Transcript No Slide Title

LASER is an Acronym For:
• Light
• Amplification by
• Stimulated
• Emission of
• Radiation
But what
does this
mean?
Photon Emission
e-
•Spontaneous
•Stimulated
γ, E = E3 - E2
•Absorption
Absorption and Emission:
Spontaneous vs. Stimulated
•Spontaneous: equally likely at thermal equilibrium
•Probability of stimulated emission depends on cross-section
•The concept of stimulated emission was proposed by Einstein
Stimulated
IN PHASE
Spontaneous
Gain
I is intensity, A is the amplification
ratio, G (0G1) is gain
coefficient of the medium, and L is
the length of the gain medium.
Resonance Cavities
and Longitudinal Modes
Since the wavelengths involved with lasers and masers
spread over small ranges, and are also absolutely small,
most cavities will achieve lengthwise resonance
L = nλ
c
f
Plane parallel
resonator
f
Hemifocal
resonator
Concentric
resonator
c
Hemispherical
resonator
Confocal
resonator
c: center of curvature, f: focal point
Unstable
resonator
Transverse Modes
Due to boundary conditions and
quantum mechanical wave equations
TEM00:
I(r) = (2P/πd2)*exp(-2r2/d2)
(d is spot size measured to
the 1/e2 points)
Population Inversions
At Thermal Equilibrium:
γ
ΔE
kB is the Boltzmann constant, T is the absolute temperature, Nk is the number of
electrons in the kth energy level in the sample, and e is the natural base
For laser action to occur, N2 must be greater than N1
Negative Temperatures
To have N2 > N1 (Population Inversion):
But this implies a negative temperature! Because of this, populations inversions
were incorrectly referred to as negative temperatures.
Pumping
Since a negative temperature isn’t possible, how is a
population inversion created and maintained?
•Optical: flashlamps and high-energy light sources
•Electrical: application of a potential difference across the
laser medium
•Semiconductor: movement of electrons in “junctions,”
between “holes”
3-Level Lasers
Highly excited level
Metastable level
LASER
TRANSITION
Blue: excitation, yellow: fast transitions, green: laser transition
4-Level Lasers
Highly excited level
Metastable level
LASER
TRANSITION
Lower laser level
Blue: excitation, yellow: fast transitions, green: laser transition
Properties of Lasers
•Monochromaticity: Δλ
•Coherence
LC=λ2/(2Δλ)
•Divergence
•Longitudinal and Transverse Modes
Divergence
R = d2/λ
(Rayleigh range - no diameter spread)
D = 2Lsinθ
(far-field divergence)
Div = λ/ (π W)
Rayleigh
range
W is the waist, or the minimum width
of the beam inside the laser cavity NOT ZERO!
Resources
•Understanding Lasers by Jeff Hecht
•Principles of Lasers by Svelto Orazio
•Calculus by James Stewart
•Mr. Bucher and Ms. Leifer