H
*
TM mode
shapes in a circular waveguide with radius 1

amplitude of longitudinal electric field represented
*
L
zeros
=
88
2.405, 5.52, 8.654
<
,
8
3.832, 7.016, 10.173
<
,
8
5.136, 8.417, 11.620
<<
88
2.405, 5.52, 8.654
<
,
8
3.832, 7.016, 10.173
<
,
8
5.136, 8.417, 11.62
<<
f
@
r_, t_, n_, z_
D
:
=
BesselJ
@
n, r
*
z
D
Cos
@
n t
D
g
@
x_, y_, n_, m_
D
:
=
f
@
Min
@
1, Sqrt
@
x^2
+
y^2
DD
, ArcTan
@
x, y
D
, n, zeros
@@
n
+
1, m
DDD
H
*
here is TM 0 1
*
L
Plot3D
@
g
@
x, y, 0, 1
D
,
8
y,

1, 1
<
,
8
x,

1, 1
<
, PlotPoints
fi
32
D
1
0.5
0
0.5
1
1
0.5
0
0.5
1
0
0.25
0.5
0.75
1
SurfaceGraphics
H
*
here is TM 0 2
*
L
waveguide.nb
1