Stimulated Emission and How a Laser Works

Follow the energy of an atom during emission. It begins in an upper level and ends in a lower level. Its lost excitation energy supplies the emitted photon. The incident light stimulates the transition; it does not provide the atom's stored energy or make each photon twice as energetic.

Spontaneous emission can happen without an incoming beam. The time of an individual decay is probabilistic. Pumping excites atoms, but it does not schedule every spontaneous decay.

Stimulated emission adds light to an optical mode already occupied by the incident field. Frequency, direction and polarization describe that mode. For a coherent incident field, the added light has a matching field phase. This field description avoids treating each photon as a small wave with a separately assigned phase.

The transition energy sets a resonance. Real spectral lines have finite widths, so stimulation is not confined to one infinitely precise frequency. Near resonance, an occupied mode can gain light as excited atoms make downward transitions.

Amplification depends on the populations of the two levels joined by the laser transition. These are not always the ground state and an excited state. This lesson uses levels with equal statistical weights, meaning the same number of quantum states in each level. For that model, the upper population must exceed the lower population for net stimulated gain.

In the three-level scheme used here, the lower laser level is the ground state. Pumping lifts atoms from ground to a higher pump level. That level empties quickly into a longer-lived upper laser level. The upper level can accumulate atoms because its population decays more slowly than the pump level's population.

Laser emission returns atoms from the upper level to ground. It therefore reduces the inversion. Pumping must replenish atoms lost through stimulated emission, spontaneous emission and other decay.

The exact inversion condition in this equal-weight model is that the upper laser population exceeds the ground population. If pump-level population is neglected, all atoms occupy those two laser levels, so inversion requires more than half the total in the upper level. With a nonzero pump-level population, more than half of the atoms outside the pump level must occupy the upper laser level for inversion. The half-total threshold is therefore approximate when pump-level population is small. There is no separate, rapidly emptied lower laser level in this three-level model.

Consider a small light signal circulating in a two-mirror cavity. Each trip through the gain medium can add light by stimulated emission, while transmission and other losses remove some light. The mirrors provide feedback. They favor resonant modes whose field patterns reproduce after a round trip. An output coupler transmits part of the circulating light as the beam.

To predict startup growth, multiply the round-trip intensity gain factor by the fraction retained after losses. A product greater than one gives growth; a product below one gives decay. Population inversion can provide gain without making that product exceed one. Once steady laser operation is established, gain saturation brings gain into balance with loss.

Mirrors do not prescribe a doubling on every pass. An inverted medium can also amplify a beam in a single pass without mirrors. Such amplification alone does not demonstrate laser oscillation.

Real laser output has a finite frequency spread and finite coherence. Coherence concerns predictable field phase relationships over times or positions. It is different from intensity, the energy arriving per unit area per second. Laser output may contain several modes. Compressing a fixed pulse shape in time widens its spectrum, so short laser pulses need not have an extremely narrow frequency spread.