L11MOCONFCS
Cartesian Coordinates for rectangular mirrors in confocal resonator.
Field distribution as contour plot.
The mode numbers m and n are for Hermitian Polynomials.
The constant in the exponential is simulated by X.
Small X correspond to small "waist width".
N := 40
i := 0 .. N
j := 0 .. N
x i := ( −20) + 1.00⋅ i
H0( x ) := 1
H0( y ) := 1
y j := −20 + 1.00⋅ j
H1( x ) := x ⋅
2
 2 ⋅ x − 2
H2( x ) := 4 ⋅ 
 X 
2
X
H1( y ) := y ⋅
2
Y
2
 2 ⋅ y − 2
H2( y ) := 4 ⋅ 
 Y 
H00 ( x , y ) := H0( x ) ⋅ H0( y )
H20 ( x , y ) := H2( x ) ⋅ H0( y )
H01 ( x , y ) := H0( x ) ⋅ H1( y )
H02 ( x , y ) := H0( x ) ⋅ H2( y )
H10 ( x , y ) := H1( x ) ⋅ H0( y )
H21 ( x , y ) := H2( x ) ⋅ H1( y )
H11 ( x , y ) := H1( x ) ⋅ H1( y )
H12 ( x , y ) := H1( x ) ⋅ H2( y )
H22 ( x , y ) := H2( x ) ⋅ H2( y )
2
R( x , y ) := ( x ) + ( ( y ) )
constant X X ≡ 100
2
Y ≡ 100
 − R( x , y) 
 X
g ( x , y ) :=  e

M00 i , j := ( g ( x i , y j) ⋅ H00 ( x i , y j) )
M10
M00
M01 i , j := ( g ( x i , y j) ⋅ H01 ( x i , y j) )
M01
M10 i , j := ( g ( x i , y j) ⋅ H10 ( x i , y j) )
2
2
M11 i , j := ( g ( x i , y j) ⋅ H11 ( x i , y j) )
M11
2
2
M20 i , j := ( g ( x i , y j) ⋅ H20 ( x i , y j) )
2
M20
M02 i , j := ( g ( x i , y j) ⋅ H02 ( x i , y j) )
M02
M21 i , j := ( g ( x i , y j) ⋅ H21 ( x i , y j) )
2
M21
M12 i , j := ( g ( x i , y j) ⋅ H12 ( x i , y j) )
2
M12
2
M22 i , j := ( g ( x i , y j) ⋅ H22 ( x i , y j) )
M22
2