Download Class 23

Announcements:
Today: LASERs!
• Exam 2 is next week (Thu., 7:30-9:00pm)
Topics: TZD, Chapters 3-5, 11.9, 11.10
• Bring your own formula sheet.
• No written HW due for next week but
reading assignments are due as usual.
Now, let's make a gigantic LAZER!
What’s so special about LASER light?
Reading Quiz
A) It doesn't diffract when it goes through two slits.
B) All the photons in the laser beam oscillate inphase with each other.
C) The photons in the laser beam travel a little bit
faster because they all go the same direction.
D) Laser light is pure quantum light, and therefore,
cannot be described with classical EM theory.
E) Laser light is purely classical light, and therefore,
it is incompatible with the photon picture.
What’s so special about LASER light?
Reading Quiz
A) It doesn't diffract when it goes through two slits.
B) All the photons in the laser beam oscillate inphase with each other.
C) The photons in the laser beam travel a little bit
faster because they all go the same direction.
D) Laser light is pure quantum light, and therefore,
cannot be described with classical EM theory.
E) Laser light is purely classical light, and therefore,
it is incompatible with the photon picture.
Spatial coherence
What’s so special about LASER light?
Remember the word 'coherence'?
(We used it occasionally in context with
interferometers, diffraction and with photons.)
There are two types of coherence:
- Spatial coherence
- Temporal coherence
LASERs produce light with excellent spatial
and temporal coherence.
Temporal coherence
Collimating lens
Flashlight
(incoherent)
Laserpointer
(coherent)
Flashlight
(incoherent)
'Mach-Zehnder'
interferometer
c ·τ1
Laser
(coherent)
c ·τ2
For very stable lasers: (τ1- τ2)max ~ 1 second.
(This corresponds to 300’000 km path difference!)
Remember this one (from class 3):
Let's make a coherent light pulp!
Bad: Throw away most of
the light and individual
photons still have random
phases φ
E-field (for a single color):
LASER
E(x,t) = A0 sin(ωt+(x ·ω)/c +φ)
ω = 2πf
E
λ
A0
φ
x
Temporal coherence: ω and φ are very well
defined constants (i.e. time independent).
How can we make identical photons?
Aperture
Loose more than
Color filter (passes only a trillion to one in
power!(=bad idea)
certain colors, ω)
Remember: Coherent light requires that ω and φ are constants.
How light interacts with atoms
e
out
Clone them!
2
1
spontaneous
emission of light:
Excited atom emits
one photon.
in
2
e
1
absorption of
light: Atom absorbs
one photon
e
in
2
out
1
stimulated
emission:
clone the photon
-- A. Einstein
Surprising fact: Chance of stimulated
emission of excited atom EXACTLY the
same as chance of absorption by lower
state atom. Critical when making a laser.
Laser: Stimulated emission to clone photon many times (~1020/s)
Light Amplification by Stimulated Emission of Radiation
Spontaneous emission
Stimulated emission
Random phase
Random direction
Similar energy (as absorbed photon)
Legend:
Photon
Identical phase
Identical energy
Identical momentum
Legend:
Atom in ground state
Atom in excited state
e
Photon
Atom in ground state
e
Atom in excited state
e
e
Excited atom
Chance of stimulated emission of
excited atom is EXACTLY the same
as chance of absorption by ground
state atom.
Atom in ground state
Glass tube below contains 9 atoms. Some are excited some
not excited (as shown). Light enters the tube on the left:
b. less come out right
3 excited atoms can emit photons,
6 ground state atoms can absorb. Absorption wins.
For the condition above: what do you expect?
a. More photons will come out (on the right) than go in.
b. Fewer photons will come out (on the right) than go in.
c. Same number as go in,
d. None will come out.
Think about statistics / probabilities
To increase the number of photons when going through the atoms, more
atoms need to be in the upper energy level than in the lower.
 Need a “Population inversion”
(This is the hard part of making laser, b/c atoms jump down so quickly.)
How to get population inversion?
e
A) Use photons with hf < ΔE
Nupper > Nlower, more cloned than eaten.
ΔE
B) Use photons with hf = ΔE
excited
e
not excited
C) Use photons with hf > ΔE
D) Use very strong lamp with hf ≈ ΔE.
E) Will never get population inversion in this system.
Nupper < Nlower, more eaten than cloned.
No population inversion in 2 level atom!
e
out
2
1
spontaneous
emission of light:
Excited atom emits
one photon.
in
2
e
1
absorption of
light: Atom absorbs
one photon
e
in
2
Need at least 3 energy levels!
 Use a second color of light to create population inversion
out
1
stimulated
emission:
clone the photon
2
2
t2
t1
1
Equal probability
Population inversion means: More atoms are in the excited
state than in the ground state.
As soon as we have the same number of atoms in the excited
state as in the ground state, the probability of creating an
excited atom is same (or smaller, when considering spontaneous
emission) as the probability of having stimulated emission!
 Can never reach population inversion in 2-level atom!
1
t3t1<>t2t2
3
t1 < t2
2
G
G
t2
1
“Pumping” process produces population
inversion
t1< t2
G
Optical resonator
Ok, if we have 'population inversion' we get 'gain'.
But where are these photons coming from?
Mirror
Partially-silvered mirror
out
}
out
From here!
Some fraction of the photons are 'recycled' through the
amplifier (feedback!). The rest is used as the laser's output.
This is done with an 'optical resonator/cavity'
Continuously supply energy to the atoms to
maintain population inversion.

Let's play!
Summary
Mirror
Half-silvered mirror
out
LASERs need:
• Population inversion  Gain
• Optical feedback (optical resonator)  Coherent light
http://phet.colorado.edu/simulations/lasers/lasers.jnlp
Semiconductor lasers are tiny!
But others can be fairly ‘involved’
…or very involved…
Various 'flavors' of Lasers
Gas lasers
All the energy of this
laser is focused into this!
(Trigger Nuclear fusion.)
Dye lasers (liquid)
Chemical lasers
Solid state lasers
Fiber lasers
Diode lasers
Gas dynamic lasers
…
Practically unlimited numbers of
applications for lasers
Just to name a few:
Medicine: Surgery (no bleeding, noncontact  eye)
Diagnostics (Two Photon-Microscopy, tomography)
Machining: Tight focus allows very high intensity.
(100 W cut through hardened steel like butter)
Science: Huge variety of applications
(Ultra precise spectroscopy / light matter interaction...)
Commercial: DVD/CD, range finding, leveling,
telecommunication…
Sharks with frickin' laser beams attached to their heads…