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Cut-off Wavelength

Definition: a wavelength above which a guided mode of a waveguide ceases to exist

German: Grenzwellenlänge

Category: fiber optics and waveguides

Formula symbol: λco

Units: m

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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.

fraction of power in fiber core
Figure 1: Fraction of the power of various guided modes (where the colors are related to the l indices of those) which is contained in the fiber core as a function of the wavelength. 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 no cut-off for the fundamental (LP10) mode. For other fiber designs, in particular for some photonic crystal fibers, there can also be a fundamental 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.

Questions and Comments from Users

2020-10-03

What is the formula for the cut-off wavelength of a fiber mode?

Answer from the author:

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.

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See also: wavelength, waveguides, fibers, modes, LP modes, bend losses
and other articles in the category fiber optics and waveguides

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