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:
• geometrical-optics description
• wave propagation
• dispersion in single-mode fibres
• 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).
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 , .
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.