Propagation Losses in Optical Fibers

When light propagates as a guided wave in a fiber core, it experiences some power losses. These are particularly important for long-haul data transmission through fiber-optic telecom cables.

Usually, the propagation losses are approximately constant on the way, with some attenuation coefficient α. The power then simply decays in proportion to exp(−αz), where z is the propagation distance. The losses are often specified in dB/km; that value is ≈4.343 times the power attenuation coefficient in 1/km. Of course, the losses are dependent on the optical wavelength.

Origins of Propagation Losses

Propagation losses in fibers can have various origins:

  • The material may have some intrinsic absorption. For example, silica fibers increasingly absorb light when the wavelength gets longer than ≈1.7 μm. Therefore, they are rarely used for wavelengths longer than 2 μm.
    Additional isolated absorption peaks can result from certain impurities. For example, silica fibers exhibit increased absorption losses around 1.39 μm and 1.24 μm if the core material is not water-free.
  • At short wavelengths, Rayleigh scattering in the glass becomes more and more important; the contribution of Rayleigh scattering to the attenuation coefficient scales with the inverse fourth power of the wavelength. Note that the core glass, being an amorphous material, is microscopically never fully homogeneous; there are “frozen-in” density fluctuations which are unavoidable even with most modern fiber fabrication technology.
  • There is also some inelastic scattering – spontaneous Raman scattering and Brillouin scattering. These effects are measurable via the scattered (and frequency-shifted) light, but normally do not contribute substantially to propagation losses. However, Raman and Brillouin scattering can lead to huge losses (by transfer of energy to other wavelengths) at high optical intensities, where stimulated scattering is possible.
  • Increased scattering losses can result from irregularities of the core/cladding interface. This problem is more severe for fibers with large refractive index contrast (high numerical aperture). Also, a large index contrast often means higher germania doping of the core, which makes it tentatively less homogeneous. Therefore, low-loss single-mode fibers for long-haul data transmission through telecom fiber cables are made with relatively small NA, even though a higher NA would provide a more robust guidance.
  • Further, there can be bend losses (see below).

Intrinsic losses are usually quite uniform over the length of a fiber. For additional losses, that is not necessarily the case; for example, irregularities of the core/cladding interface or chemical impurities may not be smoothly distributed.

Figure 1 shows the intrinsic unavoidable propagation losses of silica fibers. There is a loss minimum of ≈ 0.2 dB/km around 1.55 μm (which happens to be the wavelength region where erbium-doped fiber amplifiers work well). Some telecom fibers as developed for long-haul optical fiber communications nearly reach that low loss level, which requires a very pure glass material. If the fiber contains hydroxyl (OH) ions, additional peaks at 1.39 μm and 1.24 μm can be seen in the loss spectrum.

intrinsic losses of silica

Figure 1: Intrinsic losses of silica. At long wavelengths, infrared absorption related to vibrational resonances are dominating. At shorter wavelengths, Rayleigh scattering at the unavoidable density fluctuations of the glass is more important.

If the fiber losses are only 0.2 dB/km, this means that even after 100 km of propagation distance one still has 1% of the original optical power. That is often sufficient for reliable detection of data signals, even at very high bit rates.

Multimode fibers often have somewhat higher propagation losses, because they often have a higher numerical aperture.

Bend Losses

Bend losses are propagation losses which arise from strong bending of a fiber, for example. Typically, such losses are negligibly small under normal conditions, but steeply increase once a certain critical bend radius is reached. That critical radius is rather small for fibers with robust guiding characteristics (high numerical aperture) – it can be as small as a few millimeters. However, for single-mode fibers with large effective mode areas (large mode area fibers having a very low numerical aperture), it can be much larger – often tens of centimeters. Such fibers then have to be kept quite straight during use.

For the calculation of bend losses, there are certain analytical formulas, based on simplified models, which may or may not accurately reflect reality. Numerical beam propagation is often the method of choice; it does not require stronger simplifications and tells us in detail what happens to the light.

As an example, consider a few-mode fiber with a core radius of 20 μm and a low numerical aperture of 0.05. As a test, we arrange the fiber such that the bending becomes tighter and tighter along the length of the fiber: the inverse radius of curvature increases linearly with the propagation distance. The launched light is entirely in the fundamental mode.

amplitude distribution along the fiber

Figure 2: Amplitude distribution along the fiber for increasing bending. The beam propagation was numerically simulated with the RP Fiber Power software.

Figure 2 shows the simulated amplitude distribution in the y-z plane. One can see that the mode gets more and shifted to one side (the outer side of the bending curve), gets substantially smaller, and finally loses more and light to the cladding. In the middle (z = 100 mm), the bend radius has reached a value of 50 mm; that is about the critical bend radius.

For the LP11 mode, attenuation through bend losses gets more serious, as shown in Figure 3. Here, the bend losses set in earlier, and basically all power is lost already after 120 mm.

沿光纤的振幅分布

Figure 3: Same as Figure 2, but for the LP11 mode.

Typically, the critical bend radius is significantly larger for higher-order modes. (That is sometimes exploited for filtering out higher-order modes.) Figure 4 shows how the numerically simulated bend losses of all modes depend on the bend radius:

amplitude distribution along the fiber

Figure 4: Bend losses as a function of the bend radius for different guide modes of the fiber.

