Lasers: WTF is Coherent Light?
Laser light behaves very differently than light from other sources.
Textbooks give two reasons for this:
A bad textbook diagram, and a widespread
William Beaty 2004
What does "coherent" mean?
- Laser light is
monochromatic or very pure in color.
- Laser light is coherent or
As a kid I was always confused by explanations of coherent light. I'd
been told that coherence something to do with the sinusoidal shape of
photons. Light supposedly is made up of little wiggling strings;
transverse waves. Textbooks show photons as "little snakes" 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, 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
laser light 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. "Monochromatic light" 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 or perhaps violins. And in
holography, whenever the frequency of light is moved up and down, I could
imagine how this would slide the tiny diffraction patterns around on my
film. That blurs the patterns and makes holography impossible, so clearly
a hologram camera needs a very monochromatic light source.
So where is the equivalent power in the concept of "coherence?" How do I
use those wiggling-snakes to explain other things? Where do the snakes
clarify radio antennas, loudspeakers and water waves? And if my laser
isn't coherent enough to make holograms, can I draw a very simple picture
of the exact nature of the problem? One that any kid could understand?
No. It just didn't connect.
Well, after a few years in the physics business I finally figured 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 directly to misconceptions, and I couldn't go forward until I'd
un-learned it again. To get right down to it, light isn't a transverse
wave. Or more specifically, light not a "transverse wave in the Aether,"
instead it's a wave in magnetic and electric fields where the field
vectors point sideways. But the flux lines don't wiggle sideways. There
are no little sine-shaped snakes anywhere inside light. And photons are
either particles or waves; they're either like tiny bullets flying in
straight lines, or they're like expanding EM pond ripples from a thrown
pebble. Photon aren't shaped like twisty snakes, they're nothing like a
transverse wave on a string. So the entire "stacked wiggles" explanation
of Coherent Light falls apart.
And most important of all... I learned that in-phase emission does not
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.] 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 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
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."
THE BAD DIAGRAM
The 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, so the original wave is preserved.
In-phase emission keeps the light waveform scattering as it interacts with
the atoms in the glass. So yes, the atoms in the laser-rod or gas tube
emit some light in phase... making the material transparent, so it
preserves whatever coherence that the light might already have had.
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
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
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
"plane waves." Or simpler: "pihole light" or "pointsource light."
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 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 new layers constantly added in the
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, they focus to a point.
So coherent light is just "pointsource light?" Paraphrasing Feynman: Now
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
inventing holography before lasers existed. To create pseudo-lasers he
light from an ordinary mercury-arc lamp and passed it through a pinhole.
emission line made it nearly monochromatic, and the pinhole gave it the
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 coherent light,
use 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 Dennis Gabor-approved 1940s laser source. Make some
holograms. Heh, long exposure-time though.
In the distant past,
sources used to be microwatt light sources, no getting around it. Sending
milliwatt of light through a wavelength-diameter pinhole was basically
impossible, so all the bizarre and wonderful capabilities of lasers were
unreachable. But lasers
easily solve the problem by creating some spherewave "pinhole light" right
at the start,
as if thousands of watts of light came from a virtual pinhole less than
500nM across. Aha,
confocal resonator mirrors, the ones used in lasers, that means
the virtual pinhole in a real laser is a real-image pinhole sitting
mirrors. Semiconductor lasers with parallel mirrors: they just put the
pointsource at virtual-infinite distance, way off down the "infinite
mirror tunnel" so it behaves like the light from a distant star.
And this all 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, like those disco mirror things. On each reflection the
light gets slightly brighter, so every segment of the "tunnel" looks
slightly brighter ...and the far end of the tunnel looks like an
infinitely bright, infinitely tiny star. Look into the beam and the
"star" is small 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 can't do it, but a quarter-watt laser can burn a
tattoo permanently into the back of your eye. "Coherent" means "sharp
when focussed," since focused Coherent light all converges to an
infinitely small point.
OK, if spatially coherent light looks like an expanding bullseye, then
what does INCOHERENT light look like? In the above diagram 2A it instead
like bunches of overlapped bullseyes. Lots of interference patterns, and
probably with the nodes moving around randomly. Or it looks 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
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
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."
- 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
- Laser (coherence-leng in mms or few Meters)
- Starlight (coherence leng 1000s KM)
NO JPEG YET
Fig. 3 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.
All nasty little science-boys no doubt think 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
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
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 sharp 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 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.