Built on Facts

Shoving Sand

It’s a pretty nice time for quantum optics and laser physics at Texas A&M, with us moving into a brand new lab and acquiring several new laser systems. One of the systems we’re moving isn’t new (we’ve had it for a few years, and the technology is considerably older), but we’re about to put it to work on a new project. It’s a relatively high-power Nd:YAG laser.

The operating parameters are about 2.5 joules per pulse, with 10 pulses per second for an average power of 25 watts. Each pulse is about 8 nanoseconds long. This is a rather hefty amount of light. Though any Class 4 laser requires serious attention to safety, we’re going to treat this one pretty much like a nuclear reactor when it’s running.

Now as you may know, light carries momentum and can exert pressure on surfaces that it hits. This is true even in the purely classical field theory of Maxwell. But as a rule we don’t notice light pressure because it’s so slight. I’m a little curious as to whether it might be significant in a laser this intense. Let’s run the numbers and see what happens.

First, let’s review some definitions. Power is measured in watts, and it’s the number of joules per second. We’ll label it with a capital P. Pressure is force per area, and we’ll label it with a lower-case p. Intensity is what you might colloquially think of as the brightness, and it’s just the power per area, and we’ll use capital I for it. The relationship between light pressure and light intensity is given by:


Where c is as usual the speed of light. Now if pressure is force per area and intensity is power per area, than the force will be given by the total power divided by c:


These are just two ways of saying the same thing. We’ll start with the second one. 25 watts divided by the speed of light is: 8.34 x 10-8 N. Very slight, as you might expect because 25 watts isn’t actually much power. It’s just a lot for a laser because it’s kept in a very tight beam. But this is a laser and the beam is very tight. It can be focused on something very small. What if we focused the laser on a grain of sand? To simplify the math, say it’s a tiny cubic crystal of sand with each side having a length of 0.25mm. Sand is frequently quartz, which has a density of about 2.6 grams per cubic centimeter. As such the grain of sand has a mass of around 40 micrograms. Force is mass*acceleration, so the acceleration the grain will be about 2.05 m/s^2. This is quite a bit, certainly enough to send it sliding across the table.

Well, unless we blow it to smithereens. Remember that 25 watts is an average. The instantaneous power during the pulse is actually about 2.5 joules / 8 nanoseconds, which is about 312 million watts. Focused onto that (0.25 mm)^2 cross section, that’s an intensity of 5 x 1013 watts per square meter. Yikes, that’s about 50 billion times more intense than direct sunlight. The pressure works out to be relatively modest – I think around 25 PSI (167 kPa) – so I’m not sure mechanical stress will break up our sand grain. However, the light that’s absorbed might be enough to melt it, especially with repeated pulses. I’m not sure what the absorbance of sand is at 1063/532nm wavelengths.

Sadly I’m pretty sure I won’t be allowed to try this experiment to find out. Frankly I think my self-preservation instinct might veto my “Holy cow, lasers!” instinct anyway. Still, it’s tempting…

BLOGGY NEWS: I will be spending the next two weeks in the scenic but very small town of Casper, WY at a quantum optics / laser physics conference/school being held by our own no-kidding legendary Marlan Scully. There’s a decent bit of downtime involved, and supposedly the place is quite scenic. As such I hope to be doing a bit of a travelogue, with summaries of some of the talks and pictures of the landscape. At any rate it can’t possibly be any hotter than College Station is!


  1. #1 Bill
    July 15, 2010

    I’d be more curious about the recoil from a surface layer vaporizing than liquefying. It’s not the NIF but similar idea.

  2. #2 Anonymous Coward
    July 15, 2010

    What #1 said.

    With that kind of laser intensity, you’ll get ablation at the surface of the sand.

    You’ll get the formation of the plasma at the surface and, consequently, a relatively small “skin depth” for the light going into the sand grain. This will eject a bunch of mass from the surface, giving a impulse to the remaining part of the grain that’s a lot larger than the impulse of the light pulse.

    This is assuming that the focus is loose enough that it doesn’t break down the air before it gets to the sand grain.

  3. #3 tcmJOE
    July 15, 2010

    Very small town? Casper is our second biggest city! (Yeah, Wyoming is sparsely populated. But to think of it another way, Casper’s population is approximately 1 TAMU.)

    I can’t say there’s anything of major interest in Casper itself (though I haven’t been for years) but take every chance you can get to go out hiking–the mountains in Wyoming are generally excellent.

  4. #4 Nathan Myers
    July 15, 2010

    Won’t do the experiment?! You owe it to us. It needs to be on Youtube. I’ve never seen pure light pressure on a macroscopic object produce visible motion (aside from a Crookes radiometer being pushed around by hot air).

    Let me suggest you use a round mirror-surfaced bead rather than sand, to avoid explosions and focused reflections, and to encourage accumulated momentum. Maybe a 5W laser would suffice to boost the speck in rehearsal before you blast it with 25W.

  5. Casper is a great city for this experiment. I do think that if you liquefy the surface layer it will vaporize in due time.

  6. #6 Uncle Al
    July 16, 2010

    Quartz is exceptionally transparent in the visible. If light passes through there will be no thrust – except from the ~10% reflected normal to the impedance-mismatched interface, quartz vs. vacuum (you are doing this in hard vacuum, right? Optically levitate the target to eliminate stiction).

    The simple solution is a dielectric mirror on the intercepting quartz surface. You get twice the thrust with none of the heating. A real man would blast it with circularly polarized light to set it spinning as well as translating.

    Calculate the acceleration. Zounds.

  7. #7 Peter
    July 18, 2010

    You looked at the force generated by the pressure of the photons hitting the sand grain. Clearly a low efficiency way to transfer the 2.5 joules per pulse to the grain! Ablation might do better – does this laser have enough power to ablate the surface? Ablation would be effectively a tiny rocket engine with the impulse determined by the mass and velocity of the ejected (ablated) material.

    What other options could one investigate for converting the laser pulse energy to kinectic energy of the particle? At 100% effieciency 1/2mv^2 = 2.5J – a single pulse would give v = 350m/s or about mach 1 if my math is accurate. Even at a very low efficiency repeated pulses should be able to get our sand grain moving along.

    Absortion of the light on the surface of the grain should heat the air the air just behind the grain creating a pressure rise. Can we generate a 10 hertz theromoacoustic pressure wave to push our grain along?

    Do lasers like this move dust motes floating in the air of the beam path (or are they operated only in vacuum?)

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