What is Coherence Length?
Coherence length is the maximum path difference over which two waves can still interfere constructively or destructively. It is a measure of the temporal coherence of a wave, indicating the distance over which the wave maintains a predictable phase relationship. Beyond this length, the phase relationship becomes random, and sustained interference patterns cannot be observed.
Key Principles and Factors
The coherence length (Lc) is inversely proportional to the spectral bandwidth (Δν) of the light source, typically approximated as Lc ≈ c / Δν, where 'c' is the speed of light. Monochromatic (single-frequency) light sources have a very large coherence length, ideally infinite, because their phase relationship is perfectly predictable. Real-world light sources, however, always possess a finite spectral bandwidth, limiting their coherence length.
A Practical Example: Interferometry
In applications like Michelson interferometry, light from a source is split into two paths and then recombined. For a clear and stable interference pattern to be visible, the path difference between the two light beams must be less than the coherence length of the light source. If the path difference exceeds the coherence length, the waves recombine with a random phase, and no interference fringes will be observed.
Importance and Applications
Coherence length is crucial in many scientific and technological fields. In optics, it dictates the performance of interferometers, holography, and optical coherence tomography (OCT). In telecommunications, it influences the maximum achievable data rates in fiber optic cables. Furthermore, it plays a significant role in quantum mechanics, particularly in understanding quantum entanglement and the behavior of wave packets.