Coherence Length Calculator
Select whether your bandwidth is in wavelength (nm) or frequency (Hz).
Coherence Length (Lc)
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meters
Coherence Time (τc)
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seconds
How it works?
The Coherence Length ($L_c$) describes the distance over which a light beam maintains a fixed phase relationship. This calculator uses the relationship between the center wavelength and the spectral linewidth (bandwidth) of the source.
$$ L_c \approx \frac{\lambda_0^2}{\Delta \lambda} \quad \text{or} \quad L_c \approx \frac{c}{\Delta \nu} $$
Coherence Length Approximation
Where the variables are:
- Center Wavelength ($\lambda_0$): The nominal wavelength of the laser source (e.g., 1550 nm for telecom C-band).
- Spectral Linewidth ($\Delta \lambda$): The full-width at half-maximum (FWHM) of the source's spectrum in wavelength units.
- Frequency Bandwidth ($\Delta \nu$): The linewidth expressed in frequency (Hz). Narrower linewidths (kHz) yield much longer coherence lengths than broad sources (nm).
- Speed of Light ($c$): A constant, approximately $3 \times 10^8$ m/s.
Note: The actual shape of the spectrum (Lorentzian vs. Gaussian) introduces a small pre-factor (like $2\ln(2)/\pi$ or $1/\pi$), but the formula above provides the standard engineering approximation used for most interferometric setups.