Several factors enter into how fibers collect light and propagate it. Most arise from the structure of fibers, described in Chapter 4. This section examines the impact of those considerations.
Table of Contents
Core Size and Mode-Field Diameter
Core size is important in coupling light into a fiber. The core must be aligned with the light-emitting region of a laser or LED light source, or the output end of another fiber. To collect light efficiently, the core should be at least as large as the light source. As shown in Figure 5.3, if the light source is larger than the fiber, much of its light goes right into the cladding and quickly escapes from the fiber. The larger the core diameter, the easier it is to align with the light source to collect light. This is purely a matter of geometry, matching the light source to the collecting aperture. Core size does not directly affect the acceptance angle of a fiber, the range of angles over which it collects light.
Core size is the physical dimension of the core, but light spreads through a slightly larger volume, including the inner edge of the cladding. This mode-field diameter or effective area
Figure 5.3 The match between light-source dimensions and core diameter helps determine light transfer.
is the critical dimension for light transfer between single-mode fibers. (The difference is not enough to matter in multimode fiber.)
A second factor in determining how much light a fiber collects is its acceptance angle, the range of angles over which a light ray can enter the fiber and be trapped in its core. The full acceptance angle is the range of angles at which light is trapped; it extends both above and below the axis of the fiber. The half acceptance angle is the angle measured from the fiber axis to the edge of the cone of light rays trapped in the core; it is shown in Figure 5.4.
The standard measure of acceptance angle is the numerical aperture, NA, which is the sine of the half-acceptance angle, , for reasonably small angles. For a step-index fiber, it is defined as
where n0, is the core index and n1 is the cladding index. A typical value for step-index single-mode fiber is around 0.14.
Numerical aperture is nor calculated the same way in graded-index fibers; strictly speaking it varies across the core with the refractive index. However, you can measure numerical
Figure 5.4 Light rays have to fall within a fiber’s acceptance angle, measured by NA, to be guided in the core.
aperture by monitoring the divergence angle of light leaving a fiber core. As shown in Figure 5.5, the light emerging from a multimode fiber spreads over an angle equal to its acceptance angle. For practical measurements, care must be taken to eliminate modes guided along the cladding, and the edge of the beam is defined as the angle where intensity drops to 5% that in the center. NA can be calculated easily from the acceptance angle. Typical NA values are 0.20 for 50/125 graded-index fiber, and about 0.28 for 62.5/125 graded-index fiber.
Core diameter does not enter into the NA equation, but light rays must enter the core as well as fall within the acceptance angle to be guided along a fiber. Large core size and large NA do not have to go together, but in practice larger-core fibers tend to have larger core-cladding index differences and thus larger NAs. For example, step-index multimode fibers typically have NAs of at least 0.3, more than twice the value for single-mode step-index fibers.
The numerical aperture of single-mode fibers is defined by the same equation as for multimode fibers, but light does not spread out from them in the same way. (They carry only a single mode, and their cores are so small that another wave effect called diffraction controls how light spreads out from the end.) NA generally is not as important for single-mode fibers as it is for multimode fibers.
Cladding Modes and Leaky Modes
As we have seen earlier, not all light aimed into a fiber is guided along the core. Some enters the cladding at the end of the fiber; other light escapes from the core by hitting the core-cladding boundary at greater than the confinement angle. This light excites cladding modes, which can propagate in the cladding.
Total internal reflection at the boundary between cladding and the surrounding material can guide light in the cladding just as it guides light along an unclad fiber. This can happen as long as the surrounding material—air or a plastic coating—has a lower refractive index than the cladding. This might sound like a good way to maximize light transmission, but it's usually undesirable. It can introduce noise in communication fibers and crosstalk between adjacent fibers in an imaging bundle. To prevent this, manufacturers often coat fibers with a plastic having a higher refractive index than the cladding, so light striking the cladding-coating boundary leaks out. The fibers in rigid bundles sometimes are separated by "dark" glass, which absorbs light so it can't pass between claddings.
In multimode fibers, the boundary between modes guided in the core and modes confined to the cladding is not sharp. Some light falls into intermediate leaky modes, which propagate partly in both core and cladding. These modes travel much farther than cladding modes but also are prone to leakage and loss.
Both cladding and leaky modes can lead to spurious results in fiber measurements, so mode strippers have been developed to remove them. These devices work by surrounding part of the fiber with a material having a refractive index equal to or larger than that of the cladding, preventing total internal reflection at the outer boundary of the cladding. Light that leaks into this material is absorbed and lost from the fiber. A long length of fiber also can serve as a mode stripper if the cladding attenuation is much higher than that of the core.
A variety of outside influences can change the physical characteristics of optical fibers, affecting how they guide light. Typically these effects are modest and must be enhanced or accumulated over long distances to make the kind of sensors described in Chapter 29. However, significant losses can arise if the fiber is bent so sharply that light strikes the core-cladding interface at a large enough angle that the light can leak out.
Bending loss is easiest to explain using the ray model of light in a multimode fiber. When the fiber is straight, light falls within its confinement angle. Bending the fiber changes the angle at which light hits the core-cladding boundary, as shown in Figure 5.6. If the bend is sharp enough, it hits the boundary at an angle outside the confinement angle c, and is refracted into the cladding where it can leak out.
Bend losses fall into two broad categories. Macrobends are single bends obvious to the eye, such as a fiber bent sharply where a cable ends at a connector. The case shown in Figure 5.6 is typical. Microbends are tiny kinks or ripples that can form along the length of fibers that become squeezed into too small a space. This can happen in a cable when the cabling ma-
Figure 5.6 Light can leak out of a bent fiber.
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