1. by Alex Ellis

2. LASER is an Acronym For:
Light
Amplification by
Stimulated
Emission of
Radiation
But what does this mean?

3. Photon Emission
Spontaneous
Stimulated
Absorption e-
γ, E = E3 - E2

4. 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
Spontaneous
IN PHASE

5. 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.

6. 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
Plane parallel resonator
Hemifocal resonator f c
Concentric resonator c
Hemispherical resonator f
Confocal resonator
Unstable resonator
c: center of curvature, f: focal point

7. Transverse Modes TEM00: I(r) = (2P/πd2)*exp(-2r2/d2)
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)

8. 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

9. 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.

10. 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”

11. 3-Level Lasers Highly excited level Metastable level LASER TRANSITION
Blue: excitation, yellow: fast transitions, green: laser transition

12. 4-Level Lasers Highly excited level Metastable level LASER TRANSITION
Lower laser level
Blue: excitation, yellow: fast transitions, green: laser transition

13. Properties of Lasers Monochromaticity: Δλ Coherence Divergence
Longitudinal and Transverse Modes
LC=λ2/(2Δλ)

14. Divergence Div = λ/ (π W)
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!

15. Resources Understanding Lasers by Jeff Hecht
Principles of Lasers by Svelto Orazio
Calculus by James Stewart
Mr. Bucher and Ms. Leifer