AcademyMatter Waves
Academy
Lasers
Level 1 - Physics topic page in Matter Waves.
Principle
A laser amplifies light by stimulated emission from an inverted population of atoms or molecules.
Notation
\(E_2,E_1\)
upper and lower laser levels
\(\mathrm{J}\)
\(f\)
laser frequency
\(\mathrm{Hz}\)
\(\lambda\)
laser wavelength
\(\mathrm{m}\)
\(N_2,N_1\)
populations of upper and lower levels
\(h\)
Planck constant
\(\mathrm{J\,s}\)
\(c\)
speed of light
\(\mathrm{m\,s^{-1}}\)
Method
Derivation 1: Match the transition energy
Stimulated emission occurs when an incoming photon triggers an excited atom to emit a matching photon.
Transition energy
\[E_2-E_1=hf\]
Laser wavelength
\[\lambda=\frac{c}{f}=\frac{hc}{E_2-E_1}\]
Derivation 2: Invert the population
Net amplification requires more atoms in the upper laser level than the lower level.
Population inversion
\[N_2>N_1\]
Derivation 3: Use feedback
A cavity reflects light back through the gain medium. Allowed cavity modes are reinforced, and one output mirror lets out the beam.
Rules
Photon energy
\[E_\gamma=hf\]
Laser wavelength
\[\lambda=\frac{hc}{E_2-E_1}\]
Inversion condition
\[N_2>N_1\]
Cavity modes
\[2L=m\lambda\]
Examples
Question
A laser transition has energy gap
\[1.96\,\mathrm{eV}\]
Find the wavelength.Answer
\[\lambda=\frac{1240\,\mathrm{eV\,nm}}{1.96\,\mathrm{eV}}=633\,\mathrm{nm}\]
Checks
- Stimulated photons match frequency, phase, direction, and polarization.
- Population inversion is a nonequilibrium condition.
- A cavity narrows the allowed directions and frequencies.
- Laser light is coherent, but not automatically perfectly monochromatic.