Single-mode fiber

Single-mode fiber (SMF) is an optical fiber that guides one transverse mode. Its core, about 8–9 µm across in standard telecom fiber, is surrounded by a 125 µm cladding whose refractive index is lower by a few tenths of a percent; at wavelengths above the fiber's cutoff only the fundamental mode, LP₀₁, propagates, in two orthogonal polarizations. Because every part of the signal travels in that one mode, there is no spread between modes, and pulses broaden only through chromatic and polarization effects. Standard fiber loses typically about 0.3 dB/km near 1310 nm and 0.2 dB/km near 1550 nm, so links of tens of kilometers run without amplifiers. For a side-by-side comparison with the large-core alternative, see single-mode vs multimode fiber and the multimode fiber entry.

The single-mode condition

How many modes a step-index core guides is set by its V number,

$$V = \frac{2\pi a\,\mathrm{NA}}{\lambda}$$

where $a$ is the core radius and NA the numerical aperture of the core. Only LP₀₁ is guided while $V < 2.405$, the first zero of the Bessel function $J_0$; above that value LP₁₁ appears as well. The wavelength at which $V = 2.405$ is the cutoff wavelength,

$$\lambda_c = \frac{2\pi a\,\mathrm{NA}}{2.405}$$

Take a core radius of 4.1 µm and the datasheet NA of 0.14. These give $V = 2.75$ at 1310 nm, $V = 2.33$ at 1550 nm and $\lambda_c = 1500$ nm, which would make the fiber two-moded at 1310 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. A core-cladding index difference of about 0.36% corresponds to NA ≈ 0.123, which gives $V = 2.42$ at 1310 nm, $V = 2.04$ at 1550 nm and a theoretical cutoff of 1318 nm. The LP₁₁ mode is weakly guided just short of its cutoff and is stripped by bends within a few meters, so the cutoff measured on a cabled length lies below the theoretical value, and the fiber is effectively single mode across the telecom bands. The Numerical Aperture Calculator computes the V number, cutoff and mode field diameter for other cores.

Geometry and mode field diameter

Standard SMF is sold as 9/125: a core of about 8–9 µm and a cladding of 125 µm, with a polymer coating that brings the outside diameter to about 250 µm. The guided mode extends into the cladding, so its width, the mode field diameter, is larger than the core and grows with wavelength. Marcuse's Gaussian approximation applied to the 4.1 µm, NA 0.123 core gives 9.0 µm at 1310 nm and 10.2 µm at 1550 nm, with 81% and 73% of the power inside the core; datasheets of standard fiber quote about 9.2 µm at 1310 nm and 10.4 µm at 1550 nm, a few percent more, because real index profiles are not ideal steps. The mode field diameter sets splice and connector loss.

Standard fiber grades, bend-insensitive grades and fibers with shifted dispersion are defined by ITU-T recommendations, which set their attenuation, dispersion, cutoff and mode field figures.

What limits a single-mode link

With modal dispersion absent, three effects set the reach.

• Attenuation. A 20 dB loss budget covers about 100 km at 0.2 dB/km. With erbium-doped fiber amplifiers every 80–100 km, terrestrial and submarine links extend to thousands of kilometers.
• Chromatic dispersion. Standard fiber has its zero-dispersion wavelength near 1310 nm and about 17 ps/(nm·km) at 1550 nm, where the dispersion is anomalous. Intensity-modulated 10 Gb/s links at 1550 nm are dispersion limited to tens of kilometers; coherent receivers undo the dispersion digitally.
• Polarization mode dispersion. The two polarizations of LP₀₁ are degenerate only in a perfectly round, unstressed fiber. Small ellipticity and stress give them slightly different group delays that change randomly along the fiber and with temperature, so the differential delay grows as the square root of length.

At high power, the Kerr nonlinearity of silica adds a fourth limit, discussed under launch power.

Bending

The single mode is held by an index step of a few tenths of a percent, so a tight bend lets part of it radiate into the cladding. Bend loss rises steeply toward long wavelengths, where $V$ is smaller and more of the mode lies in the cladding; this is why bend-insensitive fibers add a low-index trench around the core or reduce the mode field diameter. The bend loss entry gives the mechanisms and typical radii.

Where single-mode fiber is used

Single-mode fiber carries nearly all long-distance traffic, fiber access networks and most datacenter links beyond a few hundred meters. Fiber lasers, interferometers and fiber sensors use it because the beam leaving it has a fixed, nearly Gaussian profile. Coupling into it requires micrometer alignment, a large part of the cost of single-mode transceivers.

Common questions

What is the core size of single-mode fiber?

Standard telecom single-mode fiber has a core about 8–9 µm in diameter and a 125 µm cladding, written 9/125. The guided mode is somewhat wider than the core, about 9–10.5 µm in the 1310 and 1550 nm bands.

Why is single-mode fiber single mode?

Its core is small and its index step weak, so the V number stays below 2.405 at the operating wavelength and only the fundamental LP₀₁ mode is guided. At shorter wavelengths, below the cutoff, the same fiber guides more modes: at 850 nm the 4.1 µm, NA 0.123 core has $V = 3.7$.

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019). G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010). D. Marcuse, "Loss analysis of single-mode fiber splices," Bell System Technical Journal 56, 703 (1977). A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).