The Optical Fiber

An optical fiber is essentially a dielectric (silica glass) waveguide consisting of a core and cladding. The core is usually has a circular cross-section (although elliptical or other cross-sections are also used) and is made of doped silica of refractive index slightly higher than that of the cladding (which is made of pure silica). Light waves are guided along the fiber via total internal reflection. If light is launched at an angle greater than the critical angle, the rays are reflected back into the core from the surface separating the core and cladding. The rays travel along the length of the fiber by continuous reflections of this type. Rays launched at different angles travel along different paths (or modes) and arrive at the receiver at different times, leading to inter-modal dispersion. Fibers are classified as single-mode or multi-mode depending on whether they support one or more. Single mode fibers have narrow cores, typically $10\nu$m. Multimode fibers have core dimensions $\sim 5$ times larger. The number of modes a given fiber can support is characterized by the $V$ number, which depends on the frequency, the core radius and the refractive indices of the core and the cladding.

$$V = {\omega \over c} a \sqrt {{n_1}^2 - {n_2}^2}$$ (22.3.2)

where $n_1,~n_2$ are the refractive indices of the core and cladding, $a$ is the radius of the core and $\omega$ is the angular frequency of the light being transmitted through the fiber. The number of modes $N$ is given by $N = V^2/2$. Multimode fibers have bandwidths that are $\sim 100$ times smaller than single mode fibers and are best suited to short haul applications. In addition to the number of modes supported, the polarization properties of the fiber are also of interest. One can make fibers that maintain the polarization state of the transmitted light by proper choice of core cross-section and refractive index gradient across the core and the cladding.

Dispersion is an important characteristic of an optical fiber, it determines the bandwidth and channel carrying capacity of the fiber. here are three kinds of dispersion viz: inter-modal dispersion, material dispersion and waveguide dispersion. Inter-modal dispersion occurs because of the different modes in which the light propagates in the fiber travel different paths. This causes differences in the arrival time of the rays at the receiver and hence a distortion of the signal. Inter-modal dispersion is less in fibers which have a parabolic refractive index parabolic profile in the core region. This change in refractive index causes a change in the light travel time in different parts of the core which partially compensates for the different path lengths. Material and waveguide dispersion are wavelength dependent. Material dispersion arises because of variation in the refractive index of the core material (i.e. silica ) across the transmission band. Waveguide dispersion is due to the propagation constant (i.e. the inverse of the group velocity) dependent property of the medium. The derivative of the propagation constant w.r.t frequency is dependent on the frequency itself, even in the absence of material dispersion.

Dispersion affects both the temporal and spectral characteristics of the signals and it is essential to minimize it as far as possible. This can be done by

1. Choosing the 1300 nm window where dispersion is minimum. It may be noted that dispersion for silica fiber is minimum in the 1300 nm band( typically 2 ps/km-nm) compared to that at the 1550 nm band (15 ps/km-nm). However the attenuation is higher in the 1300 nm band (0.31dB/km) than that in the 1550 nm band (0.15 dB/km).
2. Choosing a laser with line-width as small as possible($<1$ nm), like a single longitudinal mode type or DFB laser.
3. Using external modulation. Unlike direct modulation, external modulation does not affect the physical mechanism of the laser and does not introduce spreading of frequency or chirping.
4. Using dispersion compensation. This is essential achieved by proper design of the refractive index gradient across the fiber.