Light Guide in Glass Fiber

The fundamental function of any optical fiber is to guide light, i.e. act as a dielectric waveguide: light injected into one end should remain guided in the fiber. In other words, it must be prevented from being lost, for example by reaching outer surfaces and escaping from there. We’re talking about glass fibers here, but plastic fibers work the same way.

In principle, the simplest solution for guiding light is a uniform glass rod. (If thin enough, it can also bend to some extent.) The outer surface can reflect light by total internal reflection. Due to the large refractive index contrast, this works for a rather wide range of input beam angles, without requiring any power loss in principle.

Figure 1: Total internal reflection can be used to guide light in a homogeneous fiber. Note that only partial reflections occur on the end faces with smaller angles of incidence.

However, this simple solution has some key drawbacks:

• Due to the high refractive index contrast, even tiny scratches in the glass on the outer surface can cause substantial optical loss due to scattering. Therefore, the outer surface must be of high optical quality and be well protected against damage and dirt. This problem can only be alleviated to a certain extent with some suitable buffer coating around the fiber. Such coatings are not highly uniform and hardly provide very low optical loss.
• Even if the fiber is very thin (e.g. 0.1mm diameter), it will support a large number of modes (see part 2), which is bad, for example when maintaining high beam quality is important.

However, one can modify the very clean coating idea: use another glass region, with a slightly lower refractive index than the core glass, as cladding:

Figure 2: Multimode glass fiber with cladding, made of glass with a slightly lower refractive index. Total internal reflection occurs at the glass/glass interface, but the angle of incidence needs to be larger.

This gives us several advantages:

• Glass is cleaner and more evenly coated than plastic buffers. This has cut losses.
• Small irregularities at the interface do not cause as severe optical loss as glass/air interfaces due to the reduced refractive index contrast at the reflection point. Irregularities at the external interface no longer matter because light cannot “see” them.
• The guiding region (called the fiber core) can now be made much smaller than the entire fiber if desired. The core size can be adjusted, for example to accommodate the size of some small light emitters.
• Combined with small core size and weak index contrast, even single-mode guidance can be obtained (see below).

Note, however, that smaller index contrast means smaller acceptance angles: total internal reflection occurs only at angles of incidence above the critical angle. The maximum angle of incidence at the fiber input facet is determined by the numerical aperture (NA):

NA is the sine of the maximum angle of incidence on the input face. In the formula, n 0 is the refractive index of the medium around the fiber, which is close to 1 in air.

Consider the volatility of light

The preceding considerations are based on a simple geometric ray diagram. Especially in the domain of small cores and weak refractive index contrast, this simple picture no longer represents an accurate model of light propagation because it ignores the wave nature of light. So now let’s consider the nature of waves.

First, we imagine a Gaussian beam in a homogeneous medium (for example, some glass). Even if such a beam initially has a flat wavefront, within one Rayleigh length it starts to diverge significantly:

Figure 3: Gaussian beam at vacuum wavelength 1.5 μm in homogeneous glass. It initially spreads in an almost parallel fashion, but eventually diverges.

Divergence is closely related to the curvature of the wavefront. Clearly, the wavefront on the beam axis advances faster in the z direction than the wavefront at higher or lower positions. This observation can lead to a thought: Can’t we counteract the bending of the wavefront by slightly slowing down the light near the beam axis? This can be done by using a non-uniform structure with an increased refractive index in the central region. In fact, if we simply increase the core index by 0.014 within a radius of 3 μm, this works perfectly:

Figure 4: Gaussian beam injected into a step-index fiber structure. The two horizontal gray lines indicate the location of the core/cladding interface. Using RP Fiber Power

Then the numerical aperture is 0.3. Almost all light of the injected Gaussian beam is directed. Even lower index contrast is sufficient if we make the initial beam radius and core area larger.

Note that the guiding of the light will work even if the fiber is not perfectly straight but somewhat bent. If the bend is not too strong, the bend loss (that is, the power loss due to bending) is small enough to be ignored.