Stimulated emission

Stimulated emission is a fundamental physical process in which an incoming photon induces an excited atom or molecule to transition to a lower energy level, releasing an additional photon that is identical to the incoming one. This mechanism, first correctly predicted by Albert Einstein in 1916, later became the theoretical foundation for the development of the maser and the laser. The phenomenon contrasts with spontaneous emission, which occurs without external influence and produces photons with random phases and directions. Stimulated emission enables coherent light amplification and is central to optical technologies in physics, chemistry, communications, and quantum science.

Background and conceptual basis

In atoms and molecules, electrons occupy discrete energy levels determined by quantum mechanics. When an electron absorbs energy from photons or phonons, it may transition from a lower energy level to an excited state. However, excited states are typically unstable, and electrons eventually decay back to lower levels. In spontaneous emission, this decay occurs randomly, with photons emitted in arbitrary directions and phases. This underlies phenomena such as fluorescence and thermal radiation.
Stimulated emission, however, arises when an external electromagnetic field of appropriate frequency interacts with an already excited electron. As the electron makes the transition from the excited state to a lower energy level, it passes through an intermediate transition state that possesses a temporary dipole moment. This non-stationary dipole oscillates at the transition frequency, enhancing the probability that the electron will emit a photon identical to the incident photon. The outgoing photon matches the incoming one in frequency, phase, polarisation, and direction, thereby contributing to coherent amplification.
The process is closely related to atomic absorption, which moves electrons from lower to upper states when an incident photon is absorbed. Under normal thermal conditions, absorption dominates because lower levels are more populated. However, if a population inversion is established—meaning more electrons occupy the excited state than the lower state—the rate of stimulated emission exceeds absorption. This condition enables the medium to amplify light and is essential for lasers and masers.

Differences between spontaneous and stimulated emission

Several distinguishing characteristics set stimulated emission apart from spontaneous emission:

• Phase relationship: Stimulated emission produces photons that are phase-coherent with the incident radiation, while spontaneous emission is phase-random.
• Directional behaviour: The emitted photon in stimulated emission travels in the same direction as the incident photon; spontaneous emission occurs isotropically.
• Spectral properties: Stimulated emission generates photons with exactly the same frequency as the stimulating field, whereas spontaneous emission has a characteristic spectral linewidth.
• Dependence on external fields: Stimulated emission requires interaction with an external electromagnetic field; spontaneous emission does not.

These properties enable stimulated emission to produce coherent, monochromatic light beams, a key principle behind laser operation.

Historical development

Albert Einstein’s theoretical work in 1916 and 1917 introduced the concept of stimulated emission within the framework of quantum theory. He formulated what are now known as the Einstein coefficients, describing the rates of absorption, spontaneous emission, and stimulated emission for atomic transitions. These coefficients provided a quantitative foundation for understanding how radiation interacts with matter and demonstrated that stimulated emission must occur if Planck’s law of black-body radiation is to be satisfied.
Einstein’s predictions were well ahead of experimental capabilities at the time. Later developments in quantum electrodynamics and quantum optics elaborated on his early insights, leading eventually to the practical implementation of masers in the 1950s and lasers in 1960. Although stimulated emission is commonly described in terms of photons, classical electromagnetic models can also reproduce aspects of the phenomenon without explicitly invoking quantum particles, highlighting its conceptual robustness across different theoretical frameworks.

Mechanism and quantum description

Quantum mechanically, stimulated emission is modelled using a two-level atomic system with lower and upper states of energies E₁ and E₂. If an atom is in the upper state E₂, it may:

• decay spontaneously with the release of a photon of energy hν₀,
• or be induced by an external field of frequency ν₀ to emit an identical photon via stimulated emission.

The rate of stimulated emission is proportional to the number of atoms in the excited state and to the radiation density at the transition frequency. Einstein introduced the coefficient B₂₁ to quantify this rate. Absorption, the reverse process, is described by coefficient B₁₂, which Einstein demonstrated must be equal to B₂₁ to satisfy thermodynamic consistency.
Mathematically, the net transition rate depends on the population difference between energy levels. Optical amplification occurs when the number of excited atoms exceeds those in the lower state, achieving the population inversion condition. Without such an inversion, absorption predominates and weakens the light passing through the medium.
Stimulated emission depends strongly on the spectral lines of atoms or molecules. The emission rate decreases for frequencies that deviate from the transition frequency, often described by a line-shape function such as a Cauchy (Lorentzian) distribution under homogeneous broadening conditions.

Role in lasers and masers

The essential components enabling stimulated emission to produce useful optical output are:

• A gain medium, which supports population inversion.
• An external energy source, such as optical pumping or electrical discharge, to excite electrons.
• An optical resonator, typically composed of mirrors, providing feedback to sustain coherent amplification.

In lasers (light amplification by stimulated emission of radiation), the emitted photons form a highly monochromatic, coherent, and collimated beam. Masers operate on the same principle but at microwave frequencies. Even without resonant feedback, devices such as laser amplifiers and amplified spontaneous emission sources exploit stimulated emission for optical gain.

Applications and significance

Stimulated emission underpins numerous scientific, industrial, and medical technologies. Key applications include:

• Laser-based communication, where coherent beams enable high-speed optical data transfer.
• Spectroscopy, exploiting coherent light to probe atomic and molecular structures with precision.
• Medical technologies, such as laser surgery and photodynamic therapy.
• Metrology, including atomic clocks and interferometric measurements.
• Quantum technologies, where controlled stimulated emission contributes to quantum state manipulation and optical coherence.