## Definition

A light guide is a device used to direct light from a light source (commonly an LED) to a place where the light is needed. Light guides are also sometimes referred to as light pipes.

Light guides are usually made of glass or plastic, which typically have an index of refraction around 1.5. Light that is injected into the light guide within the correct range of angles becomes trapped inside the guide because of a phenomenon called total internal reflection, or TIR. Once trapped, the light remains inside the guide until it is extracted by an extraction feature, is fully absorbed by the material, or encounters a surface at less than the critical angle.

In some cases, the goal is to move the light from one end of the guide to the other. In other cases, the goal is to extract the light along the length of the light guide and send it in a specific direction. This makes the light guide appear lit. This extraction is achieved by adding components to the device like paint dots or textures (small bumps or holes) that influence the way the light is reflected, breaking the TIR condition and causing the light to exit the light guide.

Other types of light guides are used to homogenize light emerging from one or more light sources. By allowing light to travel down the length of a guide while reflecting off the sides, the light is “mixed,” and the light emerging from the end of the light guide is spatially and angularly uniform.

Figure 1: The light guide in this example is a mixing rod that you might find in a projector. The light guide is used to homogenize the light coming from a traditional light source and reflector. At the input side, light peaks sharply in the center; at the output side, light is spatially uniform across the exit face of the guide, which has a 16:9 aspect ratio.

## What is the index of refraction?

For materials that transmit light, such as glass, water, or air, the index of refraction indicates the speed at which light will travel through the material. The higher the index, the slower light travels through the material. The index of a material is given by the equation:

Where n is the index of refraction, c is the speed of light in a vacuum, and v is the phase velocity of the light in the material. A vacuum, while not strictly a material, has an index of 1. Water has an index of 1.3333. Glasses and plastics typically used for light guides have an index of about 1.45 to 1.6 for visible light.

When light encounters a boundary between two materials with different indexes of refraction, the light that transmits through the boundary is bent, which changes the direction of the light. This process is called refraction and is governed by Snell’s Law.

## What is Snell’s Law?

Snell’s Law tells us that the angle at which the light emerges depends on both the angle that the light hits the boundary and the difference in the refractive index of the material. The higher the index difference and the greater the angle of incidence, the greater the bending. Snell’s Law governing refraction, where n is the index of refraction, and θ is the angle of incidence of the light in either material 1 or material 2:

Figure 2: A ray of light refracting through a flat surface, bending in the process. The dotted line represents the normal to the material boundary, and the quantities used by Snell’s Law are noted on the figure.

## What is the critical angle?

If we solve Snell’s Law for the exit angle of the light, we get:

For the special case where the light starts inside the material with the higher of the two indices, we find that there is an angle θ1 beyond which the equation cannot be solved. This happens when the expression inside the square brackets is greater than 1. The value for θ1 where the expression in square brackets just evaluates to 1 is called the critical angle and is given by the equation:

As an example, for a material of index 1.5 in air (index 1), you get a critical angle of 41.81o. Light that strikes the surface at an angle greater than this critical angle cannot refract, and so 100% of the light is reflected back into the material -- causing total internal reflection.

## What is total internal reflection?

Total internal reflection occurs when light that is inside a material such as glass or plastic encounters a boundary with a material with a lower index of refraction (typically air) at an angle greater than the critical angle. For certain shapes, such as rectangular plates or pipes, cylinders, or spheres, it is possible for light to become trapped inside the guide until it reaches the edges or end of the guide. This is what allows the light to be transported from the original light source down the guide to the other end with minimal losses.

Figure 3: This fan of light rays starts inside a plate light guide with parallel boundaries. Each ray emerges from the starting point and strikes the glass-air boundary. Some of the rays refract (and exit), but those that strike the boundary at an angle above the critical angle TIR and reflect back into the light guide. Rays that TIR continue to TIR along the length of the guide.

Figure 4: A very simple cylindrical light guide with a small LED light source on the left. Light enters the light guide through the end face of the cylinder, and 100% of the light TIRs and is trapped in the light guide, transmitting to the opposite end, where it exits.

## Extracting light along the length of a light guide

If the purpose of the light guide is to extract light along the length of the guide, then the designer can use extraction features along the length of the guide. These features can take many forms, but some of the more common features are paint dots and small, prism-like structures cut into the guide often referred to as textures, shown in the figure below. These extraction features change the direction of the light that strikes the feature, breaking the TIR cycle and extracting the light from the guide. By varying the density or size of the extraction features, it is possible to achieve uniform light output or even a desired pattern from the light guide. With some textures, it is also possible to control the direction of the light that exits the light guide.

Figure 5: Here we see the same light guide as in the previous figure, but this time, extraction features have been added to the side of the light guide opposite the viewing direction. You can clearly see that some of the light previously trapped in the guide is now being extracted, and the amount of light trapped in the guide decreases the farther you go away from the light source. Notice that some of the light is also extracted in the direction opposite the viewing directly, which is normally not desired. This can be remedied by adding a reflective surface on the texture side of the light guide to recycle the light back into the guide.

