How lasers work
Explain laser operation through pumping, population inversion, stimulated emission, optical feedback, resonator modes, threshold and output coupling.
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ContinueStimulated emission can amplify light, but only if more atoms are ready to emit than to absorb, and only if the light passes through them again and again. A laser therefore needs a pump to keep the upper level more populated than the lower one, and a pair of mirrors to feed the light back. How lasers work goes beyond the 9478 syllabus.
Population inversion
For a chosen laser transition, let N₂ be the upper-level population and N₁ the lower-level population. Population inversion means
Thermal equilibrium normally favours lower energies, so an external pump is required. Inversion matters because the medium must produce more stimulated emission than absorption at the laser frequency.
The complete laser system
A working laser contains:
- a pump that supplies energy;
- a gain medium with a usable transition and a way to sustain inversion;
- an optical resonator that returns light through the medium;
- an output coupler that transmits a fraction of the amplified field.
From a seed photon to amplification
Spontaneous emission can supply an initial photon travelling near the cavity axis. It passes through the inverted medium and triggers stimulated emission. The mirrors return the growing field for repeated passes, creating more matched photons.
The resonator does not create energy. Optical energy comes from the pump and is stored temporarily in the excited medium before being transferred to the field.
Change the pump strength and cavity mirrors to compare population inversion with the build-up of laser light.
Three-level atoms pumped at 20% between two mirrors. 0% of atoms are in E₂ and 100% in E₁; 0 photons are in the rod.
- Atoms in E₁
- 100 %
- Atoms in E₂
- 0 %
- Population inversion
- no
- Photons between the mirrors
- 0
- Output beam
- 0 photons/s
Try this
0 of 4 doneRaise the pump until a strong beam builds up between the mirrors. (not done yet)
Inversion alone is not enough: the gain must beat the losses. Then each photon makes copies on every pass, all along the axis and in step: coherent light.
Make E₂ short-lived and pump the three-level atoms at 80% or more. (not done yet)
Atoms now leave E₂ as fast as they arrive, so they cannot pile up there: a laser needs a metastable level.
Pump two-level atoms as hard as you can for 15 s. (not done yet)
The pump drives atoms down as often as up, so E₂ never holds more than half of them: no inversion, no laser.
Take the mirrors away with the pump on. (not done yet)
Without feedback each photon crosses the rod once. There is inversion but too little amplification: no beam, only a weak glow in all directions.
You’ve tried every task.
Threshold and losses
Every round trip loses energy through imperfect mirrors, absorption, scattering and deliberate output coupling. Laser threshold is reached when round-trip gain equals round-trip loss. Above threshold, a steady laser field can build until saturation limits further growth.
Increasing mirror reflectivity is not always beneficial: feedback may rise, but a perfectly reflecting output mirror would provide no useful beam.
Resonant modes
For a simple cavity of effective length L, standing-wave boundary conditions give approximately
where q is an integer. Adjacent longitudinal modes have an approximate frequency spacing
for an empty linear cavity. The gain spectrum and other mode-selection effects determine which supported modes actually lase.
Worked example 1
Finding longitudinal-mode spacing
Problem
Show full solution
Choose the cavity relation
Method
Δ f = c/(2L).Reason
Adjacent standing-wave modes differ by one half-wavelength across the linear cavity’s round-trip geometry.Working
Answer
Δ f = c/2LSubstitute
Method
Δ f = 3.75 × 10⁸ Hz.Reason
Use c = 3.00 × 10⁸ m s⁻¹ and L = 0.400 m.Working
Answer
Δ f = (3.00 × 10⁸)/2(0.400) = 3.75 × 10⁸ HzExpress and interpret
Method
The mode spacing is 375 MHz.Reason
10⁶ Hz = 1 MHz; the result is a separation between adjacent modes, not their optical frequency.Working
Answer
3.75 × 10⁸ Hz = 375 MHz
Quick check
Why a simple two-level pump is insufficient
In an ideal closed two-level system driven on the same transition, absorption and stimulated emission become equally likely as the populations approach equality. Resonant pumping alone therefore cannot sustain N₂ > N₁. Practical lasers use additional levels and decay pathways to populate the upper laser level and empty the lower one.
Spot the mistake 2
Why an ideal two-level pump cannot sustain inversion
Learner claim
Try this before viewing the solution
Show solution step by step
Account for both stimulated processes
Method
Include absorption and stimulated emission driven by the same radiation.Reason
As the upper population grows, the field increasingly drives downward transitions as well as upward transitions.Working
Answer
In the ideal non-degenerate two-level limit, strong resonant driving approaches N₂ = N₁.Test the gain condition
Method
Compare the result with population inversion.Reason
Net stimulated gain requires N₂ > N₁ for the laser transition.Working
Answer
N₂ = N₁ is saturation, not inversion.
Common mistake
Try it yourself 3
Does a metastable level guarantee gain?
Problem
Try this before viewing the solution
Hints
Hint 1
compare accumulation and emptying
Track how quickly atoms enter and leave each laser level.Hint 2
connect populations to gain
State the population condition under which stimulated emission exceeds absorption.Show solution step by step
Compare the populations
Method
The medium is not inverted.Reason
The lower level contains more atoms than the upper level, so absorption exceeds stimulated emission under the stated assumption.Working
Answer
N₂/N₁ = 6/9 = 2/3 < 1: there is no net optical gain. A long lifetime alone does not guarantee inversion.Change the level populations
Method
Increase pumping into the upper laser level or empty the lower level faster.Reason
The change must make N₂ > N₁; slowing upper-level decay helps accumulation but does not by itself establish this inequality.Working
Answer
With N₁ unchanged, the upper population must exceed 9.0 × 10²⁰. Alternatively, reduce N₁ below 6.0 × 10²⁰ while maintaining N₂.Account for energy and feedback
Method
More reflective mirrors alone do not create inversion.Reason
Mirrors reduce cavity losses and return light through the medium. The pump supplies the energy and establishes the level populations.Working
Answer
Reduced losses can lower the lasing threshold of an inverted medium, but cannot turn this absorbing population distribution into optical gain.
Quick check
Common mistakes
- Describing population inversion as “all the atoms are excited”. Only the populations of the two laser levels are compared.
- Saying the mirrors make the light coherent. Stimulated emission produces matched photons; the cavity gives repeated passes and selects modes.
- Treating threshold as a fixed pump power. It depends on the cavity losses, including the output coupling.
- Saying both mirrors should reflect perfectly. The output coupler must let some light out.
- Saying intense resonant pumping can invert a two-level system. The populations only approach equality.
- Giving the mode spacing c/(2L) as the light’s frequency. It is the gap between neighbouring modes.
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Syllabus and review details
No official syllabus alignment is listed for this lesson.
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