Polarization Issues

Birefringence in Nominally Symmetric Fibers

In principle, a fiber with a fully rotationally symmetric design should have no birefringence. It should thus fully preserve the polarization of light. In reality, however, some amount of birefringence always results from imperfections of the fiber (e.g., a slight ellipticity of the fiber core), or from bending. Therefore, the polarization state of light is changed within a relatively short length of fiber – sometimes only within a few meters, sometimes much faster.

Note that the index difference between polarization directions is not necessarily larger in fibers than in other devices. However, fibers tend to be long, so that even weak index differences can have substantial effects.

Another important aspect is that the resulting polarization changes are not only random and unpredictable, but also strongly dependent on the wavelength, the fiber’s temperatures along its whole length, and on any bending of the fiber. Therefore, it often doesn’t help that much to adjust a polarization state, e.g. using a fiber polarization controller (see below); some slight changes of environmental parameters or wavelength may again spoil the polarization.

Fiber Polarization Controllers

Strong bending of a fiber introduces birefringence. This means that some appropriate length of fiber, bent with a certain radius and fixed on a coil, can have a relative phase delay of π, or π/2, for example, between the two polarization directions. It can thus act like a λ/2 waveplate (half-waveplate) or a λ/4 waveplate (quarter-waveplate). If one rotates the whole coil around an axis which coincides with the incoming and outgoing fiber, one obtains a similar effect as for rotating a bulk waveplate in a free-space laser beam. One often uses a combination of an effective quarter-waveplate coil with a half-waveplate coil and another quarter-waveplate coil in series to transform some input polarization state into any wanted polarization state. Such a fiber polarization controller (Figure 5) can work over some substantial wavelength region.

fiber polarization controller

Figure 5: A “bat ear” polarization controller, containing three fiber coils which can be rotated around the input fiber’s axis.

As mentioned before, the problem may remain that the input polarization state drifts with changing environmental conditions, so that the fiber polarization controller would have to be realigned frequently in order to preserve a constant output polarization state.

Polarization-maintaining Fibers

Fibers can be made polarization-maintaining (PM fiber) – but not by avoiding any birefringence! To the contrary, one intentionally introduces a significant birefringence. Such fibers are thus high-birefringence fibers (HIBI fibers).

There are essentially two common ways for doing that:

  • A fiber can be made with an elliptical core. This results in some level of form birefringence. Of course, the fiber modes will also be affected by the elliptical shape, and the efficiency of coupling light to or from fibers with circular core is somewhat reduced.
  • Some mechanical stress can be applied, e.g. by introducing stress rods made from a different glass. See Figure 6 for some typical realizations.

保偏光纤

Figure 6: Polarization-maintaining PANDA fiber (left) and bow-tie fiber (right). The built-in stress elements, made from a different type of glass, are shown with a darker gray tone.

Note: a polarization-maintaining fiber does not preserve any polarization state of injected light! It does so only for linearly polarized light, where the polarization direction must be one of two orthogonal directions, e.g. along a line between the stress rods or perpendicular to it. The β value for some wavelength will significantly depend on that polarization direction.

What happens if we inject monochromatic with some other linear polarization direction? That can be considered as a superposition of the two basic polarization states. After a short length of propagation, these components will have acquired significantly different phase delays (due to their different β values). Therefore, they will no longer combine to the original linear polarization state, but rather in general to some elliptical state. After integer multiples of the polarization beat length, however, one again obtains a linear polarization.

For non-monochromatic light, the situation becomes even more complicated. Over some length of fiber, the different wavelength components will experience different polarization-dependent phase shifts, so that the resulting polarization state becomes wavelength-dependent. To convert that back into a linear state would be difficult task – a simple polarization controller could not do that.

The need to align the input polarization state to a fiber axis in order to have the polarization preserved is of course a serious practical disadvantage of PM fibers. It requires more work to fabricate PM fiber-optic setups, for which additional equipment is required. Also, not all fiber components are available as PM versions. On the other hand, detrimental effects of drifting polarization states, which may otherwise require other measures, are safely avoided with PM setups.

Note that the introduced birefringence essentially removes any effect of some small additional random birefringence, as can result from moderate bending, for example. Such random influences may only very slightly change the local polarization, but will normally not have any significant effect on longer lengths. One can understand this by considering mode coupling: significant mode coupling requires a perturbation which has a period equal to the beat period of the two polarization states. For strong birefringence, that beat period (the polarization beat length) is rather short (for example, a few millimeters), and the usual perturbations are spatially too “slow” to cause any significant coupling, or at least do not have a strong spatial Fourier component according to the polarization beat.

Polarization-insensitive Designs

Another way of eliminating polarization issues is to design devices such that polarization does not matter. This approach is usually taken in optical fiber communications, for example. One simply takes care that no components are used which could cause substantial polarization-dependent losses, or which would rely on a certain polarization state. For example, one generally cannot use electro-optic modulators, and needs to carefully design any semiconductor devices for low polarization dependence. Some polarization effects still remain, which may limit the performance of very fast fiber-optic links. In particular, there is the phenomenon of polarization mode dispersion (PMD), which may be quantified as a differential group delay (DGD): signal components with different polarization may require slightly different times for traveling through a fiber cable, and that may deteriorate the signal quality. For short transmission distances and/or moderate bit rates, however, PMD is not a big issue.

 

Source:rp-photonics