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Modeling a Gaussian beam
Posted Aug 26, 2014, 1:20 p.m. EDT RF & Microwave Engineering, Modeling Tools & Definitions, Parameters, Variables, & Functions 2 Replies
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Hello everyone,
could somebody explain to me why in the COMSOL example "Nanorods" the equation for the incoming electric field (a z-polarized gaussian beam in 2D) reads
sqrt(w0/w(y))*exp(-(x/w(y))^2)*exp(j*k*x^2/(2*R(y)))*exp(j*(k*y-0.5 atan(y/z0)))
which is different from the usual definition of a gaussian beam (e.g. on wikipedia) by a square root ( "sqrt(w0/w(y))" instead of "w0/w(y)" and a factor in front of the "atan(y/z0)"?
In the example "Second harmonic generation of a gaussian beam" they use the same definition (but in the time domain).
Thank you for your help!
could somebody explain to me why in the COMSOL example "Nanorods" the equation for the incoming electric field (a z-polarized gaussian beam in 2D) reads
sqrt(w0/w(y))*exp(-(x/w(y))^2)*exp(j*k*x^2/(2*R(y)))*exp(j*(k*y-0.5 atan(y/z0)))
which is different from the usual definition of a gaussian beam (e.g. on wikipedia) by a square root ( "sqrt(w0/w(y))" instead of "w0/w(y)" and a factor in front of the "atan(y/z0)"?
In the example "Second harmonic generation of a gaussian beam" they use the same definition (but in the time domain).
Thank you for your help!
2 Replies Last Post Sep 2, 2014, 6:31 a.m. EDT
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Posted:
10 years ago
Hi Frederik,
The equation COMSOL uses is for a “2D Gaussian Beam” – one that satisfies the wave equation for a 2D geometry as described in the “Second Harmonic Generation from a Gaussian Beam” COMSOL model.
Nagi Elabbasi
Veryst Engineering
The equation COMSOL uses is for a “2D Gaussian Beam” – one that satisfies the wave equation for a 2D geometry as described in the “Second Harmonic Generation from a Gaussian Beam” COMSOL model.
Nagi Elabbasi
Veryst Engineering
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Posted:
10 years ago
Thanks for your help! Could you point me to a (non-comsol) source for this? Somehow I wasn't able to find a derivation in 2d.
EDIT: Ah, now I see how it works :) thanks!
EDIT: Ah, now I see how it works :) thanks!