What a Difference a Cladding Makes

The photographs on the previous page illustrated that whether or not light is trapped in the fiber depends upon the angle at which it enters the fiber as well as the materials used for the core and the cladding. The standard case to consider is when light enters one end of the fiber that is perpendicular to the edges defined by the core/cladding interface, as is the case in the photographs. Angles of entry θ₀ that result in light being trapped within the fiber lie within the cone of acceptance. Consider the water-clad fiber of the previous page.

(a)

light escaping the fiber
(b)

The observant student will notice that Figure (a), with its smaller entry angle θ_0a=37.9°, shows light striking the right side of the fiber at a larger angle than it does in Figure (b), which has θ_0b=52.3°. Indeed, the smaller the angle θ₀ at which light enters the fiber, the larger the angle at which the light will strike the side of the fiber. Each choice of core-cladding indices has a distinct critical angle for light to be trapped, so each will have a corresponding maximum entry angle θ_0max. This limit θ_0max is called the cut-off angle. Only light entering the fiber at an angle less than θ_0max will be trapped in the fiber. These angles lie within a cone, as shown here, so the cone of acceptance is aptly named.

To summarize: Total internal reflection occurs at the core-cladding interface for angles greater than the critical angle θ_c; such angles are achieved for angles of entry less than the cut-off angle θ_0max.

(a) An entrance angle of 37.9° results in the light being trapped within the water-clad fiber.
(b) This entry angle of 52.3 ° is outside the cone of acceptance, so light escapes the water-clad fiber.

Here we've seen that adding a non-air cladding does more than just protect the core - it restricts the size of the cone of light that can be trapped in the fiber. While at first this might seem undesirable, this restriction enables fibers with a cladding to carry information at a much higher bit rate than those without a cladding. Light entering the fiber at larger angles will strike the fiber walls at smaller angles and ultimately travel a longer distance, as illustrated below. This means that the large-θ₀ portions of a light signal will take longer to reach the end of the fiber than will the small-θ₀ portions. A pulse sent using a large cone of acceptance will thus spread out more than a pulse sent using a narrow cone of acceptance, limiting how quickly the next pulse can be sent. This topic is discussed in more depth in the module on modes.

The path of light within a fiber for two different angles of entry. Light entering at the larger angle, θ_0b, bounces more times in the fiber and thus takes a longer path as it travels down the fiber.