Download - Lecture VI
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Lecture VI
LASER
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Stimulated emissionSpontaneous emission
Light Amplification by Stimulated Emission of Radiation
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Energy level diagram• The possible energies which electrons in the
atom can have is depicted in an energy level diagram.
1E
2E3E4E
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• In 1958, Charles Townes and Arthur Schawlow theorized about a visible laser, an invention that would use infrared and/or visible spectrum light.
• Light Amplification by Stimulated Emission of Radiation- (LASER).
• Properties of Lasers– Produce monochromatic light of extremely high
intensity.
The operation of the Laser
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The operation of the Laser
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The operation of the Laser
1E
2E3E4E
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The operation of the Laser
1E
2E3E4E
absorption
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The operation of the Laser
1E
2E3E4E
Spontaneous emission
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The operation of the Laser
Spontaneous emission
1. Incoherent light
2. Accidental direction
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The operation of the Laser
1E
2E3E4E
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The operation of the Laser
1E
2E3E4E
Stimulated emission
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The operation of the Laser
Light: Coherent, polarized
The stimulating and emitted photons have the same:
frequency
phase
direction
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Two level system
absorption Spontaneous emission
Stimulated emission
h hh
E1
E2
E1
E2
h=E2-E1
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E1
E2
• n1 - the number of electrons of energy E1
• n2 - the number of electrons of energy E2
2 2 1
1
( )expn E En kT
Boltzmann’s equation
example: T=3000 K E2-E1=2.0 eV
42
1
4.4 10nn
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Einstein’s coefficients
Probability of stimulated absorption R1-2
R1-2 = () B1-2
Probability of stimulated and spontaneous emission :
R2-1 = () B2-1 + A2-1 assumption: n1 atoms of energy 1 and n2 atoms of energy 2 are in thermal equilibrium at temperature T with the radiation of spectral density ():
n1 R1-2 = n2 R2-1 n1 () B1-2 = n2 ( () B2-1 + A2-1)
2 1 2 1
1 1 2
2 2 1
/ = 1
A Bn Bn B
E1
E2
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B1-2/B2-1 = 1
According to Boltzman statistics:
() = =
12 1
2
exp( ) / exp( / )n E E kT h kTn
1)exp(
/
12
211212
kTh
BB
BA 1)/exp(
/8 33
kThch
3
3
12
12 8ch
BA
Planck’s law
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The probability of spontaneous emission A2-1 /the probability of stimulated emission B2-1(:
1. Visible photons, energy: 1.6eV – 3.1eV.
2. kT at 300K ~ 0.025eV.
3. stimulated emission dominates solely when h/kT <<1!(for microwaves: h <0.0015eV) The frequency of emission acts to the absorption:
if h/kT <<1.
1)/exp()(12
12
kThB
A
1
2
1
2
12
12
211
122122 ])(
1[)(
)(nn
nn
BA
BnBnAnx
x~ n2/n1
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Condition for the laser operation
If n1 > n2
• radiation is mostly absorbed• spontaneous radiation dominates.
• most atoms occupy level E2, weak absorption
• stimulated emission prevails
• light is amplified
if n2 >> n1 - population inversion
Necessary condition: population inversion
E1
E2
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How to realize the population inversion?
Thermal excitation:
2
1
expn En kT
Optically, electrically.
impossible.
The system has to be „pumped”
E1
E2
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Measurement disturbes the system
The Uncertainty Principle
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The Uncertainty Principle• Classical physics
– Measurement uncertainty is due to limitations of the measurement apparatus
– There is no limit in principle to how accurate a measurement can be made
• Quantum Mechanics– There is a fundamental limit to the accuracy of a measurement
determined by the Heisenberg uncertainty principle– If a measurement of position is made with precision x and a
simultaneous measurement of linear momentum is made with precision p, then the product of the two uncertainties can never be less than h/2
xx p
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The Uncertainty Principle
Virtual particles: created due to the UP
E t
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Three level laser
The laser operation
E1
E3
E2
Fast transition
Laser action
• 13 pumping• spontaneous emission 3 2.• state 2 is a metastable state • population inversion between states 2 and 1. • stimulated emission between 2 i 1.
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t
E1
E3
E2
Fast transition
lasing
- optical pumping - occupation of E3 of a short life time, 10-8s. It is a band, the metastable and ground states are narrow :
- electrons are collected on E2: population inversion
- stimulated emission (one photon emitted spontaneously starts the stimulated radiation )
- Beam of photons moves normally to the mirrors – standing wave.
The laser operation
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ruby laser• discovered in 60-ies of the XX century.• ruby (Al2O3) monocrystal, Cr doped.
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• Lasing from the Cr3+.• three level laser
Ener
gy
4A2
4T2
4T1
2T2
2E
LASING
• optical pumping: 510-600nm and 360-450nm.• fast transition on 2E.• lasing: 2E on 4A2,
•694nmrapid decay
Ruby laser
Al2O3Cr+
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Ruby laser
First laser: Ted MaimanHughes Research Labs1960