N1RECBOX
Modes of the rectangular box in two dimensions
Standing sine waves in x and y direction. Mode number and constants.
x direction n1 and a
y direction n2 and b
The wave in each direction is shown and Contour and surface plots.
The square is also shown as surface plot.
i := 0 .. N
j := 0 .. N
xi := ( −40) + 2.001⋅ i
y1( x) := sin 2 ⋅ π ⋅

λ1 := 2⋅
y j := −40 + 2.0001⋅ j
y2( y) := sin 2 ⋅ π ⋅

λ1 
x

y
a
λ2 := 2⋅
n1
b
n2

λ2 
1. One dimension
1
( )
y1 xi
1
( )
0
1
y2 y j
40
20
0
0
1
20
40
xi
2. Amplitude, 2D
M11 i , j := y1( xi) ⋅ y2( y j)
M11
20
0
yj
n1 ≡ 2
a ≡ 40
M11
n2 ≡ 2
b ≡ 40 N ≡ 20
20
3. Intensity, 2D
MM11i , j := ( y1( xi) ⋅ y2( y j) )
MM11
2
MM11