Hypergeometric-Gaussian Modes
Hypergeometric-Gaussian Modes
Hypergeometric-Gaussian modes are paraxial wave modes with cylindrical symmetry. The complex amplitude involves a confluent hypergeometric function and a gamma function. Such modes are of importance in laser beam optics.
Details
Details
In cylindrical coordinates, the paraxial equation is
1
r
∂
∂r
∂
∂r
1
2
r
2
∂
∂
2
ϕ
∂
∂z
and its solutions are of the form
f(m,p,r,ϕ)=exp(imϕ)-;m+1;
m+p+1
2
πΓ(p+m+1)
m+1
i
m
r
Γ+m+1
p
2
Γ(m+1)
1
F
1
p
2
2
r
External Links
External Links
Permanent Citation
Permanent Citation
Enrique Zeleny
"Hypergeometric-Gaussian Modes"
http://demonstrations.wolfram.com/HypergeometricGaussianModes/
Wolfram Demonstrations Project
Published: April 29, 2014