LASERS
Representative applications:
Amplifiers:
Broad-band communications (avoid down-conversion)
Oscillators: Frequency/distance reference, local oscillators,
illuminators, transmitters, CD/DVD players, sensors
Blasting:
Laser machining, labeling, weapons, laser fusion (pellet
compression). Peak > 1015W, average > 1kw; high
intensity because I ∝ |∑⎯Ei |2
i
Energy States:
ionization, Water vapor H O
2
Hydrogen atom
free
0 e.v
States:
electron
H +
electronic (visible, UV)
+
- vibrational (visible)
O
ground state
bending (IR)
H +
-13.6 e.v.
rotational (microwave)
1420 MHz
Chromium atoms in lattice (e.g. ruby), Erbium atoms in glass
L22-1
STIMULATED EMISSION AND ABSORPTION
Rate Equation:
Assume:
Then:
Two-level system, E2 > E1, and ni = atoms m-1 in state i
dn2/dt = - An2 - B(n2 – n1) [m-1s-1] (collisionless system)
Spontaneous emission
Induced emission
Spontaneous emission, states i to j:
Aij = ω3|Dij|2 (2/3hεc3) [s-1]
n2
n2
(Decay time τA = A-1)
A
B
n1
n1
Dij [C m] = quantum dipole moment (electric or magnetic)
Note: τA ∝ ω-3 ⇒ very brief “visible” τ’s, long microwave τ’s
∞
Stimulated emission and absorption:
2
Photon flux density F:
B coefficient:
Line shape gij(f):
E 1
F=
[photons m-2s-1]
2ηo hf
Bij = Fσij ∝ F gij(f)
2
1
gij (f ) =
π Δf
(f − f o )2
1+ 4
( Δf ) 2
∫ −∞gij(f)df = 1
gij(f)
Aij/ω3
Δf
(Lorentzian)
fo
f
L22-2
ENERGY LEVEL POPULATION AND WIDTH
Linewidth Broadening Mechanisms:
Electron energy E in semiconductor
Δf
Conduction band
ΔE = hf
Valence band
Energy band curvature
broadens the linewidth
Isolated
atoms
fo
k
f
Collisions ⇒ phase changes,
Fourier transform ⇒ Δf
Level Populations—Kinetic Temperature Tk: Ei [J]
Thermal equilibrium ⇒ Boltzmann distribution:
−(Ei −E j ) kT
ni
=e
nj
T = kinetic temperature
if collisions dominate
T = radiation temperature if
radiation dominates fij
⇒ ni → nj if Trad →∞, n2 > n1 if Trad < 0
State energy
n2 ∝ e-E/kT
n1
L22-3
BASIC LASER AMPLIFIER PHYSICS
Amplification Process:
Pump (repopulates level 2)
Optical
fiber
2
hf
hf
2hf ⇒
⇒
4hf ⇒
6hf
1
input
amplification, exponential growth
Intensity-limited amplification
[Each is a separate atom or molecule;
need n2 > n1 for amplification]
Amplification frequency f [Hz]:
E2 – E1 = hf [J],
h = 6.625 × 10-34 [Js]
amplification
linear growth
n2 replacement-rate limited
amplification
P(z)
exponential
growth
P(z) ≅ Pine(g-α)z
linear
z
(g is gain, α is attenuation)
L22-4
PUMPING OF LASERS
Two-Level Lasers:
Radiation pumping alone never yields n2 > n1
(some 2-level lasers spatially isolate n2 group)
Pump
1
Three-Level Lasers:
Pumping the 1-3 transition yields n1 ≅ n3
Large A32 populates L2 so n2 >> n1 ≅ n3 ≅ 0
More levels can utilize transitions with larger A’s
Large A23 fills L2, and large A41 empties L4
Laser Power Efficiency (Pout/Pin ):
Intrinsic efficiency:
B/A efficiency @ 2:
A/A efficiency @ 3:
Total efficiency:
ηi = fL/fp (P ∝ nhf [W]) < 1
ηB = B21/(A21+B21) < 1
ηA = A32/(A31+A32) < 1
η = ηiηBηA
Pump photons s-1 ∝ B >> A ∝ ω3, so x-ray
lasers need pump power ∝ hfB ∝ hfA ∝ ω4
2
Lasing?
Pump
fpump > fo
Pump
lasing
3
Large A32
2 lasing
1
3
A32
2
4
A41
1 1
Pump
A31
3
A32
2
1
A21 B =Fσ21
dn2/dt = - An2 - B(n2 – n1)
L22-5
LASER OSCILLATORS
Laser Oscillation:
Lossless:
Lossy:
With perfect mirrors at
L
both ends a lossless
P+
amplifier must oscillate
T
Amplifier
and saturate
Round-trip gain must exceed round-trip loss (threshold
condition); gain ∝ pump power Pp, so need Pp > Pthresh
Mirrors:
Exit mirror has power transmission coefficient T > 0
At threshold, Gain ≅ Loss, so: P+(1 – T)e2(g-α)L ≥ P+
⇒ round-trip gain = e2(g-α)L ≥ 1/(1 – T) for oscillation
Q-switching:
Set mirror reflectivity low ⇒
round-trip gain < threshold.
When laser is fully pumped,
increase mirror reflectivity
over threshold, yielding very
large “Q-switched pulse”
Pout
Pthresh
Ppump
L22-6
LASER RESONANCES
Oscillator Resonant Frequencies f:
Resonances
m λm
= L (mirrors ≈ short circuits)
2
λm = 2L , fm = cm (N = refractive index)
m
2LN
fi+1 − fi = c
2LN
≅ 108 Hz (100 MHz) for 1-meter fiber;
Laser
Cavity
line shape, resonances
width = Δf
≅ 50 GHz line spacing for 0.5-mm diodes
Laser Output Spectrum:
If every atom can amplify at all frequencies, then
the strongest round-trip gain wins ⇒ line narrowing
(homogeneous line broadening)
If atoms can amplify only a portion of the band,
then all lines over threshold can yield output
(inhomogeneous line broadening)
Line narrowing
L22-7
EXAMPLES OF LASERS
Electrically Pumped Solid-State Lasers:
Active region
Forward-biased GaAs p-n junction
E
Conduction
injects carriers into conduction band
band
Compact (grain of sand)
+ p-type
electrons ~50 percent efficiency
+ E
>100 W/cm2 for arrays
F
EF
+
1 mW/micron2 for diodes
holes
+
n-type
1-1000 mW typical
Valence band
z
Mirrors at both ends
Astrophysical Masers:
Stellar Pumping:
Interstellar collisions:
UV-IR pumped: H2O, OH, CO, etc.
OH, etc.
Chemical lasers:
star
Weapons (high energy, fast)
L22-8
MIT OpenCourseWare
http://ocw.mit.edu
6.013 Electromagnetics and Applications
Spring 2009
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