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 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 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