Example30​​ElectromagneticImagingwthinaLaser-Beampropagatingwiththespeedoflight:c=
1
ϵ0μ0
In[]:=
Out[]=
Book:
RisingoftheJamesWebbSpaceTelescope​
​anditsFundamentalBlindness
​​ Page15,Equation(19)​​​​
- 
1
2
c
∂
¯
E
×
¯
Η

∂t
+
ε
0
¯
E
∇. 
¯
E
−
ε
0
¯
E
×∇×
¯
E
+
μ
0
¯
Η
∇. 
¯
Η
−
μ
0
¯
Η
×∇×
¯
Η

= 0
(19)​​​​ExampleofaLASER-BEAMwithaGaussianIntensitydivison
-K2
2
x
+
2
y

,combinedwithanarbitrarydivisiong[x,y]inthe(x,y)plane,propagatinginthez-directionwiththespeedoflightc=
1
ϵ0μ0
.
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
x=.
In[]:=
y=.
In[]:=
z=.
In[]:=
t=.
In[]:=
Get["VectorAnalysis`"]
General
:VectorAnalysis` is now obsolete. The legacy version being loaded may conflict with current functionality. See the Compatibility Guide for updating information.
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
SetCoordinates[Cartesian[x,y,z]]
Out[]=
Cartesian[x,y,z]
In[]:=
{Coordinates[Cartesian],CoordinateRanges[Cartesian]}
Out[]=
{{x,y,z},{-∞<x<∞,-∞<y<∞,-∞<z<∞}}
In[]:=
K2=.
One polarized (Electric Field in the x-direction) Laser Beam f1[x,y,z,] is propagating in the z-direction. The second polarized (Electric Field in the y-direction) Laser Beam f2[x,y,z] is propagating in the x-direction. In the cross section of both Laser Beams due to “Electromagnetic Interaction” deformation takes place and deforms both different images projected by both Laser Beams in two different and perpendicular directions. This has been called “Electromagnetic Interaction Lensing”.
In[]:=
ev={f1[x,y,z]*g[t-z*Sqrt[ϵ0]*Sqrt[μ0]],f2[x,y,z]*g[t-z*Sqrt[ϵ0]*Sqrt[μ0]],0}
Out[]=
f1[x,y,z]gt-z
ϵ0
μ0
,f2[x,y,z]gt-z
ϵ0
μ0
,0
In[]:=
mv=(1/Sqrt[μ0])*Sqrt[ϵ0]*​​{0,f1[x,y,z]*g[t-z*Sqrt[ϵ0]*Sqrt[μ0]],f2[x,y,z]*g[t-z*Sqrt[ϵ0]*Sqrt[μ0]]}
Out[]=
0,
ϵ0
f1[x,y,z]gt-z
ϵ0
μ0

μ0
,
ϵ0
f2[x,y,z]gt-z
ϵ0
μ0

μ0