## Light guides come in many shapes and sizes

Light guides do not have to be long and straight. They can be bent into complicated shapes. They can taper or flare or change their cross-sectional shape as desired. They can take on very complicated shapes that are often used to light up automotive instrument panels, automotive exterior lighting applications, and keypads on hand-held devices.

Figure 6: This light guide has a complex shape that might be used in automotive interior or exterior applications. On the right, you can see a close-up of the extraction features.

Some of the most important light guides are flat sheets used to light up flat-panel displays for televisions, monitors, watches, etc. These types of light guides are thin, flat sheets of material with extraction features molded into one face. Light is injected into the light guide from one or more edges, usually with LEDs. By carefully distributing the extraction features, the desired output pattern, which usually uniform, is achieved. Because of the complexity of the system, illumination design software is required to optimize the texture placement to achieve the desired light distribution.

Figure 7: This figure shows a flat-panel type light guide for a small, hand-held device. Light is injected into the light guide at the bottom by three LEDs. Extraction features are located on the bottom of the guide only in locations where the designer wants to extract light to illuminate controls. The image on the right shows the resulting light pattern.

Light guides can also take the form of optical fibers. Optical fibers are very thin, flexible “wires” of glass composed of a high index central core and a lower index cladding. Optical fibers are very useful for transmitting light over a great distance and are widely used in diverse applications such as telecommunications, medical imaging, and laser surgery.

## What effect does shape have on the light guide?

While light guides can bend and take on more complex shapes, it is at these bends where much of the light leakage occurs. At a bend, some of the light trapped by TIR can encounter the guide boundary at less than the critical angle and escape the light guide. This needs to be carefully managed through design and simulation in software.

Figure 8: This cylindrical light guide has a 65-degree bend and loses about 10% of the light. The tighter the bend, the more light will escape the light guide at the bend.

Tapering a light guide can also cause leakage. In general, increasing the cross-section as you move away from the light source does not cause an issue, but decreasing the cross-section usually leads to losses either through leakage or by reversing the light inside the guide and sending it back toward the light source. This is especially true if the light being inserted into the light guide covers a large angular range.

Figure 9: This cylindrical light guide has been tapered to increase the cross-section toward the end opposite the light source. In this case, 100% of the light is transmitted through the guide to the exit surface.

Figure 10: This is the same light guide as in the Figure 9, but the taper is reversed to reduce the cross-section of the guide. In this case, the light leakage is substantial, and only about 6% of the light reaches the exit surface.

## Why are light guides important?

A light guide can be used to channel light to places where it’s difficult or impossible to put the light source itself. For example, a light guide can be used to separate a light source from an extreme environment, or to place the source and its associated electronics in a more convenient location. An example of this is to use extracting light guides to replace fluorescent lighting in freezer cases, allowing for the light source to be placed outside the freezer for increased energy efficiency. Another example is creating light for a surgical environment without putting electronics near a patient.

With the appropriate light extraction techniques, light guides can be designed in a variety of shapes, providing more stylistic freedom that make them especially popular for modern headlight and taillight designs. Many manufacturers use uniquely shaped exterior lighting designs as a distinctive branding element for their cars. Additional automotive applications for light guides include instrument and other dashboard lighting, as well as map lights and accent lights throughout the interior.

Figure 11: Here we see light guides used in an automotive tail lamp. The light guides are used both as a signaling device and as a styling queue.

Many light guides are used to distribute light evenly across an extended area. The applications are quite diverse, from information display to control illumination to accent lighting. By being able to distribute the light, an illumination engineer can make use of a smaller number of high-power sources, simplifying the system and saving money. And because it works with energy-saving LEDs, a light guide can provide an efficient, cost-saving solution in many lighting scenarios.

## How do you design a light guide?

Although light guides are passive devices that are relatively simple, the way light interacts with them is complex. Designing a light guide that performs properly and has the right lit appearance requires careful engineering. Illumination simulation tools such as LightTools and LucidShape provide illumination engineers with the proper set of tools for designing, optimizing, and analyzing the performance of a light guide/light source combination before spending the time, money, and effort to produce a prototype. Once satisfied with the performance of the model in software, the engineer can implement a prototype and check the simulation results against actual measurements.

Extracting light guides are even more complex to design. Textures must be properly placed to achieve the desired output from the light guide. The engineer must also verify the direction in which the extracted light goes, which impacts the brightness and appearance of the lit light guide. Doing this and managing the complex shapes required of many light guides requires a specialized tool. Both LightTools and LucidShape offer the Light Guide Designer tool, which automates the entire process of creating, designing, optimizing, and evaluating the performance of extracting light guides.