I am no scientist … even after googling I am not sure if a parallel laser is even possible, let alone commercially available.
To be specific, assuming that the beam starts off at say 10mm wide as it leaves the lens, what is the minimum diameter the spot could be after 6 miles , assuming the beam is generated by the most powerful, high-quality laser generator that could be manufactured?
I did gather from Google that a green laser can make a beam nearer to parallel than a red laser for some reason, so let’s assume a green laser.
The minimum divergence angle for a laser is somewhere around λ/πr. Green light is ~510 nm, and you specified 10 mm diameter, so that comes to 3.3e-5 radians. Over 9600 meters, that’s ~320 mm, or 330 mm when you include the original width.
Well, 10 mm is a pretty big beam. I’m sure lasers like that exist, but I don’t know of any.
Here’s a pretty nice green lab-grade diode laser. It claims a beam divergence of <0.5 mrad. By the formula above (using the smaller beam diameter of 2.3 mm and slightly different wavelength), the minimum divergence is about 0.150 mrad. So, it seems reasonable that you can get within a factor of 3 from the minimum.
That unit would have a beam width of 5 meters at 6 miles. You do a lot better if your starting diameter is higher. But that implies a very high power laser, and those get expensive (and rare) fast.
There are several facilities that do lunar ranging, but one of them is the APOLLO operation. They use a Leopard model from Continuum Lasers, which has a divergence of <0.4 mrad (just a tad better than the model I linked to). But they get an effectively lower divergence due to sending the beam through a 3.5 meter scope.
When I was in grad school I worked with a copper vapor laser that had a beam diameter of one inch (25.4 mm). Yes, it was big: 20 watts output (about 2000W input; it warmed the lab up pretty good), the laser head itself was about six feet long with a separate power supply unit on the floor.
With flat optics at the ends of the lasing chamber the beam divergence was pretty crappy (don’t remember exactly how crappy), but with curved optics, the spec was 0.4mrad, at which point it became suitable for manipulating into light sheets for flow visualization.
In answer to Bones Daleys question about commercial availability - yes, but you’ll need to come up with about $75K.
I haven’t said anything, because I figured that the question was effectively answered early on, and I didn’t see any point to saying “me, too”. But I would like to add a few comments:
1.) The formula Dr. Strangelove gives is for the lowest-order TEM[sub]00[/sub] mode, which has the lowest divergence. That makjes it appropriate for answering, since if you want the smallest divergence, you arrange to have your laser operating in that condition. But it’s worth pointing out that a laser doesn’t necessarily operate in TEM[sub]00[/sub] mode, and that a random laser might be operating in a combination of modes (or, arguably, it might not even be a proper “laser” at all, and not be in any mode).
2.) For a TEM[sub]00[/sub] mode, once you know the wavelength and the size of the beam waist (the narrowest point of the beam), you know how the beam varies with distance from the waist. The shapes of the lines of equal relative intensity form a family of hyperbolas, not varying very much over a region called the confocal parameter (also equal to twice the Rayleigh Range). In this range, the beam is approximately “parallel”. Beyond it, the beam is clearly expanding, and the limiting value is that divergence Strangelove cited. (It’s important to note that the value he gives is the angle between the curve of constant relative power and the beam axis – the actual full angle of the beam is twice as large). See here for the gory details:
3.) You can transform the beam waist to a different value by putting it through a beam-expanding telescope (as Strangelove points out), or even through a single lens. The larger the beam waist, the smaller the divergence. In a perfect world, you could get the divergence as low as you want simply by “blowing up” the waist bigger and bigger.
4.) Lasers with huge beam waists – even before being transformed by a lens or telescope – certainly exist. I’ve worked in a facility with a laser big enough to walk through, and have handled laser mirrors and windows measuring a couple of feet in diameter. The beams, though, generally aren’t any clear laser mode, and not TEM[sub]00[/sub]
5.) We don’t live in an ideal world, sadly (or not, depending on how you look at it), and all sorts of things can perturb your perfect TEM[sub]00[/sub] beam from perfection. It probably wasn’t perfect to start with – asymmetries in your lasing medium, local heating, imperfections in your windows or mirrors, and a zillion other things will keep your beam away from that aethereal ideal. Then “blowing it up” even with a single lens will subject you to the imperfections in the lens and its orientatioin. (If you use a telescope, things are worse – there are twice as many lenses to go wrong, plus you have to have them perfectly aligned). Even if all things were perfect, however, there’s a limit to how large you can practically make optics that you can use to transform the beam. The Gran Canario telescope mirror is about 10 meters in diameter. Good luck getting a single mirror bigger than that:
6.) And that’s BEFORE you start propagating through the atmosphere, with all its thermal gradient problems and thermal blooming. Better to move the whole enterprise out into space.
