Return Loss of a Glass-Air Interface

...the acquisition of knowledge is hard ... Our minds are prone to illusions, fallacies, and superstitions ....

Introduction

Figure 1: Return Loss Measurement Example.

I received an email today about a deployment issue that involved the reflection of light from unterminated connectors. When light travels down a fiber and encounters a change in the index of refraction, part of the energy will reflect back toward the transmitter because of a phenomenon called Fresnel reflection, which I define below (source).

Fresnel reflection is something we all encounter in our daily life. It is what causes the reflections we see in our windows. Here is a quote from an optics text.

When a ray of light strikes a change of refractive index, and is approaching at an angle close to normal, most of the light passes straight through....  Most of the light but not all. A very small proportion is reflected back off of the boundary. We have seen this effect with normal window glass. Looking at a clean window we can see two images. We can see the scene in front of us and we can also see the faint reflection of what is behind us. Light therefore is passing through the glass and is also being reflected off the surface.

Background

Definitions

We quantify the size of this return "echo" using a parameter called return loss. Let's begin by precisely defining both Fresnel reflection and return loss. Note the 4% transmission loss (aka reflected power) figure highlighted below – I will be explaining where this comes from later.

Fresnel Reflection

In optics, the reflection of a portion of incident light at a discrete interface between two media having different refractive indices. Fresnel reflection occurs at the air-glass interfaces at the entrance and exit ends of an optical fiber. Resultant transmission losses, on the order of 4% per interface, can be reduced considerably by the use of index-matching materials. The coefficient of reflection depends upon the refractive index difference, the angle of incidence, and the polarization of the incident radiation. For a normal ray, the fraction of reflected incident power is given by

where R is the reflection coefficient and n₁ and n₂ are the respective refractive indices of the two media.

Return Loss

In telecommunications, return loss is the loss of power in the signal returned/reflected by a discontinuity in a transmission line or optical fiber. This discontinuity can be a mismatch with the terminating load or with a device inserted in the line. It is usually expressed as a ratio in decibels (dB):

where RL(dB) is the return loss in dB, P_i is the incident power and P_r is the reflected power.

Connector Types

Figure 2 shows common ways of polishing the end of a fiber. Fiber-To-The-Home system usually use the Angle Polished Connector (APC) type because we do not want the reflections to interfere with our analog video transmission, which are VERY sensitive to reflections. The Ultra-Polished Connectors (UPC) are used for most other applications.

Figure 2: Common Fiber-Optic Connector Polishing.

Usage Example

I usually see the return loss expressed in terms of dB. For example, the following quote is from an ADC document on connectors

When connectors are unmated — such as unused ports in an FTTP distribution frame—the return loss for APC connectors is -65 dB or greater, compared to UPC connectors that will be in the neighborhood of 14 dB. This is an important consideration for building today’s FTTX architectures.

I will show that the 4% and 14 dB numbers actually represent the same value, which I will demonstrate next.

Analysis

Figure 2 shows how you compute the reflection percentage and the return loss for the fiber/air interface that you encounter with an unterminated, Ultra-Polished Connector (UPC).

Figure 2: Return Loss and Reflection Percentage Calculation.

Conclusion

Just a short calculation, but I wanted to document it so that people can see where the 4% and 14 dB numbers come from.