Fiber Attenuation

Overview

The attenuation of an optical fiber measures the amount of light lost between input and output. Total attenuation is the sum of all losses. It is dominated by imperfect light coupling into the fiber and absorption and scattering within the fiber. Sometimes other effects can cause important losses, such as light leakage from fibers that suffer severe microbending. Attenuation limits how far a signal can travel through a fiber before it becomes too weak to detect.

Absorption and scattering are both cumulative, with their effects increasing with fiber length. In contrast, coupling losses occur only at the ends of the fiber. The longer the fiber, the more important are absorption and scattering losses, and the less important coupling losses. Conversely, attenuation and scattering may be much smaller than end losses for short fibers.

To briefly review these losses, when you deliver an input power, P„, to a fiber, a fraction of that light, P, is lost. Hills only the power P0 –P gets into the fiber. This light then suffers absorption and scattering loss in the bulk of the fiber. As you learned in Chapter 2, these losses depend on length. If the light lost to absorption per unit length is and the light lost to scattering per unit length is S, the fraction of light that remains is (1 – – S). Outside the research laboratory, the quantity that matters is the attenuation per unit length, which is the sum of the absorption and scattering ( + S).

Recall that to calculate the power remaining after a distance D, you raise the fraction of light remaining after attenuation to the power D. This gives a formula for power at a distance D

That formula is more useful for looking at the process of light loss than for calculations. It reminds us that absorption and scattering combine to make attenuation, which always takes the same fraction of the light passing through each chunk of fiber. It also reminds us that attenuation acts only on light that gets into the fiber, because some light is lost on entry.

Now let's look at each of these components of loss.

Absorption

Every material absorbs some light energy. The amount of absorption depends on the wavelength and the material. A thin window of ordinary glass absorbs little visible light, so it looks transparent to the eye. The paper this book is printed on absorbs much more visible light, so it looks opaque. (You can read these words because the blank paper reflects more light than the ink, which absorbs most light striking it and reflects little.) The amount of absorption can vary greatly with wavelength. The clearest glass is quite opaque at an infrared wavelength of 10 µm. Air absorbs so strongly at short ultraviolet wavelengths that scientists call ultraviolet wavelengths shorter than about 0.2 µm the vacuum ultraviolet because only a vacuum transmits them.

Absorption depends very strongly on the composition of a substance. Some materials absorb light very strongly at wavelengths where others are quite transparent. For glass, this means that adding small amounts of certain impurities can dramatically increase absorption at wavelengths where glass is otherwise transparent. Removing such impurities was a crucial step to making the extremely transparent fibers used for communications. Typically, absorption is plotted as a function of wavelength. Some absorption peaks can look quite narrow because the material absorbs light in only a narrow range of wavelengths; others spread across a wider range.

Absorption is uniform. The same amount of the same material always absorbs the same fraction of light at the same wavelength. If you have three blocks of the same type of glass, each 1-centimeter thick, all three will absorb the same fraction of the light passing through them.

Absorption also is cumulative, so it depends on the total amount of material the light passes through. That means a material absorbs the same fraction of the light for each unit length.

If the absorption is 1% per centimeter, it absorbs 1% of the light in the first centimeter, and 1% of the remaining light the next centimeter, and so on. If the only thing affecting light is absorption, the fraction of light absorbed per unit length is a and the total length is D, the fraction of light remaining after a distance D is

In our example, this means that after passing through 1 m (100 cm) of glass, the fraction of light remaining would beAtoms and other particles inevitably scatter some of the light that hits them. The light isn't absorbed, just sent in another direction in a process called Rayleigh scattering, after the British physicist Lord Rayleigh, as shown in Figure 5.1. However, the distinction between scattering and absorption doesn't matter much if you are trying to send light through a fiber, because the light is lost from the fiber in either case.

Like absorption, scattering is uniform and cumulative. The farther the light travels through a material, the more likely scattering is to occur. The relationship is the same as for light absorption, but the fraction of scattered light is written S.

Scattering depends not on the specific type of material but on the size of the particles relative to the wavelength of light. The closer the wavelength is to the particle size, the more scattering. In fact, the amount of scattering increases quite rapidly as the wavelength decreases. For a transparent solid, the scattering loss in decibels per kilometer is given by

where A is a constant depending on the material. This means that dividing the wavelength by 2 multiplies scattering loss (in dB/km) by a factor of 16.Scattering and absorption combine to give total loss, or attenuation, which is the important number in communication systems. Figure 5.2 plots their contributions across the range of wavelengths used for communications. Attenuation normally is measured in decibels per kilometer for communication fibers. The plot shows small absorption peaks from traces of metal impurities remaining in the glass and other absorption arising from bonds that residual hydrogen atoms form with oxygen in the glass. (I picked this scale to emphasize the peaks, which look lower on other scales, and are smaller in many communication fibers.) The absorption at wavelengths longer than 1.6 µm comes from silicon-oxygen bonds in the glass; as the plot shows, the absorption increases rapidly at longer wavelengths. As a result, silica-based fibers are rarely used for communications at wavelengths longer than 1.65 µm.

