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Lasers: WTF is Coherent Light?
A bad textbook diagram, and a widespread misconception
William Beaty 2004

Laser light behaves very differently than light from other sources. Books aimed at kids & the public give two reasons for this:
  1. Laser light is monochromatic or very pure in color.
  2. Laser light is coherent or special "in-phase" light.
What does "coherent" mean?

As a kid I was always confused by explanations of coherent light. I'd been told that coherence had something to do with the sinusoidal shape of photons. Light is supposedly made up of little wiggling string shapes; transverse waves. Textbooks show each photon as a kind of little "snake" moving side to side. And, supposedly, whenever all the "snakes" pack together side by side with their wiggles aligned, that's Coherence. Atoms in a laser are all emitting their light in phase-lock, and the end result is supposedly a special kind of "Inphase Light," where the little sine-waves stack up together, sort of like egg cartons.

But somehow this explanation just wouldn't stick to my brain. It didn't fit with everything else I knew. And worse still, I couldn't use the explanation as a tool. On one hand, the typical explanation of monochromatic laser light was very useful in many situations. Pure color means single frequency, which implies narrow peaks in the spectrum graphs, and tiny spots on the radio dial. "Monochromatic light" connects with audio, where a pure tones such as flute-notes are monochromatic, while an impure broad-spectrum tone sounds like pink noise (or perhaps violins.) And in holography, whenever the frequency of light is moved up and down, I could imagine how this would slide all those tiny diffraction patterns around on my film. That would blur the patterns and make holography impossible, so clearly a hologram camera needs a very monochromatic light source. As a concept, "Monochromatic" works!

So where is the equivalent power in the concept of "coherence?" How do I use those wiggling-snakes to explain many other things? Where do the snakes clarify a radio antenna, a loudspeaker, or water waves? And if my laser isn't coherent enough to make holograms, can I draw a very simple picture of the problem's exact nature? A picture that any kid could understand? No. It just didn't connect.

Well, after a few years in the physics business I did figure it out. Jeeze, I just shoulda known...

That explanation is WRONG.
The explanation of Coherent Light found in most introductory textbooks is pure garbage. It's worse than just wrong. It gave me a mental barrier. It led me directly into misconceptions, and I couldn't go forward until I'd un-learned them again.

To get right down to it, light isn't a transverse wave. Or more specifically, light isn't a "transverse wave in the Aether," instead light is a wave in magnetic and electric fields where the field vectors point sideways. But the flux lines themselves don't wiggle sideways, and the flux doesn't contain any sine-wave shapes. Take a look at the video below left. The animated graph depicts the field strengths along a straight line: strengths when a light wave is passing towards the right. The only sinewave present is found in the pattern of intensity, a sine graph of field strength measurements. That sine wave is not a flux shape in space. The only space involved in the video is a straight-line axis with no wiggles.


 

EM field strengths graphed along a straight line.
*NOT* a plot of flux lines.

The expanding onion: flux lines surrounding a tiny light source.
No wiggling snakes in the field structure.




 

If we could see light and radio waves, might we find any little sinewave-snakes anywhere? Nope. Take a look at the second video above right. It's an animation of flux lines surrounding a very tiny light source. The EM waves expand like layers of an onion. The flux lines break loose from the source, close upon themselves to form loops, then fly off into space. The field strengths of course would form sine waves, if we graphed them as in the first video. But the flux itself points entirely sideways all the time. There is no Aether "medium" which wiggles side-to-side. No little snakes flying through space.

And photons? ...the photons are either dimensionless particles or quantized wave-energy; they're either like infinitely small bullets flying in straight lines, or they're like enormous expanding EM pond-ripples from a thrown pebble. Photons aren't shaped like twisty snakes, they're nothing like a transverse wave on a string.

In other words, the entire crazy "stacked wiggles" explanation of Coherent Light falls apart.

And even more important than all of the above... I realized that the in-phase emissions in lasers don't even create any "in-phase light" in the first place! [It's important enough to say twice: coherent light isn't created by in-phase stimulated emission. That's a big one.] In-phase emissions are important of course. But they only cause light amplification. They create amplified, brighter light.

Whenever atoms in a laser are emitting EM waves in phase with incoming EM waves, the emitted waves add to the incoming light, making it brighter. Two plus two equals four. But amplification doesn't create any "in phase light." If two plus two is four, Four is purely a number, and it isn't concealing any two-plus-two, instead it could be one plus three or nine minus five. I mean, when two waves add together to create an amplified wave, the original waves are gone. The larger wave doesn't forever travel along as two smaller "inphase waves" like all those intro laser explanations depict.

