Physics 106 - How Things Work - Spring, 1999

Problem Set #10 - Solutions

Fiber optic cables are quite important to modern communication technology. Optical fibers are essentially pipes for light, carrying that light almost without loss to destinations far away. At its most basic level, an optical fiber is a single glass filament that's coated with a layer of another glass. When light passing through the core glass hits the outer glass coating, that light reflects perfectly. As a result, the light is trapped in the fiber's core and follows it indefinitely.

1. Although the outer glass coating is as clear as the inner glass core, the two glasses are different. Light travels more slowly through the glass used to make the coating than it does through the glass used to make the core. Why does this difference in light speed cause light passing through the core to reflect perfectly whenever it tries to enter the coating at a shallow or "glancing" angle?

Answer: The light experiences total internal reflection.

Why: When light hits a surface at a shallow angle and would speed up on the far side of this surface, it bends away from the perpendicular to that surface. If the bend is extreme enough, the light won't even enter the second material at all. Instead, it will reflect perfectly in a process known as total internal reflection.

2. Although thin glass fibers are remarkably flexible, you must be careful not to bend an optical fiber too sharply. The problem isn't breakage, although it is possible to snap the fiber if you fold it completely in half. The problem is light leakage. When the fiber bends too sharply, light begins to leak out of the glass core and into the outer coating. Why does bending the fiber sharply spoil the perfect reflection?

Answer: Bending the fiber will change the angle at which light in the core hits the coating glass. When the bend is sharp enough, light won't experience total internal reflection any more and will enter the coating glass.

Why: To maintain total internal reflection through its travel, light in the fiber core must always hit the coating layer at a shallow angle. Bending the fiber increases the angle and eventually total internal reflection disappears.

3. To get light from a laser into an optical fiber, you use a converging lens. You focus the laser light onto the end of the glass fiber and most of the light that hits the fiber's core will enter the fiber. This focusing process is one of the reasons why the fiber's core must not be much smaller in diameter than the wavelength of light. If the core were much smaller than the laser's wavelength, why would it be impossible to get most of the laser's light to hit the core and thus to enter the fiber?

Answer: A lens cannot focus a beam of light to a spot much smaller than the wavelength of that light.

Why: Even a laser beam will not focus to a spot much smaller than the wavelength of the light. Instead, it will form a "beam waist" with a diameter that is typically larger than the light's wavelength. Since the smallest possible light spot is much larger than this tiny fiber core, most of the light would not be able to enter the core.

4. When light in the fiber reaches the end of the core, it emerges into the air. No matter how perfect the laser beam was before it was focused into the fiber and no matter how perfect the light's passage through the fiber, the light wave spreads substantially after it emerges from the tiny end of the fiber core. Catching this light efficiently always involves some sort of lens. Why must the light wave spread once it emerges from the core of the fiber?

Answer: Diffraction (the truncated light wave leaving the tiny end of the fiber core experiences self-interference effects that cause it to spread severely)

Why: The light wave leaving the fiber core is truly a wave, and a very narrow one at that. This wave has been so highly truncated by its passage through the narrow fiber core, that it spreads badly once it is free to do so. Like water ripples leaving a narrow channel, the wave front spread outward in ever increasing circular arcs until they are caught by a lens.

5. Sometimes an engineer needs to splice two optical fibers together so that light passing through one fiber continues through a second fiber. But just touching the two fiber cores together is often not good enough. To make sure that all of the light transfers from one fiber to the next, the engineer replaces the air separating the two fiber cores with oil. Light travels at the same speed in this oil as it does in the core glass. Why does this tiny amount of oil ensure that virtually all of the light passes from one fiber to the next?

Answer: By avoiding changes in the speed of light, reflections are avoided.

Why: The transitions from fiber core to air to fiber core would normally cause about 4% reflection each. By inserting the oil and avoiding the changes in light speed, all of the reflections can be avoided.

6. Digital information is often sent through optical fibers as very short pulses of light. A short pulse of light does not have a perfectly well defined wavelength. Instead, it contains a small range of different wavelengths that work together to give the light pulse its brief duration. Because of this mixture of wavelengths, the communications system has chose its fibers and wavelengths carefully to avoid strong dispersion. If each light pulse contains a range of wavelengths, what will dispersion do to the short pulse of light by the time that pulse has passed through many kilometers of optical fiber?

Answer: The pulses will become longer.

Why: Dispersion will cause the various components of the short pulse--the different wavelengths--to separate from one another. Instead of arriving as a single, well-structured packet of light, a pulse will arrive as a broad, dim time-rainbow of light in which different wavelengths of light arrive at slightly different times.

7. The glass used in an optical fiber is almost but not quite perfectly clear. After passing through many kilometers of fiber, the light begins to get dim. To boost the light intensity, the light can be sent through a laser amplifier. The beauty of using a laser medium to brighten the light is that all the complicated pulses that represent digital information get brighter, too. Why does a laser amplifier brighten the light without changing its wavelengths or altering the pulses?

Answer: The laser amplifier copies every aspect of the photons passing through it perfect, right down to their wavelengths and pulse characteristics.

Why: A laser medium is a perfect copier for photons. The copies it makes are completely and utterly indistinguishable from the original photons.

8. To make more efficient use of optical fibers that are already installed, companies have turned to Wavelength Division Multiplexing (WDM) and Dense Wavelength Division Multiplexing (DWDM). In these schemes, several streams of digital information are put on the same fiber. The different streams are sent using different wavelengths of light so that they don't have any effect on one another. Light emerging from the receiving end of the fiber is sent through a prism-like device that separates the various data streams according to their wavelengths. Unfortunately, WDM and DWDM make it difficult to use laser amplifiers to boost light intensity. Why will a laser amplifier have trouble brighting the light when there are many different wavelengths of light (infrared, red, green, etc.) running simultaneously through the fiber?

Answer: Laser amplifiers can only duplicate photons that the amplifying atoms (or atom-like systems) are prepared to emit. With too wide a variety of light wavelengths, it becomes impossible to find a laser amplifier that can emit all those wavelengths.

Why: Normally, laser amplifiers work on a narrow range of light wavelengths. Those wavelengths are ones which the laser medium is capable of emitting spontaneously and thus capable of emitting through stimulated emission. But when there are many different wavelengths running through a fiber, it's impossible to find a suitable laser medium. As a result, most WDM and DWDM systems must operate without amplification and cannot be used for extremely long distance communication.