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

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 a₂ to a₁, with a₁ < a₂, the optimal length of the taper is 3.198a₁a₂/λ. Here, λ is the wavelength of radiation. The fractional loss of the HE₁₁ mode in an optimized taper is [Formula: see text]. These formulae are accurate when a₂ ≲ 2a₁. Slightly more complex formulae, accurate for a₂ ≤ 4a₁, are also presented in this paper. The loss in an overmoded corrugated linear taper is less than 1 % when a₂ ≤ 2.12a₁ and less than 0.1 % when a₂ ≤ 1.53a₁. 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 a₂/a₁ may be attractive because of their simplicity of fabrication.