Calcul FWHM nm Hz
Convert optical full width at half maximum between wavelength and frequency with a premium interactive calculator. Enter the center wavelength, choose the direction of conversion, and instantly see the exact bandwidth, edge positions, approximation error, and a Gaussian spectrum chart.
Exact conversion is calculated from the upper and lower half maximum edges using ν = c / λ. A small bandwidth approximation is also shown for comparison.
Expert guide to calcul FWHM nm Hz
The term FWHM stands for full width at half maximum. In optics, spectroscopy, lasers, telecommunications, and photonics, it is one of the most practical measures of spectral linewidth. When users search for calcul FWHM nm Hz, they usually want to convert a bandwidth written in nanometers into hertz, gigahertz, or terahertz, or they want to do the reverse conversion from frequency linewidth into wavelength linewidth. This is important because instrument specifications often use wavelength units, while physical models and coherence calculations often require frequency units.
At first glance, converting between nanometers and hertz seems trivial because wavelength and frequency are tied together by the speed of light. However, linewidth conversion is not perfectly linear. The central relation is:
Because frequency is inversely proportional to wavelength, a fixed change in wavelength does not produce the same change in frequency at all wavelengths. A 1 nm linewidth around 1550 nm corresponds to a much smaller frequency width than a 1 nm linewidth around 532 nm. That is why a good calculator must always ask for the center wavelength in addition to the FWHM value.
Why the center wavelength matters
Suppose two lasers each have a spectral width of 1 nm. One operates at 1550 nm and the other at 780 nm. Even though the wavelength width is the same in nanometers, the frequency width is very different because the slope of the function ν = c / λ changes with wavelength. Mathematically, the local conversion is governed by the derivative:
This tells us that for small bandwidths, the magnitude of the frequency linewidth is approximately:
This approximation is excellent when the linewidth is small compared with the center wavelength, which is true in many laser and telecom applications. For broader spectra, especially in supercontinuum sources, filters, and lower resolution spectrometers, it is better to use an exact edge based conversion rather than the small signal formula.
Exact FWHM conversion method
An exact method starts with the wavelength band edges at half maximum. If the center wavelength is λ0 and the wavelength FWHM is Δλ, the half maximum edges are:
- λlow = λ0 – Δλ / 2
- λhigh = λ0 + Δλ / 2
Each edge is converted to frequency using ν = c / λ. The exact frequency width is then:
The reverse conversion is similar. If the center wavelength is known, the center frequency is ν0 = c / λ0. Given a frequency FWHM Δν, the half maximum frequency edges are:
- νlow = ν0 – Δν / 2
- νhigh = ν0 + Δν / 2
Then convert each frequency back to wavelength and subtract the wavelength edges. This is the safest way to report a true bandwidth conversion because it preserves the nonlinearity of the wavelength to frequency mapping.
Reference values that help you estimate nm to Hz quickly
Engineers often want fast intuition before running a formal calculator. The table below shows the optical carrier frequency associated with common wavelengths used in telecom, solid state lasers, biophotonics, and atomic physics. These numbers come directly from ν = c / λ using the defined speed of light 299,792,458 m/s.
| Common wavelength | Typical application | Carrier frequency | Approximate photon energy trend |
|---|---|---|---|
| 1550 nm | Fiber optic communications | 193.41 THz | Lower than visible band |
| 1310 nm | Telecom O band | 228.85 THz | Near infrared |
| 1064 nm | Nd:YAG fundamental | 281.76 THz | Near infrared |
| 780 nm | Rubidium spectroscopy | 384.35 THz | Near red optical region |
| 632.8 nm | HeNe laser | 473.61 THz | Visible red |
| 532 nm | Frequency doubled Nd:YAG | 563.52 THz | Visible green |
Now consider what a 1 nm FWHM means at several common center wavelengths. The exact values below show how strongly the conversion depends on the optical center. This is the main reason a calculator that ignores center wavelength cannot be trusted for serious work.
| Center wavelength | 1 nm FWHM corresponds to | Approximate value | Interpretation |
|---|---|---|---|
| 1550 nm | About 124.8 GHz | 0.1248 THz | Relatively small frequency width |
| 1064 nm | About 264.8 GHz | 0.2648 THz | More than double the 1550 nm case |
| 780 nm | About 492.6 GHz | 0.4926 THz | Large increase due to shorter wavelength |
| 532 nm | About 1059.4 GHz | 1.0594 THz | Very large frequency span for the same 1 nm |
How to use a calcul FWHM nm Hz correctly
- Identify the center wavelength of your source, filter, or spectral feature.
- Determine whether the given FWHM is in wavelength units or frequency units.
