Optical fibers are designed to transmit light from one end of the fiber to the other with minimal loss of energy. The principle of operation in an optical fiber is total internal reflection. When light passes from one material to another, its direction is changed. According to Snell’s Law, the new angle of the light ray can be predicted from the refractive indices of the two materials. When the angle is perpendicular (90º) to the interface, transmission into the second material is maximum and reflection is minimum. Reflection increases as the angle gets closer to parallel to the interface. At the critical angle and below the critical angle, transmission is 0% and reflection is 100% (see figure below).
Snell’s Law can be formulated to predict critical angle and also the launch or exit angle θmax from the index of refraction of the core (n1) and cladding (n2) materials. The angle also depends on the refractive index of the media (n).
The left side of equation is called the numerical aperture (NA), and determines the range of angles at which the fiber can accept or emit light.
Most Ocean Optics fibers have a numerical aperture of 0.22 (see table below). If the fiber is in a vacuum or air, this translates into an acceptance angle θmax of 12.7° (full angle is ~25o). When light is directed at the end of an optical fiber all the light rays or trajectories that are within the ±12.7° cone are propagated down the length of the fiber by total internal reflection. All the rays that exceed that angle pass through the cladding and are lost. At the other end of the fiber, light exits in a cone that is ±12.7°.
There are many types of fibers available, with a variety of numerical apertures. While a fiber with a larger numerical aperture will collect more light than a fiber with a smaller numerical aperture, it is important to look at both ends of the system to ensure that light exiting at a higher angle can be used. In optical sensing, one end is gathering light from an experiment and the other is directing light to a detector. Any light that does not reach the detector will be wasted.
|Fiber Type||Numerical Aperture||Full Angle|