Lasers: What is Coherence?
A bad textbook diagram, and a widespread misconception
William Beaty 2004
Laser light behaves very differently than light from other sources. Textbooks give two reasons for this:
JUST STARTED, VERY UNDER CONSTRUCTIONAs a kid I was always confused by explanations of laser coherence. I'd been told that coherence something to do with the sinusoidal shape of photons. Light is transverse waves, so we should imagine that photons are like little wiggling snakes. Whenever all the "snakes" pack together side by side with their wiggles aligned, that's "coherence." The atoms in a laser are all emitting their light in locked phase, and the end result is supposedly special kind of in-phase light where the little sine-waves stack together 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 explanation of "monochromatic" was
very useful in many situations. Pure color means single frequency, which
implies narrow peaks in spectrum graphs and tiny spots on the radio dial.
It connects with audio, where a pure tone such as the note from a flute is
"monochromatic," while an impure broad-spectrum tone sounds like pink
noise. And in holography, whenever the frequency of light moved up and
down, I could imagine how this would slide the tiny diffraction patterns
around on your film and make holography impossible. Clearly a hologram
camera needs a very monochromatic light source.
On the other hand, how do I use those wiggling-snake photons to explain
other things? Where does "coherent light" fit into radio antennas,
loudspeakers and water waves? And if my laser isn't coherent enough to
make holograms, can I draw a picture of the exact nature of the problem?
It just didn't connect.
Well, after a few years in the physics business I finally figured it out. I just shoulda known...
That explanation is WRONG.The explanation of coherence found in most introductory textbooks is pure garbage. Light is not a transverse wave. Or more specifically, it's not a "transverse wave in the Ether," instead it's a wave in magnetic and electric fields where the field vectors point sideways. There are no little lines which wiggle side-to-side. Photons are either particles or waves; they're either like tiny bullets flying in straight lines, or they're like expanding pond ripples from a thrown pebble. A photon isn't shaped like a wiggling snake or like a transverse wave on a string. The "stacked wiggles" explanation falls apart.
And most important of all... I learned that in-phase emission does not
create "in-phase light." [It's important enough to say twice: coherent
light isn't created by in-phase stimulated emittion!] Instead, in-phase
emission only causes light amplification. It creates amplified,
brighter light. When atoms in a laser are emitting EM waves in phase with
incoming EM waves, the emitted wave combine with the incoming light, making it
brighter. But amplification doesn't cause the coherence.
In-phase emission is also the basis for transparency of materials.
For example, when atoms in a glass window absorb light waves, they re-emit
those waves in phase, and the original wave is preserved. In-phase
emission keeps the wave from scattering as it interacts with the atoms in
the glass. The atoms in the laser rod or gas tube emit light in phase...
making the material transparent, so it preserves whatever coherence that
the light might already have. Those "in phase" diagrams are actually
explaining transparency, and they never tell us how the light became
coherent in the first place.
If figure 1 is wrong, then what's right? If we could 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 looks like. Coherent light comes from a very
small light source. Coherent light has another name: "sphere waves" or
A single small light source sends out electromagnetic waves in all
directions as shown above. Of course this diagram is only
two-dimensional, while the real situation is 3D. We should imagine a
lightwave to be spherical, like layers of an onion, but where the onion is
expanding at the speed of light, with more layers added in the middle.
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 passed through a converging
lens, they focus to a point.
So coherent light is just "pointsource light?" Paraphrasing Feynman: Now
Understand Evvrrreeeeeeethiiing! Finally it all makes perfect sense:
coherent, that's why Stellar Interferometry works: coherence length in
hundreds of KM, starlight is far more coherent than any human-produced
And stars are like the ultimate point sources. Then remember Dennis
inventing holography before lasers existed: to create pseudo-lasers he
light from a mercury source and passed it through a pinhole. The mercury
emission line made it monochromatic, and the pinhole gave it the spatial
coherence. Pinhole pinhole, ever hear of 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 aperture.
And finally I know why lasers are so wonderful: lasers are pinhole light
sources which are actually bright! It's easy to make coherent light, just
use an optically small pinhole (a halfwave diameter.) But an aperture this
small will block nearly all the light from a conventional source. To
experiment with this, get a slide projector and make a slide with a
pinhole, a needle-perforated foil layer. Add a narrow green filter, and
that's your 1940s laser source. In the past, monochromatic coherent
sources used to be microwatt sources, no getting around it. Sending a
milliwatt through a wavelength-diameter pinhole was basically impossible,
do it easily by creating spherewave "pinhole light" right at the start,
as if it came from a virtual pinhole. Aha, confocal resonator mirrors,
the virtual pinhole in a laser is a real image pinhole sitting between the
mirrors. Semiconductor lasers with parallel mirrors: they just put the
point source at virtual infinite distance, way off down the "infinite
mirror tunnel" so it behaves like the light from a distant star.
OK, if spatially coherent light looks like an expanding bullseye, then
what does INCOHERENT light look like? In the above diagram 2A it looks
like bunches of overlapped bullseyes. Lots of interference patterns,
probably with the nodes moving around randomly. Or it looks like bunches
of light rays where the rays come from several separate points in fig. 2b,
and the rays all cross each other in the light beam.
Sources in decreasing coherence
A perfect 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 light, but then we send it through a frosted screen, the light remains monochromatic but it becomes incoherent. Hey, I see that we can actually buy incoherent-izer opto devices. 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
And now I have the answer to a big question that plagued me in childhood.
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.
The 1cm burning spot would appear anywhere along the parallel beam. But
if you think about this, it turns out to be impossible. Adding lenses
just creates a projector, where your parallel solar deathray becomes a
wide image of the sun. No thin intense beam appears. The answer is
simple: REPLACE THE SUN WITH A 10KM WHITE DWARF STAR! Keep the
brightness the same, but shrink the sun until it appears in the sky like a
star, like an intense pinpoint. Now use a 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. It's still a projector, but if you
project the image of a pointsource into the distance, the result is a
collimated beam. Other than a bit of diffraction, this should work great:
a few hundred watts CW in a parallel beam 1mm wide. Slice off 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 sharp tool. Exactly,
exactly. But the central concept is that "pinhole light" is the reason
for the coherent sharp light that does the cutting. If our sun was 10KM
wide, or reduced to 10^5 times smaller in visual angle, its light would be
like a laser, and our retinas would be damaged quickly. The lens of your
eye will focus the whitedwarf sunlight to a pinpoint rather than to a
little solar disk on your retina. Only because our sun is an extended
source, the 1.5 KW/m^2 sunlight doesn't act like laser light. If instead
it was pointsource, then looking at the sun would be like staring into a
1.5mW laser pointer. Using binoculars would be lethally dangerous: 5000X
smaller exit aperture, creating an eight watt parallel beam 1mm in
diameter. Coherent light can be nasty.