VI.  Dispersion

Dispersion, expressed in terms of the symbol Dt, is defined as pulse spreading in an optical fiber. As a pulse of light propagates through a fiber, elements such as numerical aperture, core diameter, refractive index profile, wavelength, and laser linewidth cause the pulse to broaden. This poses a limitation on the overall bandwidth of the fiber as demonstrated in Figure 8-3.

Figure 8-3  Pulse broadening caused by dispersion

Dispersion Dt can be determined from Equation 8-7

  Dt = (Dtout – Dtin)1/2

(8-7)

and is measured in time, typically nanoseconds or picoseconds. Total dispersion is a function of fiber length. The longer the fiber, the more the dispersion. Equation 8-8 gives the total dispersion per unit length.

  Dttotal = L × (Dispersion/km)

(8-8)

The overall effect of dispersion on the performance of a fiber optic system is known as intersymbol interference (Figure 8-4). Intersymbol interference occurs when the pulse spreading caused by dispersion causes the output pulses of a system to overlap, rendering them undetectable. If an input pulse is caused to spread such that the rate of change of the input exceeds the dispersion limit of the fiber, the output data will become indiscernible.

Figure 8-4  Intersymbol interference

Dispersion is generally divided into two categories: modal dispersion and chromatic dispersion.

Modal dispersion is defined as pulse spreading caused by the time delay between lower-order modes (modes or rays propagating straight through the fiber close to the optical axis) and higher-order modes (modes propagating at steeper angles). This is shown in Figure 8-5. Modal dispersion is problematic in multimode fiber, causing bandwidth limitation, but it is not a problem in single-mode fiber where only one mode is allowed to propagate.

Figure 8-5  Mode propagation in an optical fiber

Chromatic dispersion is pulse spreading due to the fact that different wavelengths of light propagate at slightly different velocities through the fiber. All light sources, whether laser or LED, have finite linewidths, which means they emit more than one wavelength. Because the index of refraction of glass fiber is a wavelength-dependent quantity, different wavelengths propagate at different velocities. Chromatic dispersion is typically expressed in units of nanoseconds or picoseconds per (km-nm).

Chromatic dispersion consists of two parts: material dispersion and waveguide dispersion.

  Dtchromatic = Dtmaterial + Dtwaveguide

(8-9)

Material dispersion is due to the wavelength dependency on the index of refraction of glass. Waveguide dispersion is due to the physical structure of the waveguide. In a simple step-index-profile fiber, waveguide dispersion is not a major factor, but in fibers with more complex index profiles, waveguide dispersion can be more significant. Material dispersion and waveguide dispersion can have opposite signs depending on the transmission wavelength. In the case of a step-index single-mode fiber, these two effectively cancel each other at 1310 nm, yielding zero-dispersion. This makes very high-bandwidth communication possible at this wavelength. However, the drawback is that, even though dispersion is minimized at 1310 nm, attenuation is not. Glass fiber exhibits minimum attenuation at 1550 nm. Coupling that with the fact that erbium-doped fiber amplifiers (EDFA) operate in the 1550-nm range makes it obvious that, if the zero-dispersion property of 1310 nm could be shifted to coincide with the 1550-nm transmission window, high-bandwidth long-distance communication would be possible. With this in mind, zero-dispersion-shifted fiber was developed.

When considering the total dispersion from different causes, we can approximate the total dispersion by Dttot.

 

(8-10)

where Dtn represents the dispersion due to the various components that make up the system. The transmission capacity of fiber is typically expressed in terms of bandwidth × distance. For example, the bandwidth × distance product for a typical 62.5/125-mm (core/cladding diameter) multimode fiber operating at 1310 nm might be expressed as 600 MHz · km. The approximate bandwidth of a fiber can be related to the total dispersion by the following relationship

  BW = 0.35/Dttotal

(8-11)

Dispersion-shifted fiber: By altering the design of the waveguide, we can increase the magnitude of the waveguide dispersion so as to shift the zero-dispersion wavelength to 1550 nm. This type of fiber has an index profile that resembles a “W” and hence is sometimes referred to as W-profile fiber (Figure 8-6).

Figure 8-6  W-profile fiber

Although this type of fiber works well at the zero-dispersion wavelength, in systems in which multiple wavelengths are transmitted, such as in wavelength-division multiplexing, signals transmitted at different wavelengths around 1550 nm can interfere with one another, resulting in a phenomenon called four-wave mixing, which degrades system performance. However, if the waveguide structure of the fiber is modified so that the waveguide dispersion is further increased, the zero-dispersion point can be pushed past 1600 nm (outside the EDFA operating window). This means that the total chromatic dispersion can still be substantially lowered in the 1550-nm range without having to worry about performance problems. This type of fiber is known as nonzero-dispersion-shifted fiber. Figure 8-7 compares the material chromatic and wavelength dispersions for single-mode fiber and dispersion-shifted fiber.

Figure 8-7  Single-mode versus dispersion-shifted fiber