円形導波管（半径\(a\)）のTE\(_{mn}\)，TM\(_{mn}\)モードの遮断波長\(\lambda_c\)を低次モードから順に示すと次のようになる．
\begin{array}{r|lrr} \hline \hline \mbox{No.}&\mbox{Mode}&\chi '_{mn} \ \mbox{or} \ \chi _{mn}& \lambda_c \\ \hline 1 &\mbox{TE}_{11}&{\chi '_{11} = 1.841184}& 3.4126a \\ 2 &\mbox{TM}_{01}&{\chi _{01} = 2.404826}& 2.6127a \\ 3 &\mbox{TE}_{21}&{\chi '_{21} = 3.054237}& 2.0572a \\ 4,5 &\mbox{TM}_{11}&{\chi _{11} = 3.831706}& 1.6398a \\ 4,5 &\mbox{TE}_{01}&{\chi '_{01} = 3.831706}& 1.6398a \\ 6 &\mbox{TE}_{31}&{\chi '_{31} = 4.201189}& 1.4956a \\ 7 &\mbox{TM}_{21}&{\chi _{21} = 5.135622}& 1.2235a \\ 8 &\mbox{TE}_{41}&{\chi '_{41} = 5.317553}& 1.1816a \\ 9 &\mbox{TE}_{12}&{\chi '_{12} = 5.331443}& 1.1785a \\ 10 &\mbox{TM}_{02}&{\chi _{02} = 5.520078}& 1.1382a \\ 11 &\mbox{TM}_{31}&{\chi _{31} = 6.380162}& 0.9848a \\ 12 &\mbox{TE}_{51}&{\chi '_{51} = 6.415616}& 0.9794a \\ 13 &\mbox{TE}_{22}&{\chi '_{22} = 6.706133}& 0.9369a \\ 14,15&\mbox{TM}_{12}&{\chi _{12} = 7.015587}& 0.8956a \\ 14,15&\mbox{TE}_{02}&{\chi '_{02} = 7.015587}& 0.8956a \\ 16 &\mbox{TE}_{61}&{\chi '_{61} = 7.501266}& 0.8376a \\ 17 &\mbox{TM}_{41}&{\chi _{41} = 7.588342}& 0.8280a \\ 18 &\mbox{TE}_{32}&{\chi '_{32} = 8.015237}& 0.7839a \\ 19 &\mbox{TM}_{22}&{\chi _{22} = 8.417244}& 0.7465a \\ 20 &\mbox{TE}_{13}&{\chi '_{13} = 8.536316}& 0.7361a \\ 21 &\mbox{TE}_{71}&{\chi '_{71} = 8.577836}& 0.7325a \\ 22 &\mbox{TM}_{03}&{\chi _{03} = 8.653728}& 0.7261a \\ 23 &\mbox{TM}_{51}&{\chi _{51} = 8.771484}& 0.7163a \\ 24 &\mbox{TE}_{42}&{\chi '_{42} = 9.282396}& 0.6769a \\ 25 &\mbox{TE}_{81}&{\chi '_{81} = 9.647422}& 0.6513a \\ 26 &\mbox{TM}_{32}&{\chi _{32} = 9.761023}& 0.6437a \\ 27 &\mbox{TM}_{61}&{\chi _{61} = 9.936110}& 0.6324a \\ 28 &\mbox{TE}_{23}&{\chi '_{23} = 9.969468}& 0.6302a \\ 29,30&\mbox{TM}_{13}&{\chi _{13} =10.173468}& 0.6176a \\ 29,30&\mbox{TE}_{03}&{\chi '_{03} =10.173468}& 0.6176a \\ \hline \end{array}\(m=1\)のモードを\(n \leq 5\)についてまとめると次のようになる．軸対称のテーパ導波管に基本TE\(_{11}\)モードが入射した場合，このような高次モードが発生するが，\(m \ne 1\)のモードは発生しない．
\begin{array}{rlr|rlr} \hline \hline \mbox{No.}&\mbox{Mode}&\chi '_{mn}& \mbox{No.}&\mbox{Mode}&\chi _{mn}\\ \hline 1 & \mbox{TE}_{11} & \chi '_{11} = 1.841184 & 4,5 & \mbox{TM}_{11} & \chi _{11} = 3.831706 \\ 9 & \mbox{TE}_{12} & \chi '_{12} = 5.331443 & 14,15& \mbox{TM}_{12} & \chi _{12} = 7.015587 \\ 20 & \mbox{TE}_{13} & \chi '_{13} = 8.536316 & 29,30& \mbox{TM}_{13} & \chi _{13} =10.173468 \\ 37 & \mbox{TE}_{14} & \chi '_{14} =11.706005 & 48,49& \mbox{TM}_{14} & \chi _{14} =13.323692 \\ 60 & \mbox{TE}_{15} & \chi '_{15} =14.863589 & 73,74& \mbox{TM}_{15} & \chi _{15} =16.470630 \\ \hline \end{array}