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For various reasons, I have a HeNe laser setup with two external spherical mirrors that I can position and align at will. I've looked around at various sources, which all make mention of which optical resonator configurations give "decent" or "improved" mode volume and the relative amounts of diffraction losses, but am having trouble nailing down which would ideally give the best output power (I know, it's related to mode volume). I'm pretty confident, based on what I've read, that the spherical cavity configuration would produce lower power outputs, but I can't figure out which of the confocal or the long-radius configurations is better for output power.

So let's keep everything else fixed. Can't change the mirror properties, input power, tube length, etc. Let's also say I don't care about which TEM mode is output nor how hard it is to align the laser. Given this, which optical resonator configuration using two spherical mirrors is better for maximizing output power? Which gives the most bang for your buck? And what are the limitations of this configuration?

For reference, Sam's Laser FAQ - an amazing reference for all things laser - gives a great illustration of many of the common types of configurations ($r$ refers to the radius of curvature of the mirror):

enter image description here

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  • $\begingroup$ I don't know if this is possible: can a HeNe laser be used as q-switched? (if yes it could help to get higher power pulses). CO2 lasers are used in in q-switching, they are inhomogeneously broaden gas lasers, so at least the broadening does not seem a fundamental limitation of HeNe. But I cannot find any info about this, so it's probably unpractical for some reason. $\endgroup$
    – scrx2
    Sep 4, 2017 at 20:09
  • $\begingroup$ @scrx2 I'm just using this as a CW laser. No pulsing $\endgroup$
    – Jim
    Sep 8, 2017 at 12:35
  • $\begingroup$ I don’t know that output power is fundamentally limited (or even much affected by in high power regimes?) by the cavity geometry. My guess is that output power is often, instead, limited by properties of the gain medium and gain pumping mechanisms… $\endgroup$
    – Jagerber48
    Jul 31, 2021 at 0:37
  • $\begingroup$ Maybe you could show a diagram of your setup. Is the HeNe a standalone laser or have you built your own gain medium and pumping system and you’ve put a cavity around it for lasing? $\endgroup$
    – Jagerber48
    Jul 31, 2021 at 0:44
  • $\begingroup$ @Jagerber48 The latter. Gas tube is independent of the cavity. Brewster windows on both ends. Two adjustable spherical mirrors $\endgroup$
    – Jim
    Aug 4, 2021 at 12:26

2 Answers 2

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The design of optical resonator cavities is a fairly comprehensive topic that is not easily covered in such an answer. Books have been written on the topic [For instance: A. E. Siegman, Lasers, University Science Books, Mill Valley, CA (1986); and N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd edn., Springer, Berlin (2005).]

However, perhaps one principle to keep in mind, if you want to maximize the power output, given certain constraints, is that you want to maximize the region inside the active medium that is occupied by the beam/mode.

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  • $\begingroup$ it's true that I want to maximize the mode volume, which might naively make one assume that, all other things constant, the long-radius configuration would produce the maximal power output compared to the confocal configuration. However, the long-radius has greater diffraction losses than confocal, which might tip the balance. None of the many sources I have read have weighed in on output power in ideal conditions, which is why I want to try to fix as many variables as I can and ask the experts here. $\endgroup$
    – Jim
    Sep 8, 2017 at 12:17
  • $\begingroup$ Of course, if the naive answer is the correct answer, I'm also interested in the extent of that. That is, if long radius is the most power-friendly (even if it is harder to align and has high diffraction losses), then is it increasingly effective as the mirror separation becomes ever shorter than the ROC of the mirrors (obviously to the limit of the tube length), or is there some sort of ideal ratio of ROC to separation? $\endgroup$
    – Jim
    Sep 8, 2017 at 12:20
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    $\begingroup$ It completely depends on the situation, the most important factor will depend on the materials, the input and output wavelengths required. Generally it is an optimisation problem between thermal lensing and gain overlap, but that is just generally (i.e. smaller spot =/= more power). $\endgroup$
    – MJC
    Mar 11, 2019 at 14:21
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For a symmetric cavity (mode waist is largest for a confocal cavity, $R=L$. Mode volume then increases with length. But my guess is that you want the photons to spend more time in the gain medium so, unless you extend the gain medium, my guess is you don’t win for increasing length.

So that is the gain medium should entirely fill the cavity. You probably do better with more uniform mode weight so confocal is the best there again.

Id guess you get more power with a bigger gain medium but I’m sure something g limits that at some point. I’m not sure what.

I’ll post references for how to calculate cavity properties from mirror geometries and properties later.

Disclaimer: as you can see this is a lot of guesses. I’m not a laser engineer, but I do have experience with optical cavities.

*I think if you get the laser up to high enough power that you can saturate the atomic transitions even with a fraction of the circulating cavity light then second constraint will stop being relevant. This condition would be reached if the losses with the cavity round trip become small compared to the gain from the gain medium


edit: With input from the OP I can give some more info now. The OP tells us that the geometry of the gas tube is fixed with radius $R_0$ and length $L_0$.

My hypothesis is that you will get the most power (as a function of cavity geometry) when the geometry of the cavity mode closely matches that of the gas tube. That is, 1) you want the light to be hitting as many He and Ne atoms as possible but 2) you don't want the light spending time where there aren't He and Ne atoms because then you won't be saturating the atomic transitions as strongly as possible.*

The formula for the waist of the cavity mode, $w_0$, and the waists on the mirror surfaces, $w_{\text{mir}}$ in terms of mirror radius $R_1=R_2=R$ and $L$, are given by

\begin{align} w_0^2 =& \frac{\lambda}{2\pi} \sqrt{2R-L}\sqrt{L}\\ w_{\text{mir}} =& w_0 \sqrt{\frac{2R}{2R-L}} \end{align}

We want a roughly cylindrical beam since the gas tube is cylindrical. This means, from the second equation, that we want $R\gg L$ so that $w_{\text{mir}} \approx w_0$. In this case the first equation can be approximated as

$$ w_0^2 \approx \frac{\lambda}{2\pi}\sqrt{2RL} $$

From this you could estimate an optimarl $R$ such that $w_0 \approx R_0$ to make sure you use the whole gas cylinder but don't waste power outside the cylinder.

The equations above are either given directly or can be derived from equations in Siegmann's Lasers textbook.

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  • $\begingroup$ I find, experimentally, that the long radius configuration gives the highest power output. Probably because it has a larger mode volume than the confocal. This is all well and good but I'd like an explanation more sound than "trial and error". I also find it more difficult to achieve a TEM00 mode with the long radius, whereas it's easy with the confocal and presumably even easier with the spherical. There are probably other benefits and drawbacks too $\endgroup$
    – Jim
    Aug 4, 2021 at 12:32
  • $\begingroup$ yes, what you see matches with my intuition that you want a "cylindrical" beam that doesn't have any sort of tight focus. I think the first part of my answer where I suggest confocal might give you this condition might be incorrect. I think it's correct that near-planar will give you the most cylindrical beam. $\endgroup$
    – Jagerber48
    Aug 4, 2021 at 17:35
  • $\begingroup$ Regarding alignment difficulty: That is a different question entirely. I leave discussions of that out because in the question you said to assume alignment was not a problem. But yes, I am not surprised that it is hard to align the near-planar cavity. That is expected. Confocal is the easiest to align. Near concentric (or near-spherical) is difficult to align. In some ways "equally" as difficult as near-planar. This is one reason confocal geometries are sometimes prefered. $\endgroup$
    – Jagerber48
    Aug 4, 2021 at 17:36

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