THE BAD DIAGRAM

The laser's in-phase emission also is the basis for transparency of materials. For example, whenever atoms in a glass window absorb light waves, they re-emit those waves in phase, so the original wave is preserved and the material acts transparent. In-phase emission prevents the light from scattering as it interacts with the atoms in the glass. So yes, the atoms in the laser-rod or laser gas tube emit some light in phase... making the laser material transparent, so it preserves whatever coherence that the incoming light might already have have. Those "in phase" textbook laser diagrams are actually, heh, explaining transparency, and they never bothered to tell us how the light became coherent in the first place.

Fig. 1 The bad diagram. Did you learn this one in school? If so,
you may need to un-learn it before you can understand coherence.
Coherent light does not behave anything like this.


If fig. 1 is wrong, then what's right? If we could actually see individual light waves, what would coherent light look like? Fortunately the explanation is quite simple. Take a look at figure 2A below. That's what perfectly coherent light would look like if we could see the waves. Coherent light is simple: it's light which comes from a very small light source. Spatially coherent light has another name: "sphere waves" or "plane waves." Or even simpler: "pinhole light" or "pointsource light."

[tiny dot sends out a bullseye shape of red waves]
[tiny dot sends out a sunburst of red rays]
A. B.

Fig. 2 A tiny light source emits waves and/or particles


A single small light source sends out electromagnetic waves in all directions as shown above. Of course these diagrams are only two-dimensional, while the real situation is 3D. We should imagine a coherent lightwave to be spherical, like layers of an onion, but where the onion is expanding at the speed of light, with new layers constantly added in the center. OR... we could imagine that the tiny light source is sending out a stream of particles flying off in all directions. The paths of these particles are the "rays" of light. Since they all fly outwards from a single point, none of the rays cross each other. And if this light is passed through a converging lens, it's focused to a point.

So coherent light is just "pointsource light?" Paraphrasing Feynman: Now I Understand Evvrrreeeeeeethiiing! Finally it all makes perfect sense: starlight is ULTIMATELY coherent, that's why Stellar Interferometry works: starlight has coherence length in thousands of KM, starlight is far more coherent than any human-made laser light. And the most distant stars are like ideal point sources. Then I suddenly remember Dennis Gabor, inventing holography before lasers existed. To create his pseudo-lasers he just took light from an ordinary mercury-arc lamp and passed it through a pinhole. Mercury's emission line made it nearly monochromatic, and the pinhole gave it the spatial coherence.

Pinhole pinhole, ever hear of an optics device called a "Spatial Filter?" They're used to 'clean up' laser light and make it much more spatially coherent. A Spatial Filter is just a very small pinhole with a lens upstream: any "incoherent" parts of the beam will never make it through the tiny aperture. It restores the point-sourcey-ness to the imperfect laser.

And finally I know why lasers are so wonderful: lasers are pinhole light sources which are ...actually bright! It's easy to make some coherent light, just use a normal light source and an optically small pinhole (a halfwave diameter.) But an aperture this small will block nearly all the light from any conventional source. To experiment with this, get a slide projector and make a slide with a pinhole: an Al foil layer perforated by a needle. Add a narrowband green filter, and that's your Gabor-approved 1940s laser source. Make some holograms? Heh, long exposure-time though.

Fig. 3 SOMEONE GETS IT RIGHT! The above
unattributed diagram found in online archives.

In the distant past, monochromatic coherent sources were also microwatt light sources, no getting around it. Creating coherent light meant throwing away almost all of the power. Sending many milliwatts of light through a wavelength-diameter pinhole was basically impossible. So, all the bizarre and wonderful capabilities of lasers were unreachable. But lasers easily solved the problem by, right at the start, creating some spherewave "pinhole light," as if their entire light output came from a virtual pinhole; a pinhole less than 500nM across. Aha, those confocal/concentric resonator mirrors, the ones used in lasers? This means that the virtual pinhole in an actual laser is just a non-virtual pinhole-image sitting between the mirrors. (See wikipedia diagrams for optical cavities, http://en.wikipedia.org/wiki/Optical_cavity) And all of those Semiconductor Lasers with parallel mirrors: they just employ an "infinite mirror tunnel" to put their pointsource at virtual-infinity distance, where it behaves just like the light from a distant star. During its trip down the infinite tunnel, all the non-planewave light wanders out the side of the tunnel. Only planewave light can persist in the tunnel and get amplified.

Laser coherence is created by the mirror-tunnel. Or in proper terms, created by the laser's cavity, and not by any sidways packing of tiny wiggle-shaped "photons."

And all this means that we have a simple, gut-level intuitive picture of laser coherence. What is it? It's light produced by an infinite mirror-tunnel with amplification. Sort of like those disco mirror infinity things. On each reflection the light passes through the laser medium and gets slightly brighter. Viewed from the end, every deeper segment of the "tunnel" appears slightly brighter ...and the far end of the tunnel looks like an infinitely bright, infinitely tiny star. Stare into the depths of the Amplifying Disco Mirror, and the "star" is small and bright enough to punch a hole right through your retina. And it doesn't even have to be very bright to do this! A hundred-watt incandescent light bulb doesn't slice up your retina, but a quarter-watt laser can burn a tattoo permanently into the back of your eye. "Coherent" can also mean "sharp when focused," since focused Coherent light will all converge to an infinitely small point. (Yeah yeah diffraction limit. We're talking simple idealized geometrical optics here.)

