Coherencetemporal

Coherencetemporal, commonly referred to as temporal coherence, is a property of a wave, especially light, that describes how well its phase information is preserved over time. It focuses on correlations between the wave’s amplitude at different moments, rather than across different positions. Temporal coherence is a key aspect of how long a wave can produce stable interference with itself or with another signal.

The primary quantity associated with temporal coherence is the coherence time, τc. This is the characteristic time scale over which the first-order temporal correlation function g1(τ) = ⟨E*(t)E(t+τ)⟩/⟨|E(t)|2⟩ remains appreciable. A longer τc means the wave maintains a predictable phase for a longer period and can interfere with itself over larger time delays. The coherence time is related to the spectral bandwidth Δν of the source; for many practical cases, τc ≈ 1/Δν, so a narrow spectral width yields a longer coherence time. The corresponding coherence length in vacuum is lc = cτc.

In experiments, temporal coherence is commonly probed with interferometry. By introducing a controllable time delay in an interferometer (for example, a Michelson interferometer), researchers measure fringe visibility as a function of delay to map the coherence curve and determine τc. In quantum optics, temporal coherence also connects to higher-order correlations, such as g2(τ), which relate to photon statistics and arrival-time correlations.

Sources vary in coherence: ideal, stable lasers can exhibit very long coherence times, while broadband or incandescent sources have short τc. Temporal coherence has applications in spectroscopy, holography, and fiber-optic communication, where phase stability over time influences resolution and data integrity. It is distinct from, yet related to, spatial coherence, which concerns phase correlations across space.