00556]; Ministry of Education and Science of the Russian Federation [Agreement number 02.a03.21.0008].