As light propagates in the core as a guided wave, it experiences some power loss. These are especially important for long-distance data transmission over fiber optic telecommunications cables.
Usually, the propagation loss is approximately constant en route with a certain attenuation coefficient α. The power then decays simply proportional to exp(− α z ), where z is the propagation distance. Loss is usually expressed in dB/km; this value is ≈4.343 times the 1/km power attenuation coefficient. Of course, the loss depends on the wavelength of light.
Origin of propagation loss
Propagation loss in fiber optics can come from several sources:
The material may have some inherent absorption. For example, quartz fibers increasingly absorb light as the wavelength exceeds ≈1.7 μm. Therefore, they are rarely used for wavelengths above 2 μm.
Additional isolated absorption peaks may come from some impurities. For example, silica fibers exhibit increased absorption losses around 1.39 μm and 1.24 μm if the core material is not anhydrous.
At short wavelengths, Rayleigh scattering in glass becomes increasingly important; the contribution of Rayleigh scattering to the attenuation coefficient is inversely proportional to the fourth power of the wavelength. Note that core glass is an amorphous material and will never be perfectly homogeneous under the microscope. Even with the most modern fiber manufacturing techniques, there are unavoidable “frozen” density fluctuations.
There are also some inelastic scattering – spontaneous Raman scattering and Brillouin scattering. These effects are measurable by scattered (and frequency shifted) light, but usually do not have a significant effect on propagation loss. However, Raman and Brillouin scattering lead to huge losses (by transferring energy to other wavelengths) at high light intensities, in which case stimulated scattering is possible. This is a nonlinear effect and will be dealt with in Section 11.
The increased scattering loss may be due to irregularities at the core/cladding interface. This problem is exacerbated for fibers with large index contrast (high numerical aperture). Also, a greater index contrast usually means that the core is more heavily doped with germanium, which makes it temporarily less homogeneous. Therefore, low-loss single-mode fiber used for long-distance data transmission over telecommunication cables has a relatively small NA, even though a higher NA would provide more robust guidance.
Additionally, there may be bending losses (see below).
Intrinsic loss is usually very uniform over the length of the fiber. This is not necessarily the case for additional losses; for example, irregularities or chemical impurities at the core/cladding interface may not distribute smoothly.
Figure 1 shows the unavoidable propagation loss inherent in silica fibers. In the vicinity of 1.55 μm (just the wavelength region where the erbium-doped fiber amplifier works well), the minimum loss is about 0.2 dB/km. Some telecommunication fibers developed for long-distance fiber-optic communications have almost achieved low-loss levels, which require very pure glass materials. If the fiber contains hydroxyl (OH) ions, additional peaks at 1.39 μm and 1.24 μm can be seen in the loss spectrum.
Figure 1: Intrinsic loss of silica. At long wavelengths, infrared absorption associated with vibrational resonances dominates. At shorter wavelengths, Rayleigh scattering at the unavoidable density fluctuations of glass is more important.
If the fiber loss is only 0.2 dB/km, this means that even after a propagation distance of 100 km, there is still 1% of the original optical power. This is usually enough to reliably detect data signals, even at very high bit rates.
Multimode fibers generally have higher propagation losses because they generally have a higher numerical aperture.
For example, bend loss is the propagation loss caused by the strong bending of an optical fiber. Usually, this loss is negligible under normal conditions, but increases dramatically once a certain critical bending radius is reached. For fibers with strong guiding properties (high numerical aperture), the critical radius is quite small – it can be as small as a few millimeters. However, for single-mode fibers with large effective mode areas (large mode area fibers with very low numerical apertures), it can be much larger—typically tens of centimeters. Such fibers must remain straight during use.
For the calculation of bending loss, there are analytical formulas based on simplified models, which may or may not accurately reflect reality. Numerical beam propagation is usually the preferred method; it does not require stronger simplifications and tells us in detail what happens to the light.
For example, consider a few-mode fiber with a fiber radius of 20 μm and a numerical aperture of 0.05. As a test, we lined up the fiber so that the bend becomes tighter and tighter along the length of the fiber: the radius of inflection increases linearly with the propagation distance. The emitted light is entirely in the fundamental mode.
Figure 2: Amplitude distribution of increasing bends along the fiber. The beam propagation was numerically simulated using RP Fiber Power software.
Figure 2 shows the simulated amplitude distribution in the yz plane. It can be seen that the mode becomes more and shifted to one side (outside of the bend curve), becomes very small and ends up losing more and light to the cladding. In the middle (z = 100 mm), the bending radius has reached 50 mm; this is approximately the critical bending radius.
For the LP 11 mode, the attenuation due to bending loss becomes more severe, as shown in Fig. 3. Here, the bending loss is set earlier and essentially all power is lost after 120 mm.
Figure 3: Same as Figure 2, but for LP 11 mode.
In general, the critical bending radius is much larger for higher order modes. (This is sometimes used to filter out higher-order modes.) Figure 4 shows how the numerically simulated bend loss for all modes depends on the bend radius:
Figure 4: Bending loss as a function of bend radius for different guided modes of the fiber.