Laser Linewidth and Bandwidth Calculator

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Convert a laser spectral width between wavelength bandwidth (nm) and frequency bandwidth (GHz) using an exact end-point method and a quick small-bandwidth approximation. You can also estimate coherence time, coherence length in a medium, and quality factor (Q) from the same linewidth.

Pick the result you want. The calculator will hide inputs that are not needed.
The laser’s center wavelength. Use nm unless your datasheet uses a different unit elsewhere on this page.
The full width of the wavelength span you want to convert (for example, 0.10 nm). This is treated as a symmetric span around λ0.
Advanced options
Bandwidth meaning
Choose whether your delta_lambda value is already a full width, or if it is a half-width (plus/minus around λ0). The conversion uses a symmetric span around λ0.
Coherence settings
Different books use different constants. This choice affects coherence time and coherence length outputs only, not delta_lambda <-> delta_nu conversion.
Use 1.000 for vacuum/air (approx). Use about 1.468 for typical silica fiber near 1550 nm if you know it for your system.
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How to use our Laser Linewidth and Bandwidth Calculator

  1. Choose what you want to solve for: convert delta_lambda to delta_nu, or convert delta_nu to delta_lambda.
  2. Enter the center wavelength lambda0 (nm) from your laser spec (for example 1550 nm).
  3. If converting from wavelength to frequency, enter delta_lambda (nm). In Advanced options, confirm whether your value is a full width or a half-width.
  4. If converting from frequency to wavelength, enter delta_nu (GHz).
  5. Open Advanced options and set the coherence time convention if you want coherence time/length outputs.
  6. If you want coherence length in a material (like fiber), enter the refractive index n. Use n = 1.000 for vacuum/air (approx).
  7. Click Calculate.
  8. Read the exact and approximate conversions, then check the approximation error percent to see whether the small-bandwidth approximation is safe for your case.

Definitions

Wavelength (lambda): The distance between repeating points of a wave, like crest to crest. In this calculator, lambda0 is the center wavelength of the laser. [1]

Frequency (nu): How many wave cycles pass per second (Hz). Optical frequencies are often shown in THz.

Linewidth / bandwidth (delta): The width of the laser spectrum (how spread out it is). Here, delta_lambda is in nm and delta_nu is in Hz or GHz.

Refractive index (n): A number that tells how fast light travels in a material compared with vacuum; it affects coherence length in that medium. [2]

Quality factor (Q): A ratio that compares center frequency to linewidth: higher Q means a narrower line relative to its center.

Coherence time (tau_c): A time scale for how long the light stays phase-related; different books use different constant factors.

Coherence length (L_c): A distance scale related to coherence time; in a medium it is shorter when n is larger.

Methodology

Constants and unit conversions

Speed of light in vacuum:

c = 299,792,458 m/s (used for all conversions). [1]

Unit conversions used:

1 nm = 1e-9 m, 1 GHz = 1e9 Hz, 1 THz = 1e12 Hz.

Step 1: Center frequency from center wavelength

ν0 (Hz) = c / λ0 (m)

lambda0 is entered in nm and converted to meters before the math.

Step 2A: Exact conversion from wavelength width to frequency width

The calculator treats delta_lambda as a symmetric span around lambda0. If you select delta_lambda meaning = half-width, it first converts to full width:

delta_lambda_full = 2 * delta_lambda_input.

Δν_exact (Hz) = c/(λ0 - Δλ/2) - c/(λ0 + Δλ/2)

Inputs must satisfy λ0 > 0 and (λ0 - Δλ/2) > 0 (equivalently, Δλ < 2*λ0) so the end-point wavelengths stay positive.

Step 2B: Small-bandwidth approximation (useful for quick estimates)

Δν_approx (Hz) = (c / λ0^2) * Δλ

Δλ_approx (m) = (λ0^2 / c) * Δν

The approximation comes from differentiating ν = c/λ and is most accurate when delta_lambda is much smaller than lambda0.

Approximation error percent

Error (%) = 100 * (Δν_approx - Δν_exact) / Δν_exact

If Δν_exact is 0 or not finite (should not happen with valid inputs), the calculator shows N/A instead of dividing by zero. A note is shown when the absolute error is above 1% to encourage using the exact direction for better accuracy.

Q factor from linewidth

Q = ν0 / Δν

Δν is the frequency linewidth used in the active mode (computed exact when converting from delta_lambda, or taken from your entered delta_nu when converting from frequency). If the result is not finite (for example, extremely tiny delta_nu), the calculator shows a message like "Very large (check inputs)" instead of Infinity.

Coherence time and coherence length (optional)

You choose the coherence time convention. This changes only tau_c and L_c, not the wavelength-frequency conversion.

τ_c (s) = 1 / Δν

τ_c (s) = 1 / (2*π*Δν)

L_c (m) = (c / n) * τ_c

n is the refractive index of the medium (must be > 0). In a material (n > 1), the coherence length in that medium is shorter because the wave travels slower there. [2]

Sources

  1. Encyclopaedia Britannica - Wavelength
  2. NIST - Optical Waveguide Communications Glossary: Linewidth and Coherence
  3. NIST CODATA - Speed of Light in Vacuum