Simple Expressions for the Design of Linear Tapers in Overmoded Corrugated Waveguides

Abstract

Simple analytical formulae are presented for the design of linear tapers with very low mode conversion loss in overmoded corrugated waveguides. For tapers from waveguide radius a[subscript 2] to a[subscript 1], with a[subscript 1]<a[subscript 2], the optimal length of the taper is 3.198a[subscript 1]a[subscript 2]/λ. Here, λ is the wavelength of radiation. The fractional loss of the HE 11 mode in an optimized taper is 0.0293(a[subscript 2]−a[subscript 1])[superscript 4]/a[superscript 2][subscript 1]a[superscript 2][subscript 2]. These formulae are accurate when a[subscript 2]≲2a[subscript 1]. Slightly more complex formulae, accurate for a[subscript 2]≤4a[subscript 1], are also presented in this paper. The loss in an overmoded corrugated linear taper is less than 1 % when a[subscript 2]≤2.12a[subscript 1] and less than 0.1 % when a[subscript 2]≤1.53a[subscript 1]. The present analytic results have been benchmarked against a rigorous mode matching code and have been found to be very accurate. The results for linear tapers are compared with the analogous expressions for parabolic tapers. Parabolic tapers may provide lower loss, but linear tapers with moderate values of a[subscript 2]/a[subscript 1] may be attractive because of their simplicity of fabrication.