Mode Propagation in Continuously Curved Waveguides

Abstract

This paper presents the results of precise numerical computations and extensive analytical investigations of the angular propagation constants for the various electromagnetic modes which may exist in waveguide bends of rectangular cross section. Although the values of the several independent parameters have been chosen to be commensurate with microwave applications, the results are displayed and discussed in a manner which should be convenient for both the analysis and the design of such components in analogous problems in other and diverse practical situations. Moreover, special consideration is given to the relationship of this work to various efforts in the study of radio wave propagation. Two important approximations, one for “high” frequencies and the other for gradual bends, are also considered as a part of the present inquiry. These approximations, especially the latter, turn out to be remarkably good, and rather accurate values of the propagation constants can be obtained with their use for wide ranges of parameter values. The following are typical of the conclusions which can be drawn from this research: (1) cutoff frequencies for modes existing in continuously curved waveguides are curvature dependent; (2) there exist waveguide bends such that circularly polarized waves are undistorted by transmission along the curved section; (3) the angular propagation constants are generally monotonically increasing functions of the operating frequency f (for fixed mean radius) and of the mean radius R (for fixed frequency). Moreover, they vary linearly with f for frequencies far above cutoff and with R for small curvatures.

Analyzing Wave Propagation in Helical Waveguides Using Laplace, Fourier, and Their Inverse Transforms, and Applications

“…Several methods of investigation of propagation were developed for study of empty curved waveguide and bends [14][15][16][17]. The results of precise numerical computations and extensive analytical investigation of the angular propagation constants were presented for various electromagnetic modes which may exit in waveguide bends of rectangular cross section [14].…”

“…The results of precise numerical computations and extensive analytical investigation of the angular propagation constants were presented for various electromagnetic modes which may exit in waveguide bends of rectangular cross section [14]. A new equivalent circuit for circular E-plane bends, suitable for any curvature radius and rectangular waveguide type was presented in Ref.…”

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

“…Several methods of investigation of propagation were developed for study of empty curved waveguide and bends [3][4][5][6].…”

“…The results of precise numerical computations and extensive analytical investigation of the angular propagation constants were presented for various electromagnetic modes which may exit in waveguide bends of rectangular cross section [3]. A new equivalent circuit for circular E-plane bends, suitable for any curvature radius and rectangular waveguide type was presented in Ref.…”

Wave Propagation in a Curved Waveguide with Arbitrary Dielectric Transverse Profiles

“…Several methods of investigation of propagation were developed for study of empty curved waveguide and bends [7][8][9][10].…”