DA2FAGRSTEP2S
Diffraction on an step grating with width d, center to center distance of steps a,
height H, two wavelength λ1 and λ2 for 0th and first order, distance from grating to
screen X and coordinate on screen Y.
All distances and wavelength in mm, number of lines N .Normal incidence.
All parameters are globally defined above the graph.
D(θ) is the diffraction factor, I(θ) is the interference factor, normalized to 1.
II(θ) is the interference factor of the gratings with respect to the two planes.
P(A) is the product of Interference and diffraction factors.
The intensity of the zeroth order and of the first orders change depending on the heigth H.
If H is a multiple of λ, all light is in the zero order, if H is a multiple of λ/2, all light is in
the first order.
θ := −.7001 , −.6999 .. .7
2
 sin π ⋅ d ⋅ sin( θ )  
  λ1

D1( θ ) := 

  π ⋅ d ⋅ sin( θ )   I1( θ ) :=
  λ1
 
2
 sin π ⋅ d ⋅ sin( θ )  
  λ2

(
)
D2 θ := 
 I2( θ ) :=
  π ⋅ d ⋅ sin( θ )  
  λ2
 
2
 sin π ⋅ a ⋅ sin( θ ) ⋅ N 
  λ1
2


 II1( θ ) := cos  π ⋅ ( d ⋅ sin( θ ) + H) 
a
 N⋅ sin π ⋅ ⋅ sin( θ ) 
  λ1


 λ1

2
 sin π ⋅ a ⋅ sin( θ ) ⋅ N 
  λ2
2


 II2( θ ) := cos  π ⋅ ( d ⋅ sin( θ ) + H) 
a
 N⋅ sin π ⋅ ⋅ sin( θ ) 
  λ2


 λ2

.
2
 sin π ⋅ d ⋅ sin( θ )  
  λ1

(
)
D1 θ := 

  π ⋅ d ⋅ sin( θ )   I1( θ ) :=
  λ1
 
2
 sin π ⋅ d ⋅ sin( θ )  
  λ2

D2( θ ) := 
 I2( θ ) :=
  π ⋅ d ⋅ sin( θ )  
  λ2
 
2
 sin π ⋅ a ⋅ sin( θ ) ⋅ N 
  λ1
2


 II3( θ ) := cos  π ⋅ ( d ⋅ sin( θ ) + H) 
 N⋅ sin π ⋅ a ⋅ sin( θ ) 
  λ1


 λ1

2
 sin π ⋅ a ⋅ sin( θ ) ⋅ N 
  λ2
2


 II4( θ ) := cos  π ⋅ ( d ⋅ sin( θ ) + H) 
 N⋅ sin π ⋅ a ⋅ sin( θ ) 
  λ2


 λ2

P1( θ ) := D1( θ ) ⋅ I1( θ ) ⋅ II1( θ )
P3( θ ) := D1( θ ) ⋅ I1( θ ) ⋅ II3( θ )
P2( θ ) := D2( θ ) ⋅ I2( θ ) ⋅ II2( θ )
P4( θ ) := D2( θ ) ⋅ I2( θ ) ⋅ II4( θ )
d ≡ .001 a ≡ .002
N≡6
λ2 ≡ .0005 λ1 ≡ .0007
n1 ≡ 1
n2 ≡ .5
H1 ≡ n1⋅ λ1
H3 ≡ n2⋅ λ1
H2 ≡ n1⋅ λ2
H4 ≡ n2⋅ λ2
H ≡ .00035
1
P1 ( θ )
P2 ( θ )
D1( θ )
0.5
D2( θ )
0
0.8
0.6
0.4
0.2
0
θ
0.2
0.4
0.6
0.8
.