The basic principle of optical fiber light guidance

Light is an electromagnetic wave, and wave theory is generally used to analyze the basic principles of light guidance. However, according to optical theory, in a space where the size is much larger than the wavelength and the refractive index changes slowly, the propagation phenomenon of light waves can be analyzed using the method of "light", that is, geometric optics. This is completely applicable to multimode optical fibers in optical fibers. For this reason, the method of geometric optics is used for analysis.
1. Snell's Law
When light is incident from a dense material (large refractive index) to a sparse material, it is refracted, as shown in Figure (a). The angle of refraction is greater than the angle of incidence, that is, when n1＞n2, θr＞θi.
The mathematical relationship between n1, n2, θr, and θi is:

2. Fiber structure
In addition to applying Snell's theorem, the fiber structure must also be used to analyze the principle of fiber light guidance. The fiber is cylindrical and consists of a double-layer structure of two concentric cylinders: a glass fiber core (fiber core) and a glass sheath (cladding).

Fiber structure
The core is located in the center of the fiber, where light is mainly transmitted. The core refractive index n1 is slightly larger than the cladding refractive index n2. A good optical interface is formed between the two layers, and light is reflected and propagated on this interface.

3. Fiber Optic Light Guiding Principle and Numerical Aperture NA
The angle of intersection between the incident light AB and the fiber axis OO is θi. After the incident light is refracted (the refraction angle is θj) to the interface between the core and the cladding point C, and forms an angle θk with the interface normal DE at point C, and is refracted from the interface to the cladding. The angle between CK and DE is θr. Then

When θr<90º, sinθi>NA, θi>arcsin NA, and the light disappears.
This shows that arcsinNA is a critical angle. All light with incident angle θi＞arcsinNA cannot propagate into the optical fiber and disappear in the cladding; on the contrary, only light with incident angle θi＜arcsinNA can enter the optical fiber and be totally reflected and propagated.