- Enter the value with the proper scale such as pm, nm, GHz, or THz.
- Use an exact conversion whenever the linewidth is not negligible compared with the center wavelength.
- Review both the converted bandwidth and the half maximum edge values if your experiment depends on passband limits.
Example 1: telecom laser around 1550 nm
A distributed feedback laser may be specified with a wavelength linewidth of 0.08 nm at 1550 nm. Using the small bandwidth approximation:
This gives approximately 9.99 GHz. The exact edge based result is extremely close because 0.08 nm is tiny compared with 1550 nm. For wavelength selective switch design, DWDM spacing analysis, and coherence length estimates, that conversion is often the practical number engineers need.
Example 2: visible spectroscopy around 532 nm
If a filter at 532 nm has a 2 nm FWHM, the corresponding frequency bandwidth is much larger than many people expect. The approximate conversion is about 2.12 THz. This illustrates why visible spectroscopy instruments may show what appears to be a narrow width in nanometers while still spanning a very substantial region in frequency space.
Example 3: reverse conversion from GHz to pm
Imagine an optical source at 780 nm with a 6 GHz spectral width. What is the equivalent wavelength FWHM? The approximate reverse expression is:
That yields roughly 0.0122 nm, or 12.2 pm. In atomic spectroscopy and laser cooling work, pm scale widths are common, which is why reverse conversion is so useful.
Common mistakes in linewidth conversion
- Ignoring the center wavelength. A linewidth in nm cannot be converted to Hz without knowing where the spectrum is centered.
- Confusing total span with FWHM. FWHM is measured at half the peak amplitude, not necessarily from the full observable base width.
- Mixing unit scales. pm, nm, GHz, and THz differ by factors of 10, 1000, or more. One slip can lead to errors of three orders of magnitude.
- Using only the approximation for broad features. When bandwidth becomes significant, exact edge conversion is safer.
- Comparing different line shapes without noting the profile. Gaussian and Lorentzian profiles can share the same FWHM but behave differently in tails, coherence, and convolution results.
Line shape context: Gaussian versus Lorentzian
FWHM itself is only a width descriptor. It does not fully define the spectral profile. Two common profiles are Gaussian and Lorentzian. A Gaussian line often appears in systems dominated by inhomogeneous broadening, finite instrument resolution, or transform limited pulses under certain conditions. A Lorentzian line is commonly associated with lifetime broadening or natural linewidth. Both can have the same FWHM, but their wings differ strongly. That matters in etalon design, resonator analysis, and spectral filtering.
For the purposes of nm to Hz conversion, the line shape does not change the central mathematical mapping between wavelength and frequency. However, the chart in this calculator lets you visualize either Gaussian or Lorentzian intensity around the converted FWHM so you can better interpret the width in a physically familiar way.
Where the formulas come from
The key constant in all of these calculations is the speed of light in vacuum. The exact value is defined by international standards and published by the National Institute of Standards and Technology. For authoritative references, see the NIST speed of light constant page. A concise educational explanation of the relation between frequency and wavelength can also be found at HyperPhysics at Georgia State University. For spectroscopy background and practical optical metrology context, the NIST Time and Frequency Division is another strong source.
Approximation versus exact conversion in practice
In the lab, many users work with bandwidths such as 0.01 nm, 0.05 nm, or a few GHz. Under those conditions, the approximation error is usually tiny. In broadband optical systems, however, the error grows. If you are specifying a narrow telecom laser or a high finesse resonator, the approximate formula is usually sufficient for a quick estimate. If you are preparing data sheets, validating simulation results, or converting larger filter widths in visible optics, use the exact method and preserve the edge values.
Another practical detail is the medium. The equations above are based on vacuum wavelength and vacuum frequency. In materials, dispersion alters phase velocity and group velocity relationships. Most catalog wavelength specifications for lasers and spectrometers are still reported in air or vacuum terms, but advanced fiber and integrated photonics work may require separate treatment of refractive index and group index.
Summary of best practices
- Always enter a center wavelength when converting FWHM between nm and Hz.
- Use exact edge conversion for highest accuracy.
- Check whether the bandwidth is truly FWHM rather than full span or resolution bandwidth.
- Keep unit consistency throughout the calculation.
- Interpret the number in context of line shape, instrument resolution, and application goals.
With these principles, a calcul FWHM nm Hz tool becomes more than a unit converter. It becomes a practical optics aid for spectroscopy, laser characterization, telecommunications engineering, filter design, and scientific reporting. Use the calculator above to move directly between wavelength and frequency linewidth, inspect exact half maximum edges, compare against the small signal approximation, and visualize the result on a normalized spectral chart.