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Bandwidth

Definition: the width of some frequency or wavelength range

More specific terms: gain bandwidth, resonator bandwidth, modal bandwidth, phase-matching bandwidth

German: Bandbreite

Categories: light detection and characterization, physical foundations

Formula symbol: Δν, Δλ

Units: Hz, nm

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In photonics, the term bandwidth occurs in many different cases. The following sections discuss some important cases.

Bandwidth in Terms of Optical Frequency

In the following cases, bandwidth means the width of a range of optical frequencies:

A common definition of spectral width is the full width at half maximum (FWHM), but other definitions are also used. For example some authors use the half width at half maximum (HWHM), which is just half the FWHM.

bandwidth of a pulse
Figure 1: The optical spectrum of an unchirped 80-fs ultrashort light pulse. Its full width at half maximum bandwidth is 8.9 nm, corresponding to 3.9 THz.

Optical bandwidth values may be specified in terms of frequency or wavelength. Due to the inverse relationship of frequency and wavelength, the conversion factor between gigahertz and nanometers depends on the center wavelength or frequency. For converting a (small) wavelength interval into a frequency interval, the equation

wavelength to frequency interval

can be used. (It can be obtained by considering the derivative of ν = c / λ with respect to λ.) This shows that 1 nm is worth more gigahertz if the center wavelength is shorter.

Conversion between Frequency and Wavelength Bandwidth

Center wavelength:
Wavelength bandwidth: calc
Frequency bandwidth: calc

Enter input values with units, where appropriate. After you have modified some values, click a "calc" button to recalculate the field left of it.

If you choose a longer center wavelength, you will see that one nm is worth fewer GHz!

The optical bandwidth of a light source is strongly related to the temporal coherence, characterized with the coherence time.

Both for passive resonators (e.g. optical cavities) and for the output of oscillators (e.g. lasers), the Q factor is the oscillation frequency divided by the bandwidth.

Bandwidth of Modulations

A bandwidth can also indicate the maximum frequency with which a light source can be modulated, or at which modulated light can be detected with a photodetector.

In the area of optical fiber communications, the term bandwidth is also often inaccurately used for the data rate (e.g. in units of Gbit/s) achieved in an optical communication system. A more appropriate term would be data rate or data transmission capacity, avoiding any confusion with optical bandwidth.

Note that the data transmission capacity has only a limited relation to the optical bandwidth. Although a large data transmission rate is not possible without a large optical bandwidth, different communications devices can differ substantially in terms of spectral efficiency, i.e., concerning what data rate is achievable per megahertz of optical bandwidth.

Questions and Comments from Users

2020-04-07

Just a curious question about data transfer. Does the choice of light wavelength give us a cap on how much data we can transfer? And would short wavelengths give us a higher cap? And if so is there an analytical expression for this fundamental limit?

Answer from the author:

The center wavelength does not matter, only the width of the used optical frequency range.

The possible transmission bandwidth is the product of the optical bandwidth with the so-called spectral efficiency – which depends on the used modulation format and the achieved signal-to-noise ratio, which is of course influenced by propagation losses, detector noise etc. So I think there is no fundamental limit, but there are practical limits to the achievable spectral efficiency. It is typically of the order of 1 bit/s per Hertz of optical bandwidth. For more details see the article on optical data transmission.

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See also: optical spectrum, time–bandwidth product, gain bandwidth, coherence time, transform limit, modal bandwidth, bandwidth–distance product, Q factor, phase-matching bandwidth, wavelength, optical frequency, telecom fibers, The Photonics Spotlight 2007-10-11
and other articles in the categories light detection and characterization, physical foundations

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