2.1         Optical fiber

2.1.1         Optical fiber principle

An optical fiber consists of an inner cylinder with a diameter of a few micrometers (core) surrounded by an outer cylindrical layer of smaller refractive index (cladding), as seen in Fig. 2-1. The refractive index difference ensures total reflections at the core-cladding interface, allowing for propagation of the light along the fiber. The maximum entrance angle q (Fig. 2-1) corresponds to an internal reflection angle at the critical angle q_c, and it is found from the law of refraction (Snell's Law)

Fig. 2-1 Fiber geometry for total reflection at the critical angle

The numerical aperture NA of the fiber is defined as n₀×sin(q), and it can be found from equations (2-1), and the following relation is obtained :

where n1 and n2 are the refractive index of the core and the cladding, respectively. The electromagnetic field propagation in waveguides was solved at the beginning of the 20^th century from Maxwell's equations and it was shown that a finite number of modes can propagate along the fiber (Appendix A). Waveguides as optical fibers also support radiative modes, which form a continuum and correspond to unguided refracted rays. All the guided modes have their own propagation velocity and their specific field distribution. Moreover, the guided modes present a cutoff wavelength, apart from the lowest order mode.

The entire fiber can also guide modes with the propagation conditions at the cladding-air interface. Such modes are called cladding modes. Energy transfer is possible between the core modes and the cladding modes.

Pure silica glasses are mainly used to fabricate optical fibers. Adding dopants like germanium, nitrogen, and phosphorus in the fiber core creates the refractive index difference between the core and the claddings and modifies the core photosensitivity. Co-dopants like tin and boron are used to modify the fiber numerical aperture and the photosensitivity. Optically active fibers are obtained by integration of rare earth dopants. Sufficient index difference and fairly close thermal-expansion coefficients have to be guaranteed. Standard telecom fibers are made of pure silica claddings and about 3% wt. germanium doped silica core. Other glass materials are sometimes used as borosilicate (for example in polarization maintaining fibers, as shown in section 2.1.2) and fluoride glasses.