Figure 1: Total internal reflection can be used to guide light in a homogeneous fiber. Note that only partial reflection occurs at the end faces, where the angle of incidence is smaller.

However, this simple solution has some crucial disadvantages:

Due to the high index contrast, even tiny scratches of the glass on the outer surface could lead to substantial optical losses by scattering. Therefore, the outer surface would have to be made with high optical quality and well protected against damage and dirt. This problem can be mitigated only to some extent with some suitable buffer coating around the fiber; such coatings, not being highly homogeneous, can hardly provide very low optical losses.

All Dielectric Self-supporting Aerial Cable

Even if the fiber were pretty thin (e.g., with a diameter of 0.1 mm), it would support a huge number of modes, which is bad e.g. when preserving a high beam quality is important.

One can, however, modify the idea of a very clean coating: use another glass region, having a slightly smaller refractive index than the core glass, as a cladding:

Figure 2: A multimode glass fiber with a cladding, made of glass with a slightly lower refractive index. Total internal reflection can occur at the glass/glass interface, but the incidence angles need to be larger.

Numerical Aperture

The NA is the Sine of the maximum angle of incidence at the input face. In the equation, n0 is the refractive index of the medium around the fiber, which is close to 1 in case of air.

Particularly in the domain of small cores and weak index contrasts, the simple ray picture does no more represent an accurate model for light propagation, as it ignores the wave nature of light. So let us now consider the wave nature.

First, we imagine at a Gaussian beam in a homogeneous medium (e.g., some glass). Even if such a beam has flat wavefronts initially, within one Rayleigh length it will start diverging significantly:

Figure 3: A Gaussian beam with 1.5 μm vacuum wavelength in a homogeneous glass. It initially propagates in a nearly parallel fashion, but eventually diverges.

The divergence is intimately related to a curvature of the wavefronts. Apparently, the wavefronts on the beam axis progress faster in z direction than those at higher or lower positions. That observation can trigger an idea: couldn't we work against that bending of wavefronts by somewhat slowing down the light near the beam axis? That could be done by using an inhomogeneous structure, with a somewhat increased refractive index in the central region. Indeed, this works quite well if we simply increase the core index by 0.014 within a radius of 3μm:

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