# Optical Fiber Waveguides

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A circular dielectric waveguide or fiber optic has an internal core that has a higher index of refraction than the cladding. At a certain diameter there is an angle that is less than the critical angle so there is total internal reflection.

These are referred to as step index fibers. The y axis refers to the index of refraction. The x axis is the distance from the center of the core. So the highest index of refraction (n_{1}) is found in the core and there is a significant step in the index of refraction (n_{2}) at the interface with the cladding.

In most practical waveguides the refractive indices of the core and cladding differ from each other by only a few percent.

The number of modes in a step-index circular waveguide is determined by the V parameter where

where

- is the core radius

- is referred to as the numerical aperature, the larger this term the larger the number of modes.

The fiber can support only one mode when V < 2.405

For n_{1} = 1.48 and n_{2} = 1.46, the radius of the core a <2.7μm

There is current research to develop a core with a graded index of refraction that gradually decreases to equal that of the cladding. This is referred to as a graded index fiber.

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