In this chapter we will discuss properties of the linear fibre, where refractive index does not depend on field intensity. We will concentrate on the following topics:

1. • geometrical-optics description

2. • wave propagation

3. • dispersion in single-mode fibres

4. • dispersion-induced limitations.

Due to dispersion, the width of propagating pulse will increase. In multimode fibres, broadening of optical pulses is significant, about 10 ns km−1. In the geometrical-optics description, such broadening is attributed to different paths followed by different rays. In a single mode fibre, intermodal dispersion is absent; all energy is transported by a single mode. However, pulse broadening exists. Different spectral components of the pulse travel at slightly different group velocities. This effect is known as group velocity dispersion (GVD).

Geometrical-optics description

Consider an optical fibre whose cross-section is shown in Fig. 5.1. The corresponding change in refractive index profiles is shown in Fig. 5.2. We illustrate two profiles: step index and graded index.

In the following discussion we will assume validity of a geometrical optics description which holds in the limit λ ≪ a, where λ is the light wavelength, and a is the core radius [1], [2].

Numerical aperture (NA)

To start our discussion, consider the propagation of rays entering a cylindrical fibre at different angles in the plane passing through the core centre, see Fig. 5.3. Ray B will travel in the cladding region and it is known as an unguided ray, whereas ray A will stay within core region, and it will form a guided ray.