FOA Guide

Total Internal Reflection - The Basic Principle of Optical Fiber - And Fiber Numerical Aperture

Background: Optical Fiber  

Optical fiber uses the optical principle of "total internal reflection" to capture the light transmitted in an optical fiber and confine the light to the core of the fiber. An optical fiber is comprised of a light-carrying core in the center, surrounded by a cladding that acts to traps light in the core. Glass fiber is covered by a plastic buffer coating that protects it from the environment and allows easy handling for splicing or termination.


The index of refraction of glass or any optical material is a measure of the speed of light in the material and changes in index of refraction are what causes light to bend - as shown in this photo of a plastic rod in a pond:


Beyond a certain angle, the refraction will cause light to be reflected from the surface. Optical fiber uses this reflection to "trap" fiber in the core of the fiber by choosing core and cladding materials with the proper index of refraction that will cause all the light to be reflected if the angle of the light is below a certain angle. We call that "total internal reflection."

Total Internal Reflection In Optical Fiber
There is an angle that for any given fiber defines total internal reflection. At higher angles a ray of light will still be refracted but not enough to be reflected back into the core, so it is lost in the cladding of the fiber. Below that angle, it will be reflected back into the core of the fiber and transmitted to the end of the fiber. The angle of total internal reflection defines the "numerical aperture" (NA) of the fiber, a standard fiber specification.

You can demonstrate this principle with a large plastic rod (~25mm/i" diameter) and a laser pointer - a powerful green laser works  best.

    how fiber works demo

To duplicate this experiment, you need a plastic rod (Acrylic rods
~25mm/i" diameter are available from online sellers. The end used for the laser needs polishing to remove the saw marks on most commercially available rods, so first use some very fine polishing paper (1200-3000 grit) then finish with microfinishing polishing film  (30-3 microns) or polishing compound (toothpaste, jewelry of auto polishing compounds.) You should end up with a transparent end.

Total internal Reflection In Action - Step Index Multimode Fiber

Step index multimode fiber was the first fiber design. The core of step index multimode fiber is made completely of one type of optical material and the cladding is another type with different optical characteristics. It has higher attenuation and is too slow for many uses, due to the dispersion caused by the different path lengths of the various modes traveling in the core. Step index fiber is not widely used - only POF and PCS/HCS (plastic or hard clad silica, plastic cladding on a glass core) use a step index design today. POF is mainly used for consumer audio and TV links.

Step Index Optical Fiber

Let's Do The Physics And Math

Total internal reflection is a principle described by Snell's Law of optics. Snell's law describes how light bends when traveling through the boundary of two different optical materials, such as air and water as shown in the photo of a pole in water above. Here is the more scientific definition.

Snell's Law

In the drawing above, the left shows a section of an optical fiber with a ray of light. On the right is a diagram of the index of refraction of the glass in the fiber. The core glass is n1 and the cladding glass is n2, and the core glass is of slightly higher refractive index, ~1.46 to the cladding at ~1.45.

Snell's Law
Remember basic trigonometry? The sine is the ratio of the side of a right triangle to the hypotenuse - the long side opposite the right angle. The refractive index of the glass (n)  is defined as the ratio of the speed of light in a vacuum (c) to the actual speed of light in the material (v) like this:

definition of refractive index
Using Snell's Law, we can calculate the angle at which an optical fiber begins total internal reflection, which happens like this drawing below, when the refracted ray lays along the boundary between the core and the cladding. We'll do this for a core index of 1/46 and a cladding index of 1.45, the values we discussed above.

Snell's law critical angle

We need to manipulate the equations somewhat.


That indicates that a ray 6.8 degrees off axis (90 - 83.2 degrees) or less will see total internal reflection. Another way of thinking about it is the acceptance cone of the fiber is twice that angle or about 14 degrees. This also process also defines the definition of the NA or numerical aperture of the fiber, but the calculation used is a mathematical manipulation of the critical angle calculation.


The numerical aperture of an optical fiber is an abstract term for the acceptance angle of the fiber. If we continue using the fiber we define above, the equation becomes:


That's a half angle of 9.8 degrees when used to calculate the angle - the total cone angle is ~20 degrees..

Table of Contents: The FOA Reference Guide To Fiber Optics



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