An excellent example of temporal coherence, as highlighted in the provided reference, is a wave containing only a single frequency.
Temporal coherence describes the correlation between a wave and itself at different points in time. It essentially measures how long a wave maintains a predictable phase. A wave with high temporal coherence will have a phase that evolves predictably over time, making it highly correlated with itself even after a significant delay.
Understanding Temporal Coherence Through Examples
According to the reference:
- Examples of temporal coherence include: A wave containing only a single frequency (monochromatic) is perfectly correlated with itself at all time delays, in accordance with the above relation. (See Figure 1 - Note: Figure 1 is mentioned in the reference but not provided here).
This statement provides a clear benchmark for perfect temporal coherence. Here's why a monochromatic wave fits this description:
- Single Frequency: A monochromatic wave consists of just one frequency. This means its oscillations are perfectly regular and repeatable.
- Predictable Phase: Because the frequency is constant, the phase relationship between any two points in the wave separated by a specific time interval is always the same.
- High Correlation: As a result, the wave's pattern at any given time is perfectly correlated with its pattern at any earlier or later time point. This high correlation at all time delays is the definition of perfect temporal coherence.
Conversely, the reference also notes:
- "...a wave whose phase drifts quickly will have a short coherence time." This illustrates the opposite end of the spectrum – low temporal coherence. A wave with a phase that changes unpredictably loses its correlation with itself over short time periods.
Key Characteristics
| Feature | High Temporal Coherence (e.g., Monochromatic Wave) | Low Temporal Coherence (e.g., Incoherent Light) |
|---|---|---|
| Frequency | Single, constant frequency | Multiple frequencies or varying frequency |
| Phase Drift | Slow or non-existent | Fast and unpredictable |
| Self-Correlation | High, even at long time delays | Low, decreases quickly with time delay |
| Coherence Time | Long (approaching infinity for perfect coherence) | Short |
Understanding temporal coherence is crucial in fields like optics (lasers, interferometry), telecommunications, and quantum physics. Lasers, for example, are known for having high temporal coherence compared to ordinary light sources like incandescent bulbs, which are largely temporally incoherent.
[Temporal Coherence]
