Cut-off Wavelength
Definition: a wavelength above which a guided mode of a waveguide ceases to exist
German: Grenzwellenlänge
Category: fiber optics and waveguides
Units: m
Formula symbol: <$\lambda_\textrm{co}$>
Author: Dr. Rüdiger Paschotta
The number of guided modes of a waveguide (for example, an optical fiber) depends on the optical wavelength: the shorter the wavelength, the more modes can be guided. For long wavelengths, there may be only a single guided mode (→ single-mode fibers) or even none at all, whereas multimode behavior is obtained at shorter wavelengths.
When a particular mode ceases to exist beyond a certain wavelength, that wavelength is called its cut-off wavelength. For an optical fiber, the cut-off wavelength for the LP11 mode sets a limit to the single-mode regime, as below that wavelength there is at least the LP01 and the LP11 mode.
Just below the cut-off wavelength, the mode properties often vary substantially. Typically, the mode radius (and thus the effective mode area) increases sharply near the cut-off, and the fraction of power propagating within the waveguide core decreases accordingly. That effect is shown in Figure 1 for a multimode step-index fiber; similar behavior occurs for fibers with other transverse refractive index profiles.
The thin vertical lines indicate the calculated cut-off wavelengths of the modes. The diagram has been produced with the software RP Fiber Power.
For LPlm modes of a fiber, only for <$l = 0$> the fraction of the power guided in the core goes to zero when approaching the cut-off. For modes with higher <$l$>, the mode size stays finite there.
In step-index fibers, there is theoretically no cut-off for the fundamental (LP01) mode, although propagation losses at long wavelengths may still be high, even making the fiber unusable. This is essentially because long-wavelength light would have a mode size well beyond the fiber core, with such mode experiencing light guidance and thus being very sensitive e.g. to microbending. Note, however, that in such situations there is not a well-defined mode cut-off, but rather one sees gradually rising propagation losses at longer wavelengths.
For other (not step-index) fiber designs, in particular for some photonic crystal fibers, there can also be a fundamental mode cut-off.
Fibers with not radially symmetric designs (and strongly bent fibers) can have polarization-dependent cut-off wavelengths.
Just below its cut-off wavelength, the bend losses of a mode can become very high due to the increased mode area. Therefore, even for moderate bending of the fiber one may obtain sharply increasing propagation losses near the cut-off wavelength. Therefore, cut-off wavelengths can not always be precisely determined in experiments.
See also: wavelength, waveguides, fibers, modes, LP modes, bend losses
Questions and Comments from Users
2021-03-31
“In step-index fibers, there is theoretically no cut-off for the fundamental (LP01) mode.”
Does this statement mean the fundamental mode (LP01) mode, or that after the LP01-mode there is no cut-off again?
The author's answer:
It means that the fundamental mode exists for any wavelength. Just theoretically, as explained in the article.
2023-09-01
I did a little experiment and spliced about 30 cm of 630HP fiber to a G652 telecom fiber. At 1550 nm, no light goes through the 630HP fiber. The splice must be okay as plenty of light is transmitted through those fibers with a 650 nm VFL. What is going on?
The author's answer:
The 630HP fiber is specified for operation wavelengths between 600 nm and 770 nm. Its core is too small to properly guide light in the 1.5-μm region. The fundamental mode exists at 1550 nm, but is highly sensitive e.g. to microbending.
2023-09-14
HN1550 has about the same core size as 630HP, yet plenty of 1550-nm light is transmitted through this fiber in the same experiment. So the size of the core cannot be the whole story.
The author's answer:
You are right – it is not all about core size:
HN1550 is a highly nonlinear fiber. This means a fiber with relatively small mode area – indeed similar to that of 630HP. That is achieved with a rather high numerical aperture. Without that, it would not work. Note that the NA is inversely proportional to the wavelength (approximately); therefore, a high NA at 1550 nm implies a rather high NA at 630 nm.
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2020-10-03
What is the formula for the cut-off wavelength of a fiber mode?
The author's answer:
The cut-off wavelength can usually not be calculated simply with some formula, but needs to be determined e.g. with numerical means. At most for the simplest cases, e.g. LP modes of step-index-fibers, one might be able to derive analytical equations.