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Different fiber modes can be created by launching the two rays at a different launch angle 6i (see Figure 8.10). The amplitude of the electric field for each mode is 0 at the interface between the core and the cladding, as in the case of m = 0, discussed above. However, zero amplitude points (known as null points) can be also created inside the core. For instance, in Figure 8.11, we show examples of the amplitude of the electric field of a formed beam where it has a null point in the center of the core (m = 1), and where it has two null points inside the core (m = 2). In general, the different modes in a fiber are numbered 0, 1, 2, and so on. Also, the number of a mode is equal to the number of null points inside the core of the fiber associated with the mode.
As shown in Figure 8.8, a lens is used to focus the launched light onto a small area of the core. As a result, there are many different rays that enter the fiber at different launch angles, and thus many different fiber modes are created and propagated down the core of the fiber. In other words, the propagation of the light through the fiber core, is done in terms of different modes all propagating down the fiber core. In Figure 8.12, various modes for a step-index and a graded-index fiber are shown. As mentioned above, the path of a ray through a step-index fiber is a straight line until it gets reflected into another straight line. On the other hand, the path of a ray through a graded-index fiber is a curve.
m = 0 m = 1 m = 2
Figure 8.11 Electric field amplitudes for various fiber modes.
OPTICAL FIBERS AND COMPONENTS
(a) Step-index fiber
(b) Graded-index fiber
Figure 8.12 Propagation of modes.
Figure 8.13 Single-mode fiber.
The number of modes in a fiber is related to the diameter of the core. As shown in Table 8.1, multi-mode fibers have a large core diameter, and the light propagates through the core in different modes, as explained above. Single-mode fibers (see Figure 8.13) have a core with a very narrow diameter that only permits the propagation of the single ray with mode 0 (i.e., m = 0).
The transmission of light through an optical fiber is subjected to optical effects, known as impairments. There are linear and non-linear impairments.
Linear impairments are due to attenuation and dispersion. Attenuation is the decrease of the optical power along the length of the fiber. Dispersion is the distortion of the shape of a pulse. These impairments are called linear because their effect is proportional to the length of the fiber.
Non-linear impairments can be due to the dependency of the refractive index on the intensity of the applied electrical field. The most important non-linear effects in this category are: self-phase modulation and four-wave mixing. Another category of non-linear impairments includes the stimulated Raman scattering and stimulated Brillouin scattering. These two impairments are due to the scattering effects in the fiber medium because of the interaction of light waves with phonons (molecular vibrations) in the silica medium. All of these impairments are called non-linear because when they occur the response of a medium such as silica, is a non-linear function of the applied electric and magnetic field amplitude.
HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER
We now proceed to examine the two linear impairments: attenuation and dispersion. Attenuation
Attenuation varies with wavelength and is defined in decibel per kilometer. A decibel (dB) is a unit used to express the relative difference in signal strength; it is calculated as follows:
where Pi is the optical power input to the fiber and P0 is the optical power output from the fiber. The attenuation for any length of fiber is adBL, where adB is the attenuation expressed in decibels per kilometer, and L is the length of the fiber.
Attenuation is due to a number of reasons, such as: absorption, Rayleigh scattering, and reflections due to splices and connectors.
• Absorption: The light is absorbed as it passes through the optical fiber.
• Rayleigh scattering: The density of the particles of the core is not always the same due
to imperfections of the fiber. This causes the light to be scattered. Long wavelengths have less scattering.
• Reflection by splices and connections: A long fiber link typically consists of several
segments connected through splices. There might also be connectors for connecting users. Both splices and connectors reflect back in the opposite direction of the fiber
some of the light, thus reducing the power of the light moving forward.
As mentioned above, attenuation varies with the wavelength. Figure 8.14 gives the attenuation for a single-mode fiber as a function of the wavelength. The attenuation for short wavelengths (round 850 nm) is more than three times the attenuation for the long wavelengths (1300 nm and 1550 nm). Typically, the windows near 850 nm, 1300 nm, and 1550 nm are used.