Electromagnetic waves in a bent pipe of rectangular cross section

Abstract

The analysis of electromagnetic wave propagation in a bent pipe of rectangular cross section, (x = R, x = R+a, y = 0, y = b), is based on the Maxwell field equations, expressed in cylindrical coordinates (r, 6, y) (Fig. 1). As in the case of the straight pipe,1 the time variation is given by the exponential ewhere co is the angular frequency. The angular variation is given by e~xe, where 2 is the propagation constant for the bent portion. The equations may be written In (1) He, Hr, Hy, Ee, Er and Ey are the components of magnetic and electric field, « is the electric inductive capacity, and p. the magnetic inductive capacity. The electrical conductivity, c, and charge density, p, are assumed to be zero.The field components Hr, Hv, Er and Ey may be expressed in terms of He and Ee by various combinations of the equations (1). These giveHy(Gr2) = -S rdHe/dy + rjcotEe + r2jwtdEe/dr,Er(Gr2) = -2 rdEe/dr -2 Ee + r2jundHe/dy, drLGr dr J dy2 2 dy dr * Received June 29, 1943. The paper constitutes part of a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University, May, 1943. The author wishes to thank Professor L. Brillouin of Brown University for his many helpful suggestions.

Wave Propagation in a Curved Waveguide with Arbitrary Dielectric Transverse Profiles

“…The metric coefficient h ζ is dependent on x (h ζ = 1 + x/R). Thus the next diagonal matrix K (1) is defined as…”

“…Various methods for the analysis of similar problems, of wave propagation in dielectric inhomogeneous waveguides, have been studied in the literature. The propagation of general-order modes in curved rectangular waveguide examined by using asymptotic expansion method [1]. A matrix formulation of the generalized telegraphist's equation [2] used to obtain a general set of equations for a guide of arbitrary crosssection with curved axis.…”

Technique for Inhomogeneous Profiles in the Cross-Section of the Helical Rectangular Waveguide

“…The methods of curved waveguides have been proposed in the literature. The propagation in curved rectangular waveguide of general-order modes were proposed by using asymptotic expansion method [1]. An approximate method for propagation in a curved dielectric waveguide with rectangular cross section was described [2].…”

Wave Propagation in a Helical Waveguide With Slab and Rectangular Dielectric Profiles, and Applications

“…The propagation of general-order modes in curved rectangular waveguide examined by using asymptotic expansion method [1]. A matrix formulation of the generalized telegraphist's equation [2] used to obtain a general set of equations for a guide of arbitrary cross section with curved axis.…”