Lecture VI
LASER
Stimulated emission
Spontaneous emission
Light Amplification by Stimulated Emission of Radiation
Energy level diagram
The possible energies which electrons in the atom can have is depicted in an energy level diagram.
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
The operation of the Laser
The operation of the Laser
(Pumping the Laser)
The operation of the Laser
absorption
The operation of the Laser
Spontaneous emission
The operation of the Laser
Spontaneous emission
Incoherent light
Accidental direction
The operation of the Laser
The operation of the Laser
Stimulated emission
The operation of the Laser
Light: Coherent, polarized
The stimulating and emitted photons have the same:
frequency
phase
direction
Two level system
n1 – the number of electrons of energy E1
n2 – the number of electrons of energy E2
Boltzmann’s equation
example: T=3000 K E2-E1=2.0 eV
Einstein’s coefficients
Probability of stimulated absorption R1-2
R1-2 = r (n) B1-2
Probability of stimulated and spontaneous emission :
R2-1 = r (n) B2-1 + A2-1
assumption: n1 atoms of energy e 1 and n2 atoms of energy e 2 are in thermal equilibrium at temperature T with the radiation of spectral density r (n):
n1 R1-2 = n2 R2-1 n1r (n) B1-2 = n2 (r (n) B2-1 + A2-1)
B1-2/B2-1 = 1
According to Boltzman statistics:
r (n) = =
Planck’s law
The probability of spontaneous emission A2-1 /the probability of stimulated emission B2-1r(n ):
Visible photons, energy: 1.6eV – 3.1eV.
kT at 300K ~ 0.025eV.
stimulated emission dominates solely when hn /kT <<1!
(for microwaves: hn <0.0015eV)
The frequency of emission acts to the absorption:
if hn /kT <<1.
x~ n2/n1
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
How to realize the population inversion?
Thermal excitation:
Optically, electrically.
impossible.
The system has to be „pumped”
Measurement disturbes the system
The Uncertainty Principle
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 Dx and a simultaneous measurement of linear momentum is made with precision Dp, then the product of the two uncertainties can never be less than h/2p
The Uncertainty Principle
Virtual particles: created due to the UP
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.
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
ruby laser
discovered in 60-ies of the XX century.
ruby (Al2O3) monocrystal, Cr doped.
Lasing from the Cr3+.
three level laser
optical pumping: 510-600nm and 360-450nm.
fast transition on 2E.
lasing: 2E on 4A2,
694nm
rapid decay
Ruby laser
Al2O3
Cr+
Ruby laser
First laser: Ted Maiman
Hughes Research Labs
1960