Lasers & Coherence

Lasers produce highly coherent, monochromatic, directional light through stimulated emission. A population inversion is required so that stimulated emission dominates absorption, and optical feedback from mirrors sustains oscillation.

Key Concepts

Stimulated emission: an incoming photon triggers emission of an identical photon
Population inversion: more atoms in excited state than ground state
Three-level vs four-level laser systems
Cavity modes: resonant wavelengths satisfy L = mλ/2
Coherence length: l_c = λ²/Δλ

Key Equations

Einstein A and B

A_{21} = \frac{8\pi h\nu^3}{c^3}B_{21}

Gain condition

N_2 > N_1\text{ (population inversion)}

Cavity resonance

L = m\frac{\lambda}{2}

Coherence length

l_c = \frac{\lambda^2}{\Delta\lambda}

Worked Example

Example Problem

Problem

A laser cavity has L=25 cm and operates at λ=633 nm. Find the mode number m.

Solution

m = 2L/λ = 2×0.25/(633×10⁻⁹) = 790,048. ≈ 7.9×10⁵.

Practice

Exercises

7 problems

1 of 7

A He-Ne laser (λ=632.8 nm) has linewidth Δλ=0.0020 nm. Find the coherence length in mm.

Your answer

2 of 7

A laser cavity has length L=50 cm. Find the mode spacing Δν in MHz.

Your answer

MHz

3 of 7

A laser beam has power P=5.0 mW and diameter d=1.0 mm. Find the intensity in kW/m².

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4 of 7

A 4-level laser has pump photon energy 3.0 eV and lasing photon energy 1.8 eV. Find the quantum efficiency (ratio of laser photon to pump photon energy).