DIELECTRIC WAVEGUIDE 2081 is so small that the mode under consideration becomes unguided or,in other words,the "penetration depth"'in medium 4 is o.It is 1 when the guide is so large that k,=k,which means that all the field travels within the guiding rod and the"penetration depths"in media 2,3,4, and 5 are zero. The solid curves have been obtained using the exact numerical solutions of the transcendental equations (6),(7),(20),and (21); for the transverse propagation constants k and the dashed lines have been derived using the closed form approximations (12),(13),(22), and (23).In Figs.6a,6b,6e,and 6f,for comparison,we have also included the dotted-dashed lines which are the results obtained by Goell as computer solutions of the boundary value problem. The three solutions coincide even for moderately large values of b. 1.0 E,E39- 0.8 E.E2,9 E及， E2 0.6 0.4 na b 0.2 n. 1.05 <n4<n, a=4b-- na<n 1.0 2 Ed, 0.8 E品 E 0.6 04= 1.0 0. 203 d) 1.5 5 1.0 0.2 n 5 0 0.4 0.8 3.2 4.0 =(n2-n2) A
DIELECTRIC WAVEGUIDE 2081 is so small tha t the mode under consideration becomes unguided or, in other words, the "penetration depth" in medium 4 is « . It is 1 when the guide is so large tha t k, = k, , which means tha t all the field travels within the guiding rod and the "penetration depths " in media 2, 3, 4, and 5 are zero. The solid curves have been obtained using the exact numerical solutions of the transcendental equations (6), (7), (20), and (21); for the transverse propagation constants k, and k^; the dashed lines have been derived using the closed form approximations (12), (13), (22), and (23). I n Figs. 6a, 6b, 6e, and 6f, for comparison, we have also included the dotted-dashed lines which are the results obtained by Goell as computer solutions of the boundary value problem.* The three solutions coincide even for moderately large values of 6
2082 THE BELL SYSTEM TECHNICAL JOURNAL,S SEPTEMBER 1968 1.0 n4 0.8 n n 4=1.5 E,Eu. EiE2 0.6 别 a=b E，E 1 0.4- k=哭n E,E22V 0.2 7 (e) 0 1.2 n4 1.0 n.西 n4= E从、 E开、 0.8 2 E引y k= 0.6 ER 0.4 0.2 (f) 1.2 1.0 . n4=5 e培 0.8 k--日=4b-- 08 E 0.4 w2 E 0.2 31 (g) 0 0.4 0.8 1.2 1.6 2.0 2.4 28 3.2 4.0 2b (-n
2082 THE BELL SYSTEM TECHNICAL JOT^NAL, SEPTEMBER Ιθβθ Ι.Ογ 1.0 O.B γ ι •f o.e 0.4 0.2 0 1.2 π. β 04 "ib μ ^ Ε, k, a=2b / y Ε 31° ψ ιΊ I ^ / / / '¡á (f) 1.6 b A