Rayleigh scattering accounts for most attenuation at shorter wavelengths. As you can see in Figure 5.2, it increases sharply as wavelength decreases. The space between measured total attenuation and the theoretical scattering curve represents the absorption loss. The closer the two lines, the larger the fraction of total attenuation that arises from scattering. The rapid decrease in scattering at longer wavelengths makes loss lowest in the "valley" around 1.55 µm, where both Rayleigh scattering and infrared absorption are low. Except for the infrared absorption of silica, fiber loss would decrease even more at longer wavelengths.

The plot in Figure 5.2 compares theoretical scattering and the absorption of pure silica with attenuation measured across the spectrum. It is total attenuation that is important in fiberoptic communications, and that is what is generally measured. Absorption and scattering are hard to separate, and outside the laboratory there is little practical reason to bother. It's most useful to think of the power (P) at a distance D along the fiber as defined by

where A is attenuation per unit length, P0 is initial power, and P is the coupling loss, as before. In practice, it is simpler to make calculations if you first separate fiber attenuation from coupling losses by starting with the power that enters the fiber rather than the input power you attempt to couple into the fiber.

Calculating Attenuation in Decibels

As we saw in Chapter 2, attenuation measures the ratio of input to output power: Pout/Pin. It normally is measured in decibels, as defined by the equation

Output power is less than input power, so the result would be a negative number if the equation didn't include a minus sign. You should remember that in some publications decibels are defined so that a negative number indicates loss.
Decibels may seem to be rather peculiar units, which appear to understate high attenuation. For example, a 3-dB loss leaves about half the original light, a 10-dB loss leaves 10%, and a 20-dB loss leaves 1%. The larger the number, the larger the apparent understatement. A 100-dB loss leaves only 10–10 of the original light, and a 1000-dB loss leaves 10–100—a ratio smaller than one atom in the whole known universe. Appendix B translates some representative decibel measurements into ratios. You can also use the simple conversion

Decibels are very convenient units for calculating signal power and attenuation. Suppose you want to calculate the effects of two successive attenuations. One blocks 80% of the input signal, and the second blocks 30%. To calculate total attenuation using fractions, you must convert both absorption figures to the fractions of power transmitted, then multiply them, and convert that number from the fraction of light transmitted to the fraction attenuated. If you use decibels, you merely add attenuations to get total loss.

The calculations are even simpler if you know the loss per unit length and want to know total loss of a longer (or shorter) piece of fiber. Instead of using the exponential formula mentioned previously, you simply multiply loss per unit length times the distance:
You can also measure power in decibels relative to some particular level. In fiber optics, the two most common decibel scales for power are decibels relative to 1 mW (dBm) and relative to 1 µW (dBµ). Powers above those levels have positive signs; those below have negative signs. Thus 10 mW is 10 dBm, and 0.1 mW is –10 dBm, or 100 dBµ.

If everything is in decibels, simple addition and subtraction suffice to calculate output power from input power and attenuation. You also can write the equation in other ways:

Note that it is vital to keep track of the plus and minus signs. In this case, we give loss in decibels a positive sign, as we did earlier. If you ever feel confused, you can do a simple truth test, by checking to see if the output power is less than the input. (The only way output can be more than input is if you have an optical amplifier or regenerator somewhere in the system.)

As an example of how the calculations work, consider a fiber system in which 3 dB is lost at the input end and that contains 6 km of fiber with loss of 0.5 dB/km. If the input power is 0 dBm (exactly 1 mW), the output is

If you rewrite this as milliwatts, you have 0.25 mW.

Spectral Variation

As we saw before, fiber attenuation is the sum of absorption and scattering, both of which vary with wavelength. The spectral variation depends on the fiber composition. The attenuation curve in Figure 5.2 is fairly typical for single-mode communication fibers, but some types have much lower water peaks at 1380 nm, as described below.

Most single-mode communication fibers are used at wavelengths between about 1280 and 1650 nm, where attenuation is generally below 0.5 dB/km except at the water peak where it may reach 1 dB/km. The traditional transmission bands in that region are at 1310 nm, and in the region from about 1530 to 1620 nm where erbium-doped fiber amplifiers are used. Fibers are available that have water content reduced to such low levels that the 1380-nm water peak almost vanishes, allowing them to be used across the entire 1280 to 1650-nm range.

Attenuation generally is higher in commercial graded-index multimode fibers, with typical values about 2.5 dB/km at 850 nm, 0.8 dB/km at 1310 nn, and no more than 3 dB/km at the 1380 nm water peak. As can be seen from Figure 5.2, attenuation is not particularly low at 850 nm; the attraction of that wavelength is its match to the output of galliumarsenide light sources.

Other materials are used in fibers for other wavelengths. Special grades of quartz are used for ultraviolet-transmitting fibers. Some plastics have relatively even transmission across the visible spectrum. Fluoride compounds are transparent at longer infrared wavelengths than silica glass. Chapter 6 will cover various materials in more detail.

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