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by Alex Ellis
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LASER is an Acronym For:
Light Amplification by Stimulated Emission of Radiation But what does this mean?
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Photon Emission Spontaneous Stimulated Absorption e- γ, E = E3 - E2
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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
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Gain I is intensity, A is the amplification ratio, G (0G1) is gain coefficient of the medium, and L is the length of the gain medium.
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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
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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)
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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
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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.
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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”
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3-Level Lasers Highly excited level Metastable level LASER TRANSITION
Blue: excitation, yellow: fast transitions, green: laser transition
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4-Level Lasers Highly excited level Metastable level LASER TRANSITION
Lower laser level Blue: excitation, yellow: fast transitions, green: laser transition
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Properties of Lasers Monochromaticity: Δλ Coherence Divergence
Longitudinal and Transverse Modes LC=λ2/(2Δλ)
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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!
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Resources Understanding Lasers by Jeff Hecht
Principles of Lasers by Svelto Orazio Calculus by James Stewart Mr. Bucher and Ms. Leifer
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