Optical Fibres

12.1 Total Internal Reflection in Fibres

An optical fibre consists of a core (refractive index $n_1$) surrounded by a cladding ($n_2 \lt n_1$). Light is guided by total internal reflection.

The numerical aperture:

$\mathrm{NA} = \sin\theta_{\mathrm{max} = \sqrt{n_1^2 - n_2^2}}$

Where $\theta_{\mathrm{max}}$ is the maximum acceptance angle for light entering the fibre.

12.2 Modes in Optical Fibres

The number of modes supported depends on the V-number:

$V = \frac{2\pi a}{\lambda}\mathrm{NA}$

Where $a$ is the core radius.

• Single-mode fibre: $V \lt 2.405$. Only the fundamental HE$_{11}$ mode propagates.
• Multimode fibre: $V \gt 2.405$. Multiple modes propagate, causing modal dispersion.

12.3 Attenuation

Fibre attenuation is dominated by Rayleigh scattering ($\propto \lambda^{-4}$) and infrared absorption Peaks. The minimum attenuation for silica fibre is $\sim 0.2$ dB/km at $\lambda \approx 1550$ nm.