Modes of laser propagation in cylindrical optics

[Sciencestd]

I saw the solution of the light propagates in cylinder.. so in every solution there is the first order Gaussain function (the slandered one) times another function which gives I think the separation, both of them gives the intensity separation.. So what does that mean?! is it as I draw on the image on mode 10.. or is it, for example, mode 20 the intensity in the yellow divided to three or ever mode by itself is Gaussian?!

(The image source is: optique-ingenieur.org)

 

[Andy Resnick]

I'm not entirely sure what you are asking, but your 'spot shapes' are transverse Gaussian modes (more correctly, depending on the cross-section of the resonator, Laguerre–Gaussian (rotationally symmetric) or Hermite-Gaussian modes).

 

[Sciencestd]

Yes I mean about the transverse Gaussain modes... when I look at the answers I see $e^{-\frac{x^2+y^2}{w_0}}\times F(x,y)$ where $F(x,y)$ can be bessel or Hermite... So my question is: can one look at this as the Gaussian divided in the space (yellow in the image above), or every mode by itself has Gaussian behavior.. if yes so why we see the whole mode field diameter $w_0$ in the Gaussian...