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Zero Dispersion Wavelength

Definition: a wavelength where the group delay dispersion of a fiber or a material is zero

Categories: general optics, fiber optics and waveguides

Units: m

Formula symbol: <$\lambda_0$>

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Cite the article using its DOI: https://doi.org/10.61835/357

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A zero dispersion wavelength of an optical materials is a wavelength where the group delay dispersion (second-order chromatic dispersion)

$$k'' \equiv \frac{{{\partial ^2}k}}{{\partial {\omega ^2}}}$$

is zero. Note that this is not the wavelength where the wavelength (or optical frequency) derivative of the refractive index vanishes.

Many materials have only one zero dispersion wavelength within the transparency region, with normal dispersion below that wavelength and anomalous dispersion for longer wavelengths. For example, fused silica has its zero dispersion wavelength at 1.27 μm. For other optical glasses, far shorter values are common (often in the visible range), and more than one zero dispersion wavelength can occur.

The concept can also be applied to optical fibers and other waveguides, only that here one means the zero crossings of <$\partial^2\beta/\partial \omega^2$>. (See the article on the propagation constant.) For standard telecom fibers, which are based on germanosilicate glass, the zero dispersion wavelength is ≈ 1.3 μm, which is close to that of the material. However, by employing fiber designs with modified waveguide dispersion it is possible to shift the zero dispersion wavelength e.g. to the 1.5-μm region (→ dispersion-shifted fibers). Certain more sophisticated fiber designs can have two zero dispersion wavelengths – with anomalous dispersion between those and normal dispersion otherwise – or even more such wavelengths.

For photonic crystal fibers with small mode areas, which can exhibit particularly strong waveguide dispersion, the zero dispersion wavelength can be shifted e.g. into the visible spectral region, so that anomalous dispersion is obtained in the visible wavelength region, allowing for, e.g., soliton transmission. Photonic crystal fibers as well as some other fiber designs can exhibit two or even three different zero dispersion wavelengths.

Achromatic optics are generally not made by operating optical elements at their zero dispersion wavelength. Instead, one usually compensates chromatic effects from different components, e.g. in achromatic doublet lenses.

Effects of Vanishing Dispersion

When ultrashort pulses of light propagate in a medium with zero chromatic dispersion, dispersive pulse broadening is avoided. Similarly, operation of a telecom system around the zero dispersion wavelength greatly reduces dispersive broadening of optical signals.

At the same time, however, the signals become relatively sensitive to optical nonlinearities of the fiber, such as four-wave mixing, which can be phase matched under these conditions. It is therefore not always advantageous to operate in that regime; an improved approach is dispersion management in the form of alternatively using fibers with different signs of group velocity dispersion.

In other situations, phase matching of nonlinearities near the zero dispersion wavelength can be useful for nonlinear devices, such as optical parametric oscillators based on the <$\chi^{(3)}$> nonlinearity of optical fibers. Also, supercontinuum generation can lead to particularly broad optical spectra when the pump light has a wavelength near the zero dispersion wavelength.

Case Study

The following case study is available, which discusses aspects related to the zero dispersion wavelength:

  • Dispersion engineering for telecom fibers
  • We explore different ways of optimizing refractive index profile for specific chromatic dispersion properties of telecom fibers. This also involves automatic optimizations.

See also: chromatic dispersion, fibers, dispersion-shifted fibers, photonic crystal fibers

Questions and Comments from Users

2020-08-24

I have a waveguide with specific dimensions that has a certain chromatic dispersion. How to change this waveguide's structure in (width and height) such that the fundamental mode has a zero-dispersion wavelength in the near infrared, for example?

The author's answer:

I am not aware of a general method for that. I suppose you will just have to try different changes and see where you get.

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