L12MOCY1to4S
Cylindircal Coordinates for circular mirrors in confocal resonator.
Field distribution as contour plot for graph 00, 10, 01, and 11.
The L(l,p) functions are written out for 00 to 22. The constant in the exponential is
X
i := 0 .. N
j := 0 .. N
2
R( x , y) := ( x) + ( y)
2
N ≡ 30
xi := ( −3) + .20001⋅ i
β ( x , y) :=  atan 

x 
 y 
 − ( R( x , y) )  constant X


X
q( x, y) :=  e

The L's are given below.
u( x, y) := 4 ⋅
L00( x , y) := 1
R ( x , y)
X
yj := −3 + .20001⋅ j
g( x , y) := cos( 0 ⋅ β ( x , y) )
L01( x , y) := 1 − u ( x , y)
M00 i , j := ( cos( 0 ⋅ β ( xi , y j) ) ⋅ q ( xi , y j) ⋅ L00( xi , y j) )
L10( x , y) := 1
L11( x , y) := 2 − u ( x , y)
2
M10 i , j := ( cos( 0 ⋅ β ( xi , y j) ) ⋅ q ( xi , y j) ⋅ L01( xi , y j) )
M00
X≡3
M10
2
M01 i , j := ( cos( 1 ⋅ β ( xi , y j) ) ⋅ q ( xi , y j) ⋅ L10( xi , y j) )
M01
2
M11 i , j := ( cos( 1 ⋅ β ( xi , y j) ) ⋅ q ( xi , y j) ⋅ L11( xi , y j) )
M11
2