OK, if spatially coherent light looks like an expanding bullseye, then what does INCOHERENT light look like? In the above diagram 2A, incoherence instead would look like bunches of overlapped bullseyes. Lots of interference patterns, and probably with the nodes moving around randomly. Or it would look like bunches of light rays, but where where the rays come from several separate points in fig. 2b, and the rays all cross each other throughout the light beam.

With our gut-level intuitive understanding of laser Coherence, we can now construct a basic list of coherent light sources

Sources in increasing coherence

  • Bright cloudy sky (least spatially coherent)
  • Fluorescent tube lamp
  • Frosted incandescent bulb
  • Sun during clear weather
  • Clear incandescent bulb
  • Clear incandescent bulb w/noncoil filament (aquarium bulb)
  • Electric welding arc 50ft away
  • LED
  • Laser (coherence-leng in mms or few Meters)
  • Starlight (coherence leng 1000s KM)
Note that the list also is a list of DEcreasing source-width, with the cloudy sky at the top and the distant stars at the bottom. A perfect ideal pointsource gives perfectly coherent light, while a wide source gives the least coherent light. Turn the idea backwards: if we start out with perfectly coherent laser light, but then we send it through a frosted screen, the light remains just as monochromatic, but it becomes incoherent. Hey, I noticed that we can actually buy an incoherent-izer, an opto device for our optical bench. They're just a rotating frosted screen with a little motor (since an unmoving frosted screen still leaves a small bit of micro-scale coherence or "laser speckle."

NO JPEG YET

Fig. 4 A frosted screen makes light incoherent.

REAL SOLAR DEATH-RAY

And now I have the answer to a big question that plagued me in childhood. No doubt all nasty little science-boys like me had thought of this one. Why can't I make a death ray light-source? I could just focus sunlight with my big plastic fresnel lens, then somehow collimate it into a half-mm beam. The 0.50mm burning spot would appear anywhere along the parallel beam miles long. Write CHAIRFACE on the freakin' moon! But if you think about this, it turns out to be impossible. Adding extra lenses to your solar furnace just creates a projector, where your parallel solar deathray spreads out and becomes a wide image of the sun. No thin beam is possible unless you include a tenth-micron pinhole in the optical path, and that turns the power into microwatts. The solution to the problem is simple: JUST REPLACE THE SUN WITH A 10KM WHITE DWARF STAR HA HAAAA! Keep the sun's brightness the same, but shrink the sun until it appears in the sky like a tiny star, like an intense pinpoint. Now just use your big lens to gather a square meter of sunlight, focus it down to 1mm, then collimate it with a 1mm water-cooled short-focus quartz lens stolen from an ultraviolet microscope. Yes, the whole device is still a projector, but if you project the image of a pointsource into the distance, the result is an intense collimated beam. Other than a bit of diffraction it should work great: a few hundred watts in a parallel CW beam 1mm wide. Slice-a offs you fingas! Winston Kock, one of the early laser people at Bell Labs, said that laser light is "sharper light" which can be used as a cutting tool. Exactly, exactly! Winston Kock actually gets it.

But the central concept actually is that coherence or "pinhole light" is the whole reason for the "sharp light" that does the laser cutting. If our sun was 10KM wide, or reduced to 10^5 times smaller in visual angle, then its light would be spatially coherent like lasers, or like an electric welding arc, and glancing upwards during the day might slice grooves across our retinas. The lens of your eye will focus the white-dwarf sunlight to a pinpoint rather than to a dim and safe little solar disk on your retina. Only because sunlight is non-parallel, because our sun is an extended source, the 1.5 KWatt/m^2 sunlight doesn't act like dangerous laser light. Hmmm, hold on a sec. If sunlight is about 1500 watts per square meter, and your eye's pupil is about 1mm, then your pupil intercepts 1500W/.001^2 = 1.5mW. DOH! WRONG! OK, staring at white-dwarf sunlight would actually be just like staring into a cheap laser pointer. Those things don't become dangerous to human eyes until up around 5mW. AHA, but using binoculars would be lethally dangerous to your eyesight: 5000X smaller exit aperture, creating an eight watt parallel beam 1mm in diameter. Binoculars become like icepicks aimed at your eyeballs. Coherent light can be nasty.

 



 
SEE ALSO:

Common Laser Misconceptions







http://amasci.com/miscon/coherenc.html
Created and maintained by Bill Beaty. Mail me at: .