optical transitions (original) (raw)

Author: the photonics expert (RP)

Definition: changes in the quantum states of atoms, ions or solids due to the absorption or emission of photons

Category: laser devices and laser physics

• optical transitions
  • forbidden transitions
  • laser transitions
  • multiphoton absorption
  • spontaneous emission
  • stimulated emission
  • transmission gratings

Related: optical pumpingtransition cross-sectionsnon-radiative transitionslaser physics

DOI: 10.61835/val Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What is an Optical Transition?

An optical transition is the change in the quantum state of an atom, ion, molecule, or solid-state system due to the absorption or emission of one or more photons. Such transitions underlie many fundamental processes in photonics, including lasers, spectroscopy, and the operation of various optoelectronic devices. Examples include:

• The transparency or opacity of materials is determined by the possibility of absorption transitions.
• Lasers exploit stimulated emission on selected laser transitions.
• Spectroscopy investigates material properties through their optical transitions.

Optical pumping is the use of such transitions for populating certain quantum states, e.g. the upper laser level in a laser gain medium.

Types of Optical Transitions

Different types of optical transitions can be distinguished:

Absorption

In most cases, absorption means that a single photon is absorbed and its energy is transferred to the absorbing species, exciting it into a higher quantum state.

At very high optical intensity, several photons may be absorbed simultaneously; this is called multiphoton absorption (e.g. two-photon absorption if two photons are absorbed). The combined photon energy excites the system into a higher state than a single photon could reach.

See the article on absorption for more details.

Spontaneous and Stimulated Emission

If a system is in an excited state, it may decay radiatively by emitting a photon:

• Spontaneous emission occurs without external prompting. Such emission between states of the same spin multiplicity is called fluorescence, while spin-forbidden, longer-lived emission is called phosphorescence. The general term is luminescence.
• Stimulated emission: If a photon interacts with an excited system, it can trigger a transition to a lower state, releasing an additional photon in the same mode, i.e., with equal optical frequency, polarization and propagation direction.

Stimulated-emission transitions that provide amplification are called laser transitions. Other transitions in laser media are used for optical pumping.

See the articles on spontaneous emission and stimulated emission for more details.

Competing Processes

Optical transitions may compete with other (non-optical) decay channels, collectively called non-radiative transitions. These include multi-phonon transitions, internal conversion, intersystem crossing, Auger recombination, and defect- or surface-assisted transitions. High nonradiative rates can suppress radiative emission, a phenomenon called quenching.

Involved Quantum States

The nature of the quantum states involved depends on the material:

• Isolated atoms or ions (e.g. in a low-pressure gas cell) exhibit discrete atomic or ionic electronic states.
• Rare-earth-doped solids, including rare-earth-doped laser gain media: 4f–4f transitions of individual ions are partially shielded from the host lattice, so that they interact relatively weakly with it. That can yield relatively narrow transition lines, but there can be substantial inhomogeneous broadening, essentially related to site-dependent lattice interactions. One generally considers Stark level manifolds, where one can often not resolve individual sub-levels.
• Transition-metal-doped solids, including transition-metal-doped laser gain media: Strong electron–phonon coupling produces broad vibronic transitions.
• Semiconductors exhibit transitions occur between Bloch band states:
  • Interband transitions: Electrons are excited from the valence band to the conduction band, creating electron–hole pairs or excitons. In indirect band gap semiconductors, phonons assist momentum conservation.
  • Intraband transitions: These include free-carrier absorption within a band and intersubband transitions in quantum wells and nanostructures.

Additional transitions can involve defects, impurities, or color centers.

Properties of Optical Transitions

Rabi Oscillations

In a simple two-level model where a single atom or ion interacts coherently with a resonant optical field, the population of the excited state does not increase monotonically but oscillates sinusoidally. Such Rabi oscillations occur at the (angular) Rabi frequency ($\Omega = \mu E / \hbar$), where ($\mu$) is the transition dipole moment and ($E$) the field amplitude.

In real ensembles, Rabi oscillations are often obscured by detuning, inhomogeneous broadening, variations in optical intensity and environmental decoherence (finite coherence time). Different atoms or ions lose phase coherence and their oscillations dephase, so the ensemble average shows only smooth excitation dynamics. For this reason, statistical rate equation modeling with population numbers and transition probabilities is commonly used; such models do not exhibit oscillatory population dynamics.

Clear Rabi oscillations can still be observed in well-isolated systems such as trapped ions, semiconductor quantum dots, or superconducting qubits, where long coherence times are maintained.

Transition Probability

When a photon interacts with an atom, ion, or solid-state system, the probability of an optical transition depends on several factors:

• Energy matching: The system must have states with an appropriate energy difference.
• Selection rules:
  • For electric-dipole transitions in atoms/molecules, there needs to be parity change: Δℓ = ±1; Δm = 0, ±1; ΔS ≈ 0.
  • In solids, additional crystal momentum (k) conservation applies; phonons, spin–orbit coupling, strain, or external fields can relax these rules.
  • Transitions that violate these rules are termed forbidden transitions, though higher-order multipole processes (magnetic dipole, electric quadrupole) or phonon-assisted processes may still allow them at reduced rates.

The polarization of light can also influence transition probabilities in addition to the optical frequency or wavelength.

Transition strengths may be quantified by oscillator strength, Einstein coefficients (A, B), or absorption and stimulated-emission transition cross sections. Net rates of such transitions may be limited by transitions in the opposite direction, which are often triggered by the same light.

Rates of spontaneous emission can (possibly together with competing non-radiative transitions) limit the lifetimes of excited states. For example the upper-state lifetime of laser transitions is often limited by the rate of spontaneous emission events.

Transition Bandwidth and Line Shape

The optical bandwidth over which a transition has substantial probability can vary widely from many terahertz (broad vibronic bands) down to well below 1 Hz for ultra-narrow lines used in optical frequency standards. Several factors determine the observed linewidth:

• Lifetime (natural) broadening: A high spontaneous emission rate (short upper-state lifetime ($\tau$)) imposes a minimum homogeneous linewidth ($\Delta\nu = 1 / (2\pi\:\tau)$).
• Dephasing and power broadening: Collisions, environmental fluctuations (pure dephasing), and strong driving fields increase the homogeneous width (often summarized by the coherence time ($T_2$)​, with ($\Delta\nu_{\rm hom} = 1 / (\pi\:T_2)$).
• Unresolved manifolds / nearby lines: Multiple transitions with similar center frequencies (e.g., Stark-split sublevels) can overlap and produce a broader apparent feature even if each component is narrow.
• Inhomogeneous broadening in ensembles: Variations across emitters broaden the ensemble spectrum:
  • In gases, different velocities and directions produce Doppler broadening (with Gaussian line shape).
  • In solids and glasses, different local sites of dopant ions (strain, composition, local fields) lead to inhomogeneous broadening. -/Advanced measurement techniques such as Doppler-free spectroscopy, cryogenic cooling and spectral hole burning can reveal the underlying homogeneous linewidth.

Saturation Behavior

Optical transitions in ensembles can be saturated when optical intensities are high enough to substantial modify the population of quantum states. Characteristic quantities in that context are the saturation intensity and saturation fluence.

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