Coherence Length
Definition and meaning of Coherence Length in chemistry.
Coherence length is the maximum distance a wave train (such as a beam of light) can travel while still maintaining a fixed, predictable phase relationship with itself, so that it can produce a stable interference pattern.
In more detail
Coherence length is set by the spectral purity of the source: a perfectly monochromatic wave would have infinite coherence length, but any real source has a finite bandwidth Δν, giving a coherence length of roughly L_c ≈ c/Δν (equivalently λ²/Δλ). Beyond this distance, different frequency components drift out of phase and interference fringes wash out. The concept is central to interferometry (Michelson, Fabry–Pérot), optical coherence tomography, and laser-based spectroscopies such as CARS and ultrafast pump–probe experiments, where path-length differences must stay within L_c for a clean signal.
Key facts
| Formula | L_c ≈ c/Δν ≈ λ²/Δλ |
|---|---|
| Typical laser value | ~m to 100 m (narrow-linewidth laser) |
| Typical white-light value | ~1 μm |
| Field | Physical Chemistry |
A stabilized helium–neon laser (linewidth ~1 MHz) has a coherence length of tens of meters, allowing it to form sharp interference fringes in a Michelson interferometer even with large arm-length mismatches; ordinary white light, with its broad bandwidth, has a coherence length of only a few micrometers.
Frequently asked questions
How is coherence length related to linewidth?
They are inversely related: a narrower spectral linewidth Δν gives a longer coherence length, L_c ≈ c/Δν, because the wave stays in phase with itself for longer before frequency components dephase.
Why does coherence length matter in spectroscopy?
Techniques like interferometry and coherent nonlinear spectroscopy (e.g., CARS) require path or pulse-timing differences shorter than the coherence length to produce a measurable, stable interference or coherent signal.