The phenomenon of light propagating in a curved optical fiber, despite traveling in a straight line, is known as total internal reflection. It occurs due to the principle of Snell's law and the specific geometry of the fiber.
When light travels from one medium to another with a different refractive index (such as from air to the core of an optical fiber), it bends or refracts at the interface between the two mediums. The amount of bending depends on the angle of incidence and the refractive indices of the two materials involved.
In an optical fiber, the core, which is the region through which light propagates, has a higher refractive index compared to the cladding surrounding it. This refractive index difference allows for the phenomenon of total internal reflection to occur.
When light enters the core of the optical fiber at an angle larger than the critical angle (a specific angle determined by the refractive indices of the core and cladding), it undergoes total internal reflection. This means that instead of refracting out of the fiber, the light reflects off the boundary between the core and cladding, bouncing back into the core.
As the light continues to propagate through the fiber, it encounters multiple reflections at different points along the fiber's curved path. These reflections effectively "trap" the light within the core and guide it along the fiber, allowing it to propagate over long distances without significant loss of intensity.
The curved shape of the fiber helps maintain the total internal reflection by ensuring that the light continually strikes the core-cladding interface at angles larger than the critical angle, even if the fiber bends. This is why light can propagate in a curved optical fiber without deviating from its path or escaping the fiber.
It's important to note that while the light travels in a curved path within the fiber, the individual photons or light particles still follow a straight-line trajectory between reflections. It's the collective effect of all the photons bouncing off the fiber's boundaries that gives rise to the curved propagation of light in an optical fiber.