7.) That said, I have no idea what the World Record for Lowest Diverging Beam ever created is. A quick search failed to find any contenders, but I’m sure someone will find an answer.
I thought I just implied that in my previous entry, with “parallel” I n quotes. The lines of equal relative intensity (for example – 1/2 of the intensity of the on-axis light) are hyperbolae that aren’t really straight or parallel, but can be regarded as approximately straight and parallel within the RAyleigh Range, for practical purposes.
Laser light is generally referred to as “collimated.” So the OP’s question could be rephrased as " how close to perfectly collimated can a laser beam be?"
As a cute add-on to this discussion, the relationship between the laser beam diameter and the angular divergence can be thought of as a consequence of the Heisenberg uncertainty principle. The smaller the beam diameter is (at a particular point), the more certain you are about the positions of the photons in the beam; and so the less certain you can be about their momentum, which means that the photons will spread out as they travel “downstream”.
Or alternately, you can look at the other way, and derive the divergence from principles of wave propagation, and then take the Heisenberg uncertainty principle as a special case of those wave principles, as applied to quantum mechanical waves.
To expand a bit on this one:
TEMxy refers to the transverse mode of the beam. This how one describes how a cross-section of the beam changers with time.
Drum heads are a close physical analogy. Imagine a simple round drum, and give it a tap in the middle. The entire surface will move up and down with respect to time at the natural frequency of the drum. This is basically the same as the TEM[sub]00[/sub] mode for a laser.
There are other modes, however. If you tap the left side of the drum, it’s possible to get it vibrating such that when the left side is up, the right side is down, or vice versa. This is the TEM[sub]01[/sub] mode.
Or, it’s possible to get rings on the drum moving in opposite directions. Imagine a gun target such that the red rings are moving up while the white circles are moving down. These are the TEM[sub]10[/sub], TEM[sub]20[/sub], etc. modes.
Wikipedia has a nice picture of some of the modes. The black areas are where there’s zero amplitude (on the transition between areas with opposite phase).
Thanks for all replies so far … I was actually aware of the term “collimated” , but refrained from using it in the OP lest it should imply a familiarity with the subject which I certainly do not possess.
I might as well explain why I asked the question in the first place … a few days ago, somebody mentioned the " flat earth society " in conversation. I had heard of such a group before, but had always assumed that this was some kind of semi-serious organization , much like the Apostrophe Preservation Society .
Lo and behold , I was amazed to discover that there are thousands of people out there who actually *do *believe the earth is flat. My first thought was that the way to prove to these unfortunates the error of their beliefs would be to take a laser and shine it across an expanse of still water, recording accurate heights from the surface of the water at intervals.
I further discovered that there have in fact been a few experiments along these lines, involving theodolites and other surveying paraphernalia, but as far as I am aware, nobody has done it with a laser beam.
I am of course assuming that the light from the laser does in fact travel in a straight line, and doesn’t get refracted, or curved by gravity or any other impediment …
I think you’ll find that if you present such an experiment to a flat Earther, they will latch on to refraction or some other second-order effect, and plug in numbers until they fuck up the calculation in precisely the right way to cancel the Earth’s actual curvature, and finally claim that your experiment proved that Earth is flat after all.
Even weirder is the case of Crus Teed and his Koreshan Society, which was convinced that we live inside a hollow sphere – an ai bubble in a universe of drt – and that thesun and a sphere of stars orbit near the center of the bbble. They reportedly did xperiments along a long, straightcanal,and proved that a line hat started parallel to the surface of th earthnd level, ut a few feet high, would eventually plunge down int the eath – proving that the surface of the earth is *cocave[/], not flat, and not covex
Sort of “beyond flat”.
