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Encyclopedia of Laser Physics and Technology

© Dr. Rüdiger Paschotta

Last update: 2009-09-26

Acronym: SMF

Definition: optical fibers supporting only a single guided mode per polarization direction

Single-mode fibers (also called monomode fibers) are optical fibers which are designed such that they support only a single propagation mode per polarization direction for a given wavelength. They usually have a relatively small core (with a diameter of only a few micrometers) and a small refractive index difference between core and cladding. The mode radius is typically a few microns.

A peculiar property of single-mode fibers is that the transverse intensity profile at the fiber output has a fixed shape, which is independent of the launch conditions and the spatial properties of the injected light, assuming that no cladding modes can carry substantial power to the fiber end. The launch conditions only influence the efficiency with which light can be coupled into the guided mode.

Conditions for Efficiently Launching Light into a Single-mode Fiber

Efficiently launching light into a single-mode fiber requires that the transverse complex amplitude profile of that light at the fiber's input end matches that of the guided mode. This implies

• that the light source has a high beam quality (with M² ∼ 1)
• that the light has a focus at the fiber's input end (for matching the plane wavefronts of the fiber mode)
• that this focus has the correct size and is precisely aligned (concerning position and direction) to the core. More precisely, the error in position must be well below the beam radius, and the angular misalignment must be small compared with the beam divergence of the mode.

Generally, a long-term stable efficient launch of a free-space laser beam into a single-mode fiber requires well designed mechanical parts, which allow to precisely align and keep fixed the focusing lens and the fiber end while not exhibiting excessive thermal drifts.

For single-mode fibers with particularly large effective mode area (see below), it is easier to obtain the correct alignment concerning the focus position, but the angular alignment is more critical.

Conditions for Single-mode Guidance

For step-index fibers, the condition for single-mode guidance can be formulated using the V number (normalized frequency), which can be calculated from the wavelength, the core radius, and the numerical aperture (NA): the V number must be below ∼ 2.405 [1]. This requires that the core radius is small, particularly for fibers with high NA.

Figure 1: Mode function of a single-mode step-index fiber. The refractive index change is 0.002 in that case, and the core radius is 4 μm. This leads to a V number of 1.95 at a wavelength of 1 μm.

Figure 2: Mode functions of a multimode step-index fiber, having the same index contrast as above, but a larger core radius of 10 μm. The V number is 4.87. This fiber supports four modes, disregarding different polarization states.

Typically, a fiber has single-mode characteristics only over a limited wavelength range with a width of a few hundred nanometers. The limit towards smaller wavelengths is given by the single-mode cut-off wavelength, beyond which the fiber supports multiple modes. This transition is very sharp and can easily be seen e.g. when tuning the launched wavelength around the cut-off wavelength: the shape of the transmitted beam varies rapidly in the multimode regime but remains constant in the single-mode regime. The long-wavelength limit of the useful single-mode region is usually given by excessive bend losses, by absorption of the material or (for certain fiber designs, e.g. with index-depressed cladding) by leakage into the cladding.

Photonic crystal fibers can have substantially broader or narrower wavelength regions with single-mode propagation. For example, there are endlessly single-mode fibers with a very wide single-mode wavelength region. On the other hand, there are photonic bandgap fibers with narrow single-mode regions and no guidance at other wavelengths.

ITU Standards for Single-mode Fibers

The International Telecommunications Union (ITU) has developed a number of standards for various types of fibers as used for optical fiber communications. Some of the most important of those standards concerning single-mode fibers are given in Table 1.

Table 1: Standards for single-mode fibers.

Large Mode Area Single-mode Fibers and Effectively Single-mode Fibers

For some applications, single-mode fibers with relatively large core diameters of tens of micrometers (→ large mode area fibers) are required. This can be achieved in different ways, e.g. by making a large core with a small index difference (small numerical aperture), or with a photonic crystal fiber. In general, single-mode fibers with large mode areas tend to be more sensitive to bend losses, compared with multimode fibers, because the guiding is relatively weak.

In some cases, strictly single-mode guidance is not required; it is possible to use effectively single-mode fibers, having a few transverse modes, where however all higher-order modes have relatively high losses, and mode coupling from the fundamental mode to higher-order modes is weak. Some bending of the fiber is often used to suppress higher-order modes more efficiently, if they exhibit higher bend losses.

Applications

Single-mode guidance is important for many applications. Examples are:

• In fiber lasers and amplifiers made of rare-earth-doped fibers, single-mode guidance is the basis for achieving a high beam quality of the output.
• In optical fiber communication systems, single-mode guidance avoids the problem of intermodal dispersion, which (in multimode fibers) would lead to the occurrence of multiple copies of the input signals at the receiver.
• Single-mode fibers are used for connecting different components in fiber-optic setups, such as interferometers. They can be fusion-spliced or put together with fiber connectors.
• In measurement setups, the fact is often exploited that the output of a single-mode fiber has a fixed spatial shape, independent of the launch conditions. A single-mode fiber may serve as a kind of mode cleaner.
• Nonlinear interactions in long single-mode fibers may be exploited. For example, this can be signal amplification via stimulated Raman scattering, or strong spectral broadening (supercontinuum generation).

As a standard single-mode fiber for use in optical fiber communications in the 1.3-μm or 1.5-μm wavelength region, the SMF-28 of Corning (or the enhanced version SMF-28e) is common. This has a core diameter of 8.2 μm and a numerical aperture of 0.14. The mode field diameter is ∼ 9.2 μm at 1310 nm, or 10.4 μm at 1550 nm. The single-mode cut-off is at ∼ 1260 nm.

Bibliography

See also: fibers, numerical aperture, V number, mode radius, multimode fibers, waveguides, mode matching, effective mode area, Spotlight article 2008-02-22

Category: fibers and other waveguides

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