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Lasers in SF, Part I: Did James really need to fear for his junk?

January 26, 2012
Note: this post is the first in a series about lasers in science fiction that I’m writing in preparation for a talk at Madison NerdNite on February 22.  If you have any suggestions on improving these posts before I give the talk, feedback is much appreciated! ~J
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When my brother was about ten years old, he went through a James Bond phase.  We watched nearly every Bond movie ever made, and until recently, I thought I’d seen the entire Bond canon.  But I realized a few years ago that I somehow missed Goldfinger.

So, I rented it.  And, being a laser jock, there was one particular scene that caught my eye.

If you’ve seen the movie, I’m sure you know which scene I’m talking about. 007 is strapped to a solid gold table, legs spread, and there’s a scary-looking laser burning slowly up toward his crotch.  Bond looks a little panicked, and justifiably so – he knows that if that laser reaches its target, there’s no way he’s going to be able to shag Pussy Galore at the end of the movie.  That, and, you know, it might kill him.

Laser cutters are used in industrial settings all the time, but not usually for cutting through a piece of gold more than an inch thick in order to kill a spy.  So, the question is, could a laser really do this?  Does James really need to fear for his junk?

To answer this, we need to know a little bit about how laser cutting works.  Metals are usually cut using a process called “fusion cutting.”  In fusion cutting, the laser beam heats up the metal and melts it.  Then, high-pressure air pushes the molten metal out of the way, leaving a clean cut.

This process takes a lot of energy, especially if you want to cut through a very thick piece of material like the table Bond is lying on.  Cutting through a one-inch-thick piece of steel requires a tightly-focused laser with a power output of about 5 kilowatts (see here, here, here, and here).  Remember that power is a measure of how much energy something supplies in a given amount of time: a 5 kW laser delivers 5 kilojoules (kJ) of energy in one second, about the same amount of energy as is released by the explosion of a gram of TNT.

Note that I said it has to be a tightly-focused laser with a power output of 5 kW.  This is actually really important.  Melting a certain amount of metal takes a certain amount of energy.  If the laser beam is tightly focused, then it hits a very small part of the metal surface, and we can dump all of the laser’s energy into melting that very small bit of metal.

But, if the laser beam is loosely focused, then it spreads out over much more of the surface, and now we’re trying to use the same amount of energy to melt a much larger amount of metal.  If the spot size is too large, then the whole surface under the laser beam heats up but no one part gets hot enough to melt.  So here’s rule #1 that you should know about lasers:

The larger the spot size, the lower the power density (or power per unit area).
If you want to get technical, the power density is inversely proportional to the beam area, or inversely proportional to the beam radius squared.

Theoretically, the smallest spot you can focus a laser to is about the same size as the wavelength of the laser light.  Carbon dioxide lasers, which are used in most industrial laser cutters, have a wavelength of 10.6 um (about a hundredth of a millimeter), so around 0.01 mm is the smallest diameter you can possibly focus one of these lasers to.

Usually, however, you can’t get lenses good enough to actually focus the beam this small.  And in industrial laser cutters, the lens needs to be several inches from the metal surface, because otherwise, molten metal can splash back and damage the lens.  This further limits the smallest spot size you can get, and brings us to rule #2 about lasers:

The longer the focal length, the larger the spot size.
More precisely, the beam size at the focus increases roughly linearly with the focal length, though this isn’t strictly true for very short focal lengths.

For a 10.6 um laser focused through a lens 4 inches from the surface, the smallest spot size you can get on the surface is about 0.2 mm diameter (there are good explanations here and here).  This means that the cut width is also about that narrow.  Here’s a video of an industrial laser cutter at work – note how close the nozzle is to the surface, and how narrow the cuts are:

Goldfinger, however, has a MUCH larger spot size.  He’s focusing the laser from at least a meter away, so the smallest spot size he should be able to get is about 2 or 3 mm in diameter.  However, from the video, it looks like the diameter is more like a quarter of an inch, so he’s probably not focusing it as tightly as he could.

At any rate, if Goldfinger’s beam has a diameter of a quarter of an inch, that’s about 25 times the diameter of the 0.2 mm beam in an industrial laser cutter.  In terms of area, his beam is 25^2 or 625 times larger.

That means that the power density (power per unit area) is 625 times smaller.  So, if it takes a 5 kW laser to cut through an inch of steel when the beam is focused to 0.2 mm, then when the beam is focused to a half-inch diameter, it should take a laser with 625 times as much power to cut through the same inch of steel.  This means that Goldfinger needs a laser that can deliver at least 3000 kW of power, or 3 megawatts (MW).(*)

And as it turns out, that’s actually not unreasonable.  Carbon dioxide lasers can’t usually generate that much power, but other types of lasers can.  For example, chemical lasers like deuterium-fluoride lasers and oxygen-iodine lasers, which get their energy from a chemical reaction, can put out a few megawatts of power, and have been developed for various military purposes (see these news articles, for example).

So, lasers (almost) this powerful do in fact exist.  And since I assume that Goldfinger has enough money to buy any laser he wants?  Bond might actually be in a bit of trouble!

(*) This is a really rough approximation, because we’ve ignored a lot of other factors that are important in laser cutting.  For example, we haven’t dealt with the fact that the table is gold rather than steel, and we haven’t taken heat conduction into account.  However, we’re just after an order-of-magnitude estimate here, so this number seems like a good place to start.

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3 Comments
  1. Awesome post! I don’t really understand the whole “focal length” issue though. I read the wikipedia description of focal length, but don’t really understand what that is or why/how it relates to laser spot size. Any help would be appreciated. 🙂

    • Ah! Yes, the wikipedia page on focal length doesn’t really talk about this issue. But we can use it as a jumping off point. Remember that the focal length of a lens tells you how far away the focus will be from the lens. A lens with a short focal length will focus the beam very close to the lens, so the beam diameter decreases really quickly as you move away from the lens. A lens with a long focal length will focus the beam farther away from the lens, and the beam diameter decreases more slowly.

      In optics, it’s easier to talk about what happens as we move away from the focus. After the focus, the beam basically reverses what happened before the focus, and starts expanding again. For the beam that was focused with a short focal length lens, the diameter increases quickly. In optics, we’d say that it “diverges” quickly. For the beam that was focused with the long focal length lens, the diameter will increase (or diverge) more slowly.

      Now, why does this relate to how big the diameter is at the focus? This is actually kind of a tricky issue, because the answer has a lot to do with how light propagates.

      Light is a wave. If you force a wave to come from a very small point source, it expands in all directions. But if you create a wave from a larger source, it can have a more defined direction. Think about dropping a pebble in a lake: if you drop a single pebble in, you see circular waves expanding out in all directions. If you dropped a line of pebbles in the lake all at the same time, however, you might see a curved rings coming from the end of your line of pebbles, but in the middle you’d see a straight line. This is because of the way that the waves coming from the different pebbles interfere with each other.

      This is tied directly to how quickly the beam size changes as you move away from the focus. I think it’s easiest to see this by playing with it. In the image below, I used a ripple tank simulator (available here) to show what happens when you have a wave coming from a single source (left), a small line of sources (middle) and a larger line of sources (right).

      Ripple Tank Divergence

      As you can see, the wave on the left has no direction. It radiates equally in all directions. The wave in the middle starts to have a well-defined direction, but because the source is still pretty small, it still behaves a little like the single point source and the width increases (diverges) quickly. The wave on the right, on the other hand, comes from a wider line of sources and diverges much more slowly. This is all because of the way the waves interfere with each other.

      So, bringing this back to optics, a beam with a small spot size will diverge really quickly. Conversely, a short lens (which causes the beam diameter to decrease quickly) will create a small spot size. A beam with a larger spot size will diverge much more slowly, so a long focal length lens (which causes the beam diameter to decrease slowly) will create a large spot size.

      Anyway, this is a pretty tricky concept, and one that I sometimes still struggle to understand even though I work with this stuff every day! But I hope that helps a little. Let me know if you’re still confused 🙂

      • Awesome! That is super tricky indeed. Thanks for the explanation. I still find it really hard to wrap my mind around anything to do with light or electrons, but am a little bit closer now. Thanks!

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