Cutoff wavelength

The cutoff wavelength ${\lambda }_c$ of an optical fiber is the wavelength above which the fiber guides only its fundamental mode, LP₀₁. At shorter wavelengths the LP₁₁ mode is guided as well, and the fiber is no longer single mode. For a step-index fiber, cutoff is where the V number reaches 2.405, the first zero of the Bessel function $J_0$:

$${\lambda }_c=\frac{2\pi a\text{NA}}{2.405}=\frac{2\pi a\sqrt{n_1^2-n_2^2}}{2.405},$$

where $a$ is the core radius, $n_1$ and $n_2$ are the core and cladding indices, and NA is the numerical aperture of the core. Standard single-mode fiber (ITU-T G.652) has a specified cable cutoff of 1260 nm or less, so it is single mode in every telecom band from the O-band, which starts at 1260 nm, to the L-band at 1625 nm, and multimode at 850 nm. Three cutoff values are in use: the theoretical cutoff calculated from the index profile, and the fiber and cable cutoffs measured on 2 m and 22 m lengths. The cable cutoff is the shortest of the three, and it is the one that decides whether an installed link is single mode. The Fiber Numerical Aperture and V Number Calculator computes the theoretical cutoff from the core diameter and NA.

Theoretical, fiber and cable cutoff

The formula gives the wavelength at which LP₁₁ stops being a guided mode in a perfectly straight, infinitely long fiber. At wavelengths just short of that point, LP₁₁ is guided only weakly, with most of its power in the cladding, and in a real fiber it is lost within a short length, at bends and small perturbations. A measured cutoff is therefore shorter than the theoretical one, and shorter again when measured on a longer, coiled length. ITU-T G.650.1 and IEC 60793-1-44 define the fiber cutoff on 2 m of fiber and the cable cutoff on 22 m of cable; G.652 specifies only the cable cutoff.

Standard single-mode fiber shows how far apart the numbers can be. Its core is about 8.2 µm across and its datasheet NA is 0.14; put into the formula, those give a cutoff of 1500 nm. The datasheet NA, however, is measured from the far-field angle at 1% of the peak power and overstates the NA of the equivalent step-index core. The core-cladding index difference of about 0.36% corresponds to an NA of about 0.123 and a theoretical cutoff near 1.3 µm, and the cable cutoff is specified at 1260 nm or less. The V number entry works through the same example.

Graded-index and other profiles have their own cutoff values of $V$, higher than 2.405 for a graded core, so the formula above applies only to step-index fibers.

Choosing the cutoff

Just above cutoff, $V$ is close to 2.405 and the fundamental mode is tightly confined, with about 81% of its power in the core in the Gaussian approximation. As the wavelength increases, $V$ falls, the mode spreads into the cladding, and it becomes easier to lose at bends: the macrobend loss of a single-mode fiber rises steeply toward long wavelengths, which is why G.652 specifies it at 1625 nm and G.657 at 1550 and 1625 nm, rather than at 1310 nm. A fiber is therefore designed with its cutoff a little below its shortest operating wavelength, keeping $V$ between about 2 and 2.4 across its band. Moving the cutoff closer to the band improves bend tolerance; moving it further away widens the single-mode range at the cost of bend sensitivity at the long end. Bend-insensitive G.657 fibers ease the trade-off with a smaller mode field diameter or a low-index trench around the core, and keep the cable cutoff at 1260 nm or less.

Operating below the cutoff lets LP₁₁ carry part of the power. Its share changes with bends, connectors and temperature, so the transmitted power fluctuates and interference between the modes produces modal noise, which is why a short jumper of fiber whose fiber cutoff lies above the operating wavelength can misbehave even when the cable cutoff is met. At 850 nm, standard single-mode fiber guides LP₁₁ as well as LP₀₁.

Specialty fibers for shorter wavelengths use smaller cores, and every fiber becomes multimode at a short enough wavelength, since $V$ is inversely proportional to $\lambda$. At a wavelength where a fiber has a known $V$, its cutoff is ${\lambda }_c=\lambda V\mathrm{/}2.405$.

Measuring the cutoff

The standard transmitted-power method compares the spectrum transmitted through the test fiber with a reference in which LP₁₁ cannot survive: either the same fiber with a small extra loop that strips LP₁₁ without disturbing LP₀₁, or a multimode fiber. Below cutoff, the test fiber carries extra power in LP₁₁ and the ratio of the two spectra rises above its long-wavelength baseline; the cutoff is the longest wavelength at which that excess is still detectable above a small threshold set by the standard. The same measurement on 2 m of fiber and on 22 m of cable gives the fiber and cable cutoffs.

Cutoff in planar waveguides

Chip waveguides have the same behavior, usually described through a width or thickness at fixed wavelength rather than a wavelength. A symmetric slab of thickness $d$ guides one TE and one TM mode when $V=(\pi d\mathrm{/}\lambda )\sqrt{n_{\text{core}}^2-n_{\text{clad}}^2}<\pi \mathrm{/}2$; for silicon in silica at 1550 nm the limit is 245 nm, which is why silicon photonics uses layers about 220 nm thick. Rectangular channel waveguides have no closed-form cutoff and are solved numerically: the common 500 nm × 220 nm silicon wire in silica guides only the fundamental TE and TM modes at 1550 nm, and wider strips add higher-order TE modes, which multimode interference couplers several micrometers wide use deliberately. Strip and rib waveguides differ in how their higher-order modes are cut off, since a rib's slab lets them leak away.

Common questions

What is the cutoff wavelength of standard single-mode fiber?

ITU-T G.652 specifies a cable cutoff of 1260 nm or less, measured on 22 m of cable. The theoretical cutoff of the index profile is near 1.3 µm, and the fiber cutoff measured on 2 m lies between the two.

Why is a fiber single mode above its cutoff wavelength but not below it?

The V number is inversely proportional to wavelength. Above the cutoff wavelength $V$ is below 2.405 and only LP₀₁ is guided; below it, $V$ exceeds 2.405 and LP₁₁ is guided as well.

How do you calculate the cutoff wavelength?

For a step-index fiber, ${\lambda }_c=2\pi a\text{NA}\mathrm{/}2.405$, with $a$ the core radius. A core 8 µm across with an NA of 0.12 gives 1254 nm. With the NA quoted on a datasheet the result is only an estimate, because that NA is usually measured from the far field and overstates the step-index value.

Does a fiber stop guiding light below its cutoff wavelength?

No. It still guides the fundamental mode, but it guides LP₁₁ and possibly further modes as well, so it behaves as a few-mode fiber. The fundamental mode has no cutoff.

References: D. Gloge, "Weakly guiding fibers," Applied Optics 10, 2252 (1971). A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983). ITU-T G.650.1, Definitions and test methods for linear, deterministic attributes of single-mode fibre and cable. ITU-T G.652, Characteristics of a single-mode optical fibre and cable. IEC 60793-1-44, Optical fibres, Part 1-44: Measurement methods and test procedures, Cut-off wavelength.