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Diffraction through an aperture gives a half-angle divergence of $1.22\lambda/a$ where a is the aperture diameter. The half-angle divergence of a Gaussian beam is $\lambda/\pi w_0$ where $w_0$ is the $1/e^2$ beam waist.

Are the output aperture of a laser and the beam waist the same things in this instance, ie $a=w_0$? Then why don't the two expressions for divergence equate, ie $1.22 \ne 1/\pi$

Can you equate the two half-angle equations to get the $1/e^2$ beam waist: $w_0=a/1.22\pi$

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  • $\begingroup$ @coc333: beam divergence for a laser is usually a measured quantity. $\endgroup$ – Peter Diehr May 6 '16 at 22:09
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The diameter of the output aperture of a laser is not necessarily the same as the Gaussian beam waist, the latter is typically less than the former, as otherwise you won't get a Gaussian beam.

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  • $\begingroup$ Say I have a lens some distance after the laser output coupler. How would I use the lens equation for a Gaussian beam only knowing the beam divergence and size of the output coupler? This equation is a function of beam waist and distance from the waist, which I don't know. $\endgroup$ – cpc333 May 8 '16 at 16:05
  • $\begingroup$ @cpc333: You should look at the laser's specs, but the laser's output mirror is often flat, as far as I know, so the waist is where the output mirror is. I guess your "output coupler" is the same as output mirror, but I am not sure. $\endgroup$ – akhmeteli May 8 '16 at 17:08
  • $\begingroup$ I'm trying to get the waist radius from the manufacturer, but I'm not sure they've measured this! They did mention the waist location should be at the output aperture. My two mirrors are flat. I know the size of the output aperture. Is there an equation to get the waist radius from that information? $\endgroup$ – cpc333 May 9 '16 at 18:57
  • $\begingroup$ @cpc333: I doubt it. And it looks strange to me that both mirrors are flat (do you mean the mirrors at both ends of the laser?). You can calculate the waist if you know the angular divergence of the beam. You can also determine the waist experimentally, if you have appropriate instruments. $\endgroup$ – akhmeteli May 10 '16 at 0:27

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