Basic optical laws and definitions

FTTH - Optical laws

We shall next review some of the basic optical laws and definitions relevant to optical fibers. A fundamental optical parameter of a material is the refractive index (or index of refraction). In free space a light wave travels at a speed c = 3e8 m/s. The speed of light is related to the frequency ν and the wave-lenght λ by c = νλ. Upon entering a dielectric or nonconducting medium the wave now travels at a speed of light in a vacuum to that in matter is the index of refraction n of the material and is given by
n = c/ν

Typical values of n are 1.00 for air, 1.33 for water, 1.50 for glass, and 2.42 for diamond. The concepts of reflection and refraction can be interpreted most easily by considering the behavior of light rays associated with plane waves traveling in a dielectric material. When a light ray enconunters a boundary separating two different media, part of the ray is reflected back into the first medium and the remainder is bent (or refracted) as it enters the second material. This is shown in the next figure where n2n1 sin(ϕ1) = n2 sin(ϕ2)

or, equivalently, as
n1 cos((ϕ1) = n2 cos(ϕ2)

where the angles are defined in the figure. The angle ϕ1 between the incident ray and the normal to the surface is known as the angle of incidence.

According to the law of reflection, the angle θ1 at which the incident ray strikes the interface is exactly equal to the angle that the reflected ray makes with the same interface. In addition, the incident ray, the norhaml to the interface, and the reflected ray all lie in the same plane, which is perpendicular to the interface plane between th two materials. This is called the plane of incidence. When light traveling in a certain medium is reflected off an optically denser material (one with a higher refractive index), the process is referred to as external reflection. Conversely, the reflection of light off of less optically dense material (such as light traveling in glass being reflected at a glass-air interface) is called internal reflection.

As the angle of incidence ϕ1 in an optically denser material becomes larger, the rfracted angle ϕ2 approaches (pi)/2. Beyond this point no refraction is possible and the light rays become totally internally reflected. The conditions requiered for total internal reflection can be determined by using Snell`s law. Consider the next figure, wich shows a glass surface in air. A light ray gets bent toward the glass surface as it leaves the glass in accordance withs Snell`s law. If the angle of incidence ϕ1 is increased, a point will wventually be reached where the light ray in air is parallel to the glass surface. This point is known as the critical angle of incidence ϕc. When the incidence angle (fi)1 is greater than the critical angle, the condition for total internal reflection is satisfied; that is, the light is totally reflected back into the glass with no light escaping from the glass surface. (This is an idealized situation. In practice, there is always some tunneling of optical energy throug the interface. This can be explained in terms of the electromagnetic wave therory of light).

As an example, consider the glass-air interface shown in last figure. When the light ray in air is parallel to the glass surface, then ϕ2 = 90º so that sinϕ2 = 1. The critical angle in the glass is thus
sinϕc = n2/n1

In addition, when light is totally internally reflected, a phase change δ occurs in the reflected wave. This phase change depends on the angle θ1 < π/2 - ϕc

17-4-2008

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