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In reference to the specifications of a laser diode below:

http://www.thorlabs.de/thorcat/11900/L780P010-SpecSheet.pdf

I wish to be able to model it as a gaussian laser beam. I understand there is a formula (see below) Formula

where if I know the wavelength and the divergence angle I can work out the waist size. The laser diode specifications give me a divergence angle, but where on the actual laser diode is the waist located? Is it right on the diode surface? Is the waist location the same for both the fast and slow axis?

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    $\begingroup$ I think the waist is nominally located on the diode surface and the astigmatism parameter in the data sheet gives the possible relative positions of the waist in both axes. $\endgroup$ – Stephen Blake Dec 5 '14 at 19:54
  • $\begingroup$ I think you are right Stephen you have answered the question perfectly. Put an answer down and I will accept it. $\endgroup$ – BigAl Dec 8 '14 at 9:20
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My impression is the beam is not Gaussian at all, as the beam divergence in two orthogonal planes differs dramatically.

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    $\begingroup$ It is still often called a Gaussian beam in such a case, there are just different parameters for both $x$ and $y$. So you have independent waist parameters $w_x,\,w_y$ and wavefront curvatures $\kappa_x,\,\kappa_y$ so that the transverse field varies like $\exp\left(-\frac{x^2}{w_x^2}-\frac{y^2}{w_y^2} + i\,\frac{k}{2}\,\kappa_x\,x^2 + i\,\frac{k}{2}\,\kappa_y\,y^2\right)$. Different curvatures $\kappa_x\neq\kappa_y$ correspond to astigmatism, there is no transverse plane where the phase is uniform across the plane and thus coupling into a single mode fibre is limited. $\endgroup$ – WetSavannaAnimal Dec 5 '14 at 23:10
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    $\begingroup$ @WetSavanna: It looks like such beams are called "asymmetric Gaussian". $\endgroup$ – akhmeteli Dec 6 '14 at 1:48
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Looks like the Astigmatism is measured from the diodes surface as per Stephern Blake's answer. The fast axis divergence is measured from the diodes surfaces and then the astigmatism is the position of the beam source point of the lens behind the diode surface. The fast axis beam waist must be on the diodes surface at Py and the slow axis beam waist at Px. There is an excellent tutorial on laser beam astigmatism and how to correct it found at https://www.coherent.com/downloads/LaserDiodeTechNote1Rev2